HP 32SII RPN Scientific Calculator Owner’s Manual HP Part No. 00032–90068 Printed in Singapore Edition 5 File name 32sii-Manual-E-0424 Printed Date : 2003/4/24 Size : 17.7 x 25.
Notice This manual and any examples contained herein are provided “as is” and are subject to change without notice. Hewlett-Packard Company makes no warranty of any kind with regard to this manual, including, but not limited to, the implied warranties of merchantability and fitness for a particular purpose. Hewlett–Packard Co. shall not be liable for any errors or for incidental or consequential damages in connection with the furnishing, performance, or use of this manual or the examples contained herein.
Contents Part 1. 1. Basic Operation Getting Started Important Preliminaries ................................................... 1–1 Turning the Calculator On and Off.............................. 1–1 Adjusting Display Contrast ......................................... 1–1 Highlights of the Keyboard an Display .............................. 1–1 Shifted Keys............................................................. 1–1 Alpha Keys ..............................................................
Number of Decimal Places....................................... 1–15 SHOWing Fu ll 12–Digit Precision ......................... 1–16 Fractions..................................................................... 1–17 Entering Fractions ................................................... 1–17 Displaying Fractions ................................................ 1–19 Messages ................................................................... 1–19 Calculator Memory ............................................
3. Storing Data into Variables Storing and Recalling Numbers........................................ 3–1 Viewing a Variable without Recalling It ............................. 3–2 Reviewing Variables in the VAR Catalog............................ 3–3 Clearing Variables ......................................................... 3–3 Arithmetic with Stored Variables ....................................... 3–4 Storage Arithmetic .................................................... 3–4 Recall Arithmetic..........
Factorial................................................................ 4–11 Gamma ................................................................ 4–11 Probability Menu .................................................... 4–12 Parts of Numbers ......................................................... 4–14 Names of Function ....................................................... 4–14 5. Fractions Entering Fractions........................................................... 5–1 Fractions in the Display..
Parentheses in Equations ............................................ 6–7 Displaying and Selecting Equations .................................. 6–7 Editing and Clearing Equations........................................ 6–9 Types of Equations ....................................................... 6–10 Evaluating Equations .................................................... 6–11 Using ENTER for Evaluation ..................................... 6–12 Using XEQ for Evaluation....................................
For More Information...................................................... 8–9 9. Operations with Comb Numbers The Complex Stack ........................................................ 9–1 Complex Operations ...................................................... 9–3 Using Complex Number in Polar Notation ......................... 9–6 10. Base Conversions and Arithmetic Arithmetic in Bases 2, 8, and 16.................................... 10–2 The Representation of Numbers.................................
Summation Statistics.............................................. 11–11 The Statistics Registers in Calculator Memory ............ 11–12 Access to the Statistics Registers .............................. 11–13 Part 2. Programming 12. Simple Programming Designing a Program ................................................... 12–2 Program Boundaries (LBL and RTN) ........................... 12–3 Using RPN and Equations in Programs....................... 12–4 Data Input and Output ...........................
Program Memory....................................................... 12–20 Viewing Program Memory ..................................... 12–20 Memory Usage .................................................... 12–20 The Catalog of Programs (MEM)............................. 12–21 Clearing One or More Programs ............................ 12–22 The Checksum...................................................... 12–22 Nonprogrammable Functions....................................... 12–23 Programming with BASE .
The Indirect Address, (i) ......................................... 13–21 Program Control with (i)......................................... 13–22 Equations with (i) .................................................. 13–24 14. Solving and Integrating Programs Solving a Program ....................................................... 14–1 Using SOLVE in Program............................................... 14–5 Integrating a Program...................................................
Part 3. Appendixes and Regerence A. Support, Batteries, and Service Calculator Support......................................................... A–1 Answers to Common Questions .................................. A–1 Environmental Limits ....................................................... A–2 Changing the Batteries ................................................... A–3 Testing Calculator Operation ........................................... A–4 The Self–Test ..............................................
Neutral Operations................................................... B–5 The Status of the LAST X Register ...................................... B–6 C. More about Solving How SOLVE Finds a Root ................................................ C–1 Interpreting Results ......................................................... C–3 When SOLVE Cannot Find Root ....................................... C–8 Round–Off Error .......................................................... C–14 Underflow..................
Part 1 Basic Operation File name 32sii-Manual-E-0424 Printed Date : 2003/4/24 Size : 17.7 x 25.
1 Getting Started Important Preliminaries Turning the Calculator On and Off To turn the calculator on, press . ON is printed below the key. . That is, press and release the { To turn the calculator off, press { shift key, then press (which has OFF printed in blue above it). Since the calculator has Continuous Memory, turning it off does not affect any information you've stored, (You can also press z to turn the calculator off.
names are printed in orange and blue above each key. Press the appropriate shift key (z or {) before pressing the key for the desired function. For example, to turn the calculator off, press and release the { shift key, then press . Pressing z or { turns on the corresponding or ¡ annunciator symbol at the top of the display. The annunciator remains on until you press the next key. To cancel a shift key (and turn off its annunciator), press the same shift key again.
Keys for Clearing Key a Description Backspace. Keyboard–entry mode: Erases the character immediately to the left of "_" (the digit–entry cursor) or backs out of the current menu. (Menus are described in "Using Menus" on page 1–4.) If the number is completed (no cursor), a clears the entire number. Equation–entry mode: Erases the character immediately to the left of "¾ " (the equation–entry cursor). If a number entry in your equation is complete, a erases the entire number.
Keys for Clearing (continued) Key z b Description The CLEAR menu ({º } {# } { } {Σ} Contains options for clearing x (the number in the X–register), all Data, all variables, all of memory, or all statistical data. If you select { }, a new menu ( @ {& } { }) is displayed so you can verify your decision before erasing everything in memory. During program entry, { } is replaced by { }.
1. Menu choices. 2. Keys matched to menu choices. 3. Menu keys. HP 32II Menus Menu Name PARTS PROB L.R. x,y s,σ SUMS BASE Menu Description Numeric Functions Chapter Number–altering functions: integer part, fractional part, and absolute value. Q8T Q,T Probability functions: combinations, permutations, seed, and random number. ˆ TPE º̂ ¸ 4 4 11 Linear regression: curve fitting and linear estimation.
HP 32II Menus (continued) Menu Name Menu Description Chapter Other functions MEM QQQ)Q # Memory status (bytes of memory available); catalog of variables; catalog of programs (program labels). MODES * 8 Angular modes and " ) ' or " 8 " radix (decimal point) convention. DISP % Fix, scientific, engineering, and ALL display formats. CLEAR Functions to clear different portions of memory—refer to z b in the table on page 1–4.
the functions built into the calculator nor search through the names printed on its keyboard. Exiting Menus Whenever you execute a menu function, the menu automatically disappears, as in the above example. If you want to leave a menu without executing a function, you have three options: Pressing a backs out of the 2–level CLEAR or MEM menu, one l evel a t a t i me. Refer to z b in the table on page 1–4. Pressing a or cancels any other menu.
HP 32SII Annunciator Annunciator Meaning Chapter Upper Row: TS The z and z keys are active for stepping through a list. 1, 6 When in Fraction–display mode (press z ), only one of the "S " or "T " halves of the "TS "' annunciator will be turned on to indicate whether the displayed numerator is slightly less than or slightly greater than its true value. If neither part of "ST "' is on, the exact value of the fraction is being displayed. 5 Left shift is active. 1 ¡ Right shift is active.
HP 32SII Annunciator (continued) Annunciator Meaning Chapter Lower Row: The top–row keys on the calculator are redefined according to the menu labels displayed above menu pointers. 1 , There are more digits to the left or right. Use { to see the rest of a decimal number; use the left and right–scrolling keys ( <, 6) to see the rest of an equation or binary number.
Making Numbers Negative The _ key changes the sign of a number. To key in a negative number, type the number, then press _. To change the sign of a number that was entered previously, just press _. (If the number has an exponent, _ affects only the mantissa — the non–exponent part of the number.) Exponent of Ten Exponents in the Display Numbers with exponents of ten (such as 4.2 × 10–5 are displayed with an preceding the exponent (such as ) . ).
Keys: 6.6262 Display: ) _ 2. Press `. Notice that the cursor moves behind the : ` ) _ 3. Key in the exponent. (The largest possible exponent is ±499.) If the exponent is negative, press _ after you key in the E or after you key in the value of the exponent: 34 _ ) . _ For a power of ten without a multiplier, such as 1034, just press ` 34. The calculator displays . Other Exponent Functions To calculate an exponent of ten (the base 10 antilogarithm), use z (.
< ) Digit entry is terminated. Pressing terminates digit entry. To separate two numbers, key in the first number, press to terminate digit, entry, and then key in the second number 123 ) A completed number. 4 ) Another completed number. If digit entry is not terminated (if the cursor is present), a backspaces to erase the last digit. If digit entry is terminated (no cursor), a acts like and clears the entire number.
1. Key in the number. ( You don't need to press .) 2. Press the function key. (For a shifted function, press the appropriate z or { shift key first.) For example, calculate 1/32 and and change its sign. Keys: 32 Display: ) 148.84 < ) z: _ ) Then square the last result Description: Operand. _ 3 148.84 Reciprocal of 32. Square root of 148.84. Square of 12.2. . ) Negation of 148.8400.
For example: To calculate: Press: Display: 123 + 3 12 3 ) 12 – 3 12 3 ) 12 × 3 12 3 y ) 123 12 3 0 8 ) Percent change from 8 8 5 { S . ) to 5 The order of entry is important only for non–commutative functions such as ,p, 0 or { S. If you type numbers in the wrong order, you can still get the correct answer (without re–typing them) by pressing Z to swap the order of the numbers on the stack. Then press the intended function key.
Number of Decimal Places All numbers are stored with 12–digit precision, but you can select the number of decimal places to be displayed by pressing z (the display menu). During some complicated internal calculations, the calculator uses 15–digit precision for intermediate results. The displayed number is rounded according t the display format.
Engineering Format ({ }) ENG format displays a number in a manner similar to scientific notation, except that the exponent is a multiple of three (there can be up to three digits before the ")" or "8 " radix mark). This format is most useful for scientific and engineering calculations that use units specified in multiples of I03 (such ass micro–, milli–, and kilo–units.) After the prompt, _, type in the number of digits you want after the first significant digit. For 10 or 11 places, press 0 or 1.
Keys: Display: z { %} 4 45 1.3 y ) z { } 2 ) Description: Displays four decimal places. Four decimal places displayed. Scientific format: two decimal places and an exponent. z { } 2 ) z { } ) Engineering format. All significant digits; trailing zeros dropped. z { %} 4 ) Four decimal places, no exponent. Reciprocal of 58.5.
terminate digit entry. The number or result is formatted according to the current display format. The a b/c symbol under the key is a reminder that the key is used twice for fraction entry. For example, to enter the fractional number 12 3/8, press these keys: Keys: Display: Description: 12 _ Enters the integer part of the number. )_ The key is interpreted in the normal manner. 3 ) _ Enters the numerator of the fraction (the number is still displayed in decimal form).
Displaying Fractions Press z to switch between Fraction–display mode and the current decimal display mode. Keys: Display: Description: 12 3 8 + ) Terminates digit entry; displays the Displays characters as you key them in. number in the current display format. z + Displays the number as a fraction. Now add 3/4 to the number in the X–register (12 3/8): Keys: Display: 34 + Description: Displays characters as, you key them in.
Calculator Memory The HP 32SII has 384 bytes of memory in which you can store any combination of data (variables, equations, or program lines). The memory requirements of specific activities are given under "Managing Calculator Memory" in appendix B. Checking Available Memory Pressing z X displays the following menu: ) # Where ) is the number of bytes of memory available.
@ {&} { }, which safeguards against the unintentional clearing of memory. 2. Press {& } (yes). Getting Started File name 32sii-Manual-E-0424 Printed Date : 2003/4/24 Size : 17.7 x 25.
2 The Automatic Memory Stack This chapter explains how calculations take place in the automatic memory stack. You do not need to read and understand this material to use the calculator, but understanding the material will greatly enhance your use of the calculator, especially when programming. In part 2, "Programming", you will learn how the stack can help you to manipulate and organize data for programs.
T 0.0000 Z 0.0000 Y 0.0000 X 0.0000 “Oldest” number Displayed The most "recent" number is in the X–register: this is the number you see in the display. In programming, the slack is used to perform calculations, to temporarily store intermediate results, to pass stored data (variables) among programs and subroutines, to accept input, and to deliver output. The X–Register Is in the Display The X–register is what you see except when a menu, a message, or a program line is being displayed.
Reviewing the stack R¶ (Roll Down) The 9 (roll down) key lets you review the entire contents of the stack by "rolling" the contents downward, one register at a time. You can see each number when it enters the X–register. Suppose the stack is filled with 1, 2, 3, 4 (press 1 2 3 4.
Exchanging the X– and Y–Registers in the Stack Another key that manipulates the stack contents is Z (x exchange y). This key swaps the contents of the X– and Y–registers without affecting the rest of the stack. Pressing Z twice restores the original order of the X– and Y–register contents. The Z function is used primarily for two purposes: To view the contents of the Y–register and then return them to y (press Z twice). Some functions yield two results: one in the X–register and one in the Y–register.
3+4–9 T 1 1 1 1 Z 2 1 2 1 Y 3 2 7 2 X 4 1 7 2 9 –2 3 1. The stack "drops" its contents. The T– (top) register replicates its contents. 2. The stack "lifts" its contents. The T–register's contents are lost. 3. The stack drops. Notice that when the stack lifts, it replaces the contents of the T– (top) register with the contents of the Z–register, and that the former contents of the T–register are lost. You can see, therefore, that the stack's memory is limited to four numbers.
5+6 2 lost T 1 2 3 3 3 Z 2 3 4 4 3 Y 3 4 5 5 4 X 4 1 1. 2. 3. 4. 1 lost 5 5 2 3 6 11 4 Lifts the stack. Lifts the stack and replicates the X–register. Does not lift the stack. Drops the stack n replicate the T–register. replicates the contents of the X–register into the Y–register. The next number you key in (or recall) writes over the copy of the first number left in the X–register. The effect is simply to separate two sequentially entered numbers.
Example: Given bacterial culture with a constant growth rate of 50%, how large would population of 100 be at the end 3 days? Replicates T–register 1.5 T 1.5 1.5 1.5 1.5 1.5 Z 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 150 y 225 Y X 1.5 100 1 1. 2. 3. 4. 5. 1 100 y 2 y 337.5 3 4 Fills the stack with the growth rate. Keys in the initial population. Calculates the population after 1 day. Calculates the population after 2 days. Calculates the population after 3 days.
or a cancel that display and shows the X–register. When viewing an equation, a displays the cursor at the end the equation to allow for editing. During equation entry, a backspaces over the displayed equation, one function at a time. For example, if you intended to enter 1 and 3 but mistakenly entered 1 and 2, this what you should do to correct your error: T Z Y X 1 1 1 2 2 1 1. 2. 3. 4. 5. 1 3 4 1 1 0 3 5 Lifts the stack Lift the stack and replicates the X–register.
See appendix B for a comprehensive list of the functions that save x in the LAST X register. Correcting Mistakes with LAST X Wrong One–Number Function If you execute the wrong one–number function, use z to retrieve the number so you can execute the correct function. (Press first if you want to clear the incorrect result, from the stack.) Since { P and { S don't cause the stack to drop, you can recover from these functions in the same manner as from one–number functions.
Suppose you made a mistake while calculating 16 × 19 = 304. There are three kinds of mistakes you could have made: Wring Calculation: Mistake: Correction: 16 19 Wrong function z zy 15 19 y Wrong first number 16 z y 16 18 y Wrong second z p 19 y number Reusing Numbers with LAST X You can use z to reuse a number (such as a constant) in a calculation.
T t t t Z z z t 96.704 Y 96.704 96.704 z X 96.704 52.3947 52.3947 LAST X l T t t Z z t l 52.3947 Y 149.0987 z X 52.3947 96.704 p 52.3947 2.8457 52.3947 Display: ) 149.0987 z LAST X 52.3947 Keys: 52.3947 ) z ) Description: Enters first number. Intermediate result. Brings back display from before . p ) Final result. Example: Two close stellar neighbors of Earth are Rigel Centaurus (4.3 light–years away) and Sirius (8.
To Rigel Centaurus: 4.3 yr × (9.5 × 1015 m/yr). To Sirius: 8.7 yr × (9.5 × 1015 m/yr). Keys: 4.3 9.5 ` 15 y Display: ) ) Description: Light–years to Rigel Centaurus. Speed of light, c. Meters to R. Centaurus. ) 8.7 z ) y ) Retrieves c. Meters to Sirius. Chain Calculations The automatic lifting and dropping of the stack's contents let you retain intermediate results without storing or reentering them, and without using parentheses.
You don't need to press to save this intermediate result before proceeding; since it is a calculated result, it is saved automatically. Keys: Display: ) 7y Description: Pressing the function key produces the answer. This result can be used in further calculations. Now study the following examples. Remember that you need to press only to separate ,sequentially–entered numbers, such as at the beginning of a problem The operations themselves ( ,, etc.
Work through the problem the same way with the HP 32SII, except that you don't have to write down intermediate answers—the calculator remembers them for you. Keys: Display: 34 ) 56 ) y ) Description: First adds (3+4) Then adds (5+6) Then multiplies the intermediate answers together for the final answer. Exercises Calculate: (16.3805x 5) = 181.0000 0.05 Solution: 16.3805 5 y < .05 p Calculate: [(2 + 3) × (4 + 5)] + [(6 + 7) × (8 + 9) = 21.
Order of Calculation We recommend solving chain calculations by working from the innermost parentheses outward. However, you can also choose to work problems in a left–to–right order. For example, you have already calculated: 4 ÷ [14 + (7 × 3) – 2] by starting with the innermost parentheses (7 × 3) and working outward, just as you would with pencil and paper. The keystrokes were 7 3 y 14 2 4 Z p If you work the problem from left–to–right, press 4 14 7 3 y 2 p.
73 At this point the stack is full with _ numbers for this calculation. y 2 p ) Intermediate result. ) Intermediate result. ) Intermediate result. ) Final result. More Exercises Practice using RPN by working through the following problems: Calculate: (14 + 12) × (18 – 12) ÷ (9 – 7) = 78.0000 A Solution: 14 12 18 12 y 9 7 p Calculate: 232 – (13 × 9) + 1/7 = 412.1429 A Solution: 23 z : 13 9 y 7 3 Calculate: (5.4 × 0.8) ÷ (12.5 − 0.73 ) = 0.
4 5.2 8.33 y z 7.46 0.32 y p 3.15 2.75 4.3 y 1.71 2.01 y p < The Automatic Memory Stack File name 32sii-Manual-E-0424 Printed Date : 2003/4/24 Size : 17.7 x 25.
3 Storing Data into Variables The HP 32II has 384 bytes of user memory: memory that you can use to store numbers, equations, and program lines. Numbers are stored in locations called variables, each named with a letter from A through Z. (You can choose the letter to remind you of what is stored there, such as B for bank balance and C for the speed of light.) 3-1 Picture 1. Cursor prompts for variable. 2. Indicates letter keys are active. 3. Letter keys.
Example: Storing Numbers. Store Avogadro's number (approximately 6.0225 × 1023 ) in A. Keys: Display: Description: 6.0225 ` 23 ) _ Avogadro's numbers. H ! _ Prompts for variable. A (HOLD < key) ! Displays function as long as key is held down. (release) ) Stores a copy of Avogadro's numbers in A. This also terminates digit entry (no cursor present) K ) _ A Clears the number in the display. Prompts for variable.
To cancel the VIEW display, press a or once. Reviewing Variables in the VAR Catalog The z X (memory) function provides information about memory: QQQ)Q # where nnn.n is the number of bytes of available memory. Pressing the {# } menu key displays the catalog of variables. Pressing the { } menu key displays the catalog of programs. To review the values at any or all non–zero variables: 1. Press z X {VAR}. 2. Press z or z to move the list and display the desired variable.
Store zero in it: Press 0 H variable. To clear selected variables: 1. Press z X {# } and use z or z to display the variable. 2. Press z b. 3. Press to cancel the catalog. To clear all variables at once: Press z b {# }. Arithmetic with Stored Variables Storage arithmetic and recall arithmetic allow you to do calculations with a number stored in a variable without recalling the variable into the stack. A calculation uses one number from the X–register and one number from the specified variable.
A 15 A 12 T t T t Z z Z z Y y Y y X 3 X 3 H Results: 15–3 thatis, A–x Recall Arithmetic Recall arithmetic uses a K , K y, or K p to do arithmetic in the X–register using a recalled number and to leave the result in the display. Only the X–register is affected. New x = Previous x {+, –, ×, ÷ } Variable For example, suppose you want to divide the number in the X–register (3, displayed) by the value in A(12). Press K p A. Now x = 0.25, while 12 is still in A.
Example: Suppose the variables D, E, and F contain the values 1, 2, and 3. Use storage arithmetic to add 1 to each of those variables. Keys: Display: Description: 1HD ) Stores the assumed values into the 2HE ) variable. 3HF ) 1HD Add 1 to D, E, And F. H E H F ) {D / ) {E / ) {F / ) @ ) Displays the current value of D. Clears the VIEW display; displays X-register again.
Example: Keys: Display: 12 H A ) 3 _ {YA ) Description: Stores 12 in variable A. Display x. Exchange contents of the X–register and variable A. {YA ) Exchange contents of the X–register and variable A. A 12 A 3 T t T t Z z Z z Y y Y y X 3 X 12 {Y The Variable "i" There is a 27th variables that you can access directly–the variable i. The key is labeled "i", and it means i whenever the A..Z annunciator is on.
4 Real–Number Functions This chapter covers most of the calculator's functions that perform computations on real numbers, including some numeric functions used in programs (such as ABS, the absolute–value function): Exponential and logarithmic functions. Power functions. ( 0 and .) Trigonometric functions. Hyperbolic functions. Percentage functions. Conversion functions for coordinates, angles, and units. Probability functions. Parts of numbers (number–altering functions).
To Calculate: Press: Natural logarithm (base e) - Common logarithm (base 10) z+ Natural exponential * Common exponential (antilogarithm) z( Power Functions To calculate the square of a number x, key in x and press z :. To calculate a power x of 10, key in x and press z (. 'To calculate a number y raised to a power x, key in y x, then press 0.(For y > 0, x can be any rational number; for y < 0, x must be are integer; for y = 0, x must be positive.
−1.4 .37893 1.4 _ z . .37893 ) Trigonometry Entering π Press { M to place the first 12 digits of π into the X–register. (The number displayed depends on the display format.) Because π is a function, it doesn't need to be separated from another number by . Note that calculator cannot exactly represent π, since π is an irrational number. Setting the Angular Mode The angular rode specifies which unit of measure do assume for angles used in trigonometric functions.
Trigonometric Functions With x in the display: To Calculate: Press: Sine of x. N Cosine of x. Q Tangent of x. T Arc sine of x. zL Arc cosine of x. zO Arc tangent of x. zR Note Calculations with the irrational number π cannot be expressed exactly by the 12–digit internal precision of the calculator. This is particularly noticeable in trigonometry. For example, the calculated sin π (radians) is not zero but –2.0676 × 10–13, a very small number close to zero.
Programming Note: Equations using inverse trigonometric functions to determine an angle θ, often look something like this: θ = arctan (y/x). If x = 0, then y/x is undefined, resulting in the error: # & . For a program, then, it would be more reliable to determine θ by a rectangular– to polar conversion, which converts (x,y) to (r,θ). See "Coordinate Conversions" later in this chapter. Hyperbolic Functions With x in the display: To Calculate Press: Hyperbolic sine of x (SINH).
To Calculate Press: x% of y Percentage change from y to x. (y≠ 0) yx{P yx{S Example: Find the sales tax at 6% and the total cost of a $15.76 item. Use FIX 2 display format so the costs are rounded appropriately. Keys: z { %} 2 Display: Description: Rounds display to two decimal places. 15.76 6{P ) ) ) Calculates 6% tax. Total cost (base price + 6% tax). Suppose that the $15.76 item cost $16.12 last year.
Conversion Functions There are four types of conversions: coordinate (polar/rectangular), angular (degrees/radians), time (decimal/minutes–seconds), and unit (cm/in, °C/°F, l/gal, Kg/lb). Coordinate Conversions The function names for these conversions are y,x θ,r and θ,r y,x. Polar coordinates (r,θ) and rectangular coordinates (x,y) are measured as shown in the illustration. The angle θ uses units set by the current angular mode.
y, x Y X θ, r y θ x r θ, r y, x Example: Polar to Rectangular Conversion. In the following right triangles, find sides x and y in the triangle on the left, and hypotenuse r and angle θ in the triangle on the right. 10 r y θ 30 o x Keys: 3 Display: z { } 30 10 { ) r Z ) 4 3 z q ) Z ) 4–8 4 Real–Number Functions File name 32sii-Manual-E-0424 Printed Date : 2003/4/24 Size : 17.7 x 25.2 cm Description: Sets Degrees mode. Calculates x. Displays y.
Example: Conversion with Vectors. Engineer P.C. Bard has determined that in the RC circuit shown, the total impedance is 77.8 ohms and voltage lags current by 36.5 º. What a .re the values of resistance R and capacitive reactance XC in the circuit? Use a vector diagram as shown, with impedance equal to the polar magnitude, r, and voltage lag equal to the angle, θ, in degrees. When the values are converted to rectangular coordinates, the x–value yields R, in ohms; the y–value yields XC ,in ohms. R θ _ 36.
To convert between decimal fractions and minutes–seconds: 1. Key in the time or angle (in decimal form or minutes–seconds form) that you want to convert. 2. Press { t or z s. The result is displayed. Example: Converting Time Formats. How many minutes and seconds are there in 1 ÷ 7 of an hour? Use FIX 6 display format. Keys: z { %} 6 17 {t z { %} 4 Display: + Description: Sets FIX 6 display format. 1 ÷ 7 as a decimal fraction. ) Equals 8 minutes and 34.29 seconds.
Unit conversions The HP 32SII has eight unit–conversion functions on the keybord: kg, lb, ºC, ºF, cm, in, l, gal.
Probability Menu Press { [PROB] to see the PROB (probability) menu shown, in the following table. It has functions to calculate combinations and permutations, to generate seeds for random numbers, and to obtain random numbers from those seeds. PROB Menu Menu Label Description { Q , T } Combinations. Enter n first, then r (nonnegative integers only). Calculates the number of possible sets of n items taken r at a time.
Example: Combinations of People. A company employing 14 women and 10 men is forming a six–person safety committee. How many different combinations of people are possible? Keys: 24 6 Display: Description: Twenty–four people grouped six _ at a time. { [PROB] Probability menu. Q8T Q8T { Q ,T } 8 ) Total number of combinations possible.
Parts of Numbers The functions in the PARTS menu ({ [PARTS]) shown in the following table and the z I function alter the number in the X–register in simple ways. These functions are primarily used in programming. PARTS Menu Menu Label { } Description Integer part. Removes the fractional part of x and replaces it with zeros. (For example, the integer part of 14.2300 is 14.000.) { } Fractional part. Removes the integer part of x and replaces it with zeros. (For example, the fractional part of 14.
5 Fractions "Fractions" in chapter 1 introduces the basics about entering, displaying, and calculating with fractions: To enter a fraction, press twice—after the integer part, and between the numerator and denominator. To enter 2 3/8, press 2 3 8. To enter 5/8, press 5 8 or 5 8. To turn Fraction–display mode on and off, press z . When you turn off Fraction–display mode, the display goes back to the previous display format. (FIX, SCI, ENG, and ALL also turn off Fraction–display mode.
Example: Keys: z 1.5 134 z z Display: Description: Turns on Fraction–display mode. + Enters 1.5; shown as a fraction. + Enters 1 3/4. ) Displays x as a decimal number. + Displays x as a fraction. If you didn't get the same results as the example, you may have accidentally changed how fractions are displayed. (See "Changing the Fraction Display" later in this chapter.) The next topic includes more examples of valid and invalid input fractions.
The denominator is no greater than 4095. The fraction is reduced as far as possible. Examples: These are examples of entered values and the resulting displays. For comparison, the internal 12–digit values are also shown. The S and T annunciators in the last column are explained below. Entered Value Internal Value Displayed Fraction 2 3/8 2.37500000000 14 15/32 14.4687500000 54/12 4.50000000000 6 18/5 9.60000000000 34/12 2.83333333333 T 15/8192 .
This diagram shows how the displayed fraction relates to nearby values — S means the exact numerator is "a little above" the displayed numerator, and T means the exact numerator is "a little below". 0 7/16 0 7/16 6.5 6 /16 /16 (0.40625) 7 /16 (0.43750) 0 7/16 7.5 /16 8 /16 (0.46875) This is especially important if you change the rules about how fractions are displayed. (See "Changing the Fraction Display" later.
Example: Keys: Display: Description: Calculates e14. + 14 * ... { HA {A Shows all decimal digits. ) ... Stores value in A. + /... Views A. + Clears x. Changing the Fraction Display In its default condition, the calculator displays a fractional number according to certain rules. (See "Display Rules" earlier in this chapter.) However, you can change the rules according to how you want fractions displayed: You can set the maximum denominator that's used.
the default if you use 4095 or greater.) This also turns on Fraction–display mode. The /c function uses the absolute value of the integer part of the number in the X–register. It doesn't change the value in the LAST X register. Choosing Fraction Format The calculator has three fraction formats. Regardless of the format, the displayed fractions are always the closest fractions within the rules for that format. Most precise fractions.
You can change flags 8 and 9 to set the fraction format using the steps listed here. (Because flags are especially useful in program, their use us covered in detail in chapter 13.) 1. Press { x to get the flag menu. 2. To set a flag, press { } and type the flag number, such as 8. To clear a flag, press { ) and type the flag number. To see if a flag is set, press { @} and type the flag number. Press or a to clear the & or response.
The following table shows how different numbers are displayed in the three fraction formats for a /c value of 16. Fraction Format Number Entered and Fraction Displayed 2 2 2/3 2.5 216/25 2.9999 Most precise 2 2 1/2 S2 2/3 T3 S2 7/11 Factors of denominator 2 2 1/2 T2 11/16 T3 S2 5/8 Fixed denominator 2 0/16 2 8/16 T2 11/16 T2 16/16 S2 10/16 For a / F value of 16. Example: Suppose a stock has a current value of 48 1/4.
and 9. The accuracy indicator turns off if the fraction matches the decimal representation exactly. Otherwise, the accuracy indicator stays on, (See "Accuracy Indicators" earlier in this chapter.) In an equation or program, the RND function does fractional rounding if Fraction–display mode is active. Example: Suppose you have a 56 3/4–inch space that you want to divide into six equal sections.
When you're evaluating an equation and you're prompted for variable values, you may enter fractions — values are displayed using the current display format. See chapter 6 for information about working with equations. Fractions in Programs When you're typing a program, you can type a number as a fraction — but it's converted to its decimal value. All numeric values in a program are shown as decimal values — Fraction–display mode is ignored.
6 Entering and Evaluating Equations How You Can Use Equations You can use equations on the HP 32SII in several way: For specifying an equation to evaluate (this chapter). For specifying an equation to solve for unknown values (chapter 7). For specifying a function to integrate (chapter 8). Example: Calculating with an Equation. Suppose you frequently need to determine the volume of a straight section of pipe. The equation is V = .25 π d2 l There d is the inside diameter of the pipe, and l is its length.
K Begins a new equation, turning on ¾ the "¾ " equation–entry cursor. K turns on the A..Z annunciator so you can enter a variable name. V{c K V types # and moves the #/¾ cursor to the right. .25 Digit entry uses the "_" digit–entry #/ ) _ cursor. y { M y #/ ) ºπº¾ y ends the number and restores the "¾ " cursor. KD02 yKL / ) ºπº : Terminates and displays the #/ ) ºπº : º equation. shows that part of the 0 types :. _ ) ºπº : º ¾ #/ scrolls o f the left side of the display.
Keys: Display: Description: Prompts for D first; value is the current value of D. + Enters 2 1/2 inches as a fraction. 212 @ f @value Stores D, prompts for L; value is current value of L. 16 f #/ ) Stores L; calculates V in cubic inches and stores the result in V. Summary of Equation Operations All equations you create are saved in the equation list. This list is visible whenever you activate Equation mode. You use certain keys to perform operations involving equations.
Key Operation {G Enters and leaves Equation mode. Evaluates the displayed equation. If the equation is an assignment, evaluates the right–hand side and stores the result in the variable on the left–hand side. If the equation is an equality or expression, calculates its value like W. (See "Types of Equations" later in this chapter.) W Evaluates the displayed equation. Calculates its value, replacing "=" with "–" if an "=" is present.
To enter an equation: 1. Make sure the calculator is in its normal operating mode, usually with a number in the display. For example, you can't be viewing the catalog of variables or programs. 2. Press { G. The EQN annunciator shows that Equation mode is active, and an entry from the equation list is displayed. 3. Start typing the equation. The previous display is replaced by the equation you're entering — the previous equation isn't affected. If you make a mistake, press a as required. 4.
To enter a number in an equation, you can use the standard number–entry keys, including , _, and `. Press _ only after you type one or more digits. Don't use _ for subtraction. When you start entering the number, the cursor changes from "¾ " to "_" to show numeric entry. The cursor changes back when you press a nonnumeric key. Functions in Equations You can enter many HP 32SII functions in an equation. A complete list is given tinder "Equation Functions" later in this chapter.
Parentheses in Equations You can include parentheses in equations to control the order in which operations are performed. Press { \ and { ] to insert parentheses. (For more information, see "Operator Precedence" later in this chapter.) Example: Entering an Equation. Enter the equation r = 2 × c × cos (t – a). Keys: {G Display: Description: Shows the last equation used in the #/ ) ºπº : º equation list. K R { c /¾ Starts a new equation with variable R.
To display equations: 1. Press { G. This activates Equation mode and turns on the EQN annunciator. The display shows an entry from the equation list: ! ! if there are no equations in the equation list or if the equation pointer is at the top of the list. The current equation (the last equation you viewed). 2. Press z or z to step through the equation list and view each equation. The list "wraps around" at the top and bottom. ! ! marks the "top" of the list. To view a long equation: 1.
right. < / º º 1!. Shows one character to the left. Leaves Equation mode. Editing and Clearing Equations You can edit or clear an equation that you're typing. You can also edit or clear equations saved in the equation list. To edit an equation you're typing: 1. Press a repeatedly until you delete the unwanted number or function. If you're typing a decimal number and the "_" digit–entry cursor is on, a deletes only the rightmost character.
To clear a saved equation: 1. Display the desired equation. (See "Displaying and Selecting Equations" above.) 2. Press z b. The display shows the previous entry in the equation list. To clear all equations, clear them one at a time: scroll through the equation list until you come to ! ! , press z , then press z b repeatedly as each equation is displayed until you see ! ! . Example: Editing an Equation. Remove the optional right parenthesis in the equation from the previous example.
Expressions. The equation does not contain an "=". For example, x3 + 1 is an expression. When you're calculating with an equation, you might use any type of equation—although the type can affect how it's evaluated. When you're solving a problem for an unknown variable, you'll probably use an equality or assignment. When you're integrating a Function, you'll probably use an expression.
The following table shoves the two ways to evaluate equations. Type of Equation Result for Equality: g (x) = f(x) Example: x2 + y2 = r2 Result for W g (x) – f(x) x2 + y2– r2 Assignment: y = f(x) Example: A = 0.5 × b x h f(x) y – f(x) 0.5 × b × h A – 0.5 × b × h Expression: f(x) Example: x3 + 1 f(x) x3 + 1 Also stores the result in the left–hand variable, A for example. To evaluate an equation: 1. Display the desired equation. (See "Displaying and Selecting Equations" above.) 2. Press or W.
If the equation is an assignment, only the right–hand side is evaluated. The result is returned to the X–register and stored in the left–hand variable, then the variable is VIEWed in the display. Essentially, finds the value of the left–hand variable. If the equation is an equality or expression, the entire equation is evaluated — just as it is for W. The result is returned to the X–register. Example: Evaluating an Equation with ENTER.
Using XEQ for Evaluation If an equation is displayed in the equation list, you can press W to evaluate the equation. The entire equation is evaluated, regardless of the type of equation. The result is returned to the X–register. Example: Evaluating an Equation with XEQ. Use the results from the previous example to find out how much the volume of the pipe changes if the diameter is changes to 35.5 millimeters. Keys: {G W Display: Description: Displays the desired equation.
To leave the number unchanged, just press f. To change the number, type the new number and press f.This new number writes over the old value in the X–register. You can enter a number as a fraction if you want. If you need to calculate a number, use normal keyboard calculations, then press f. For example, you can press 2 5 0 f. To calculate with the displayed number, press before typing another number. To cancel the prompt, press . The current value for the variable remains in the X–register.
Order Operation Example 1 Functions and Parentheses 2 Unary Minus (_) . 3 Power ( 0 ) %: 4 Multiply and Divide %º&, ª 5 Add and Subtract - , . 6 Equality / 1%- 2, 1%- 2 So, for example, all operations inside parentheses are performed before operations outside the parentheses. Exampl es: Equations Meaning º : / a × (b3) = c 1 º 2: / (a × b)3 = c - ª / a + (b ÷ c) = 12 1 - 2ª / (a + b) ÷ c = 12 0 1!- [%CHG(t + 12), (a – 6)]2 .
Equation Function The following table lists the functions that are valid in equations. Appendix F, "Operation Index," also gives this information.
0 1.% 0 1% . 2 1.&22 Six of the equation functions have names that differ from their equivalent RPN operations: RPN Operation Equation function x2 SQ ex EXP 10x ALOG 1/x INV y X ROOT yx ^ X Example: Perimeter of a Trapezoid. The following equation calculates the perimeter of a trapezoid.
Parentheses used to group items P=A+B+Hx(1÷SIN(T)+1÷SIN(F)) Single letter name No implied multiplication Division is done before addition The next equation also obeys the syntax rules. This equation uses the inverse function, #1 1!22, instead of the fractional form, ª 1!2 . Notice that the SIN function is "nested" inside the INV function. (INV is typed by 3.) / - - º1 #1 1!22-1 #1 1 222 Example: Area of a Polygon.
/ ) º º : º 1 π ª 2ª 1 πª 2 Notice how the operators and functions combine to give the desired equation. You can enter the equation into the equation list using the following keystrokes: { G K A { .25 y K N y K D 0 2 y Q {MpKN{]pN{MpKN{] Syntax Errors The calculator doesn't check the syntax of an equation until you evaluate the equation and respond to all the prompts–only when a value is actually being calculated. If an error is detected, # is displayed.
The checksum and length allow you to verify that equations you type are correct. The checksum and length of the equation you type in an example should match the values shown in this manual. Example: Checksum and Length of an Equation. Find the checksum and length for the pipe–volume equation at the beginning of this chapter. Keys: Display: Description: Displays the desired equation. { G ( z #/ ) ºπº : º as required) Display equation's checksum and { (hold) / ) length.
7 Solving Equations In chapter 6 you saw how you can use to find the value of the left–hand variable in an assignment–type equation. Well, you can use SOLVE to find the value of any variable in any type of equation. For example, consider the equation x2 – 3y = 10 If you know the value of y in this equation, then SOLVE can solve for the unknown x. If you know the value of x, then SOLVE can solve for the unknown y.
for a value for every other variable in the equation. 3. For each prompt, enter the desired value; If the displayed clue is the one you want, press f. If you want a different clue, type or calculate the value and press f. (For details, see "Responding to Equation Prompts" in chapter 6.) You can half a running calculation b pressing or f. When the root is found, it's stored in the unknown variable, and the variable value is VIEWed in the display.
or current equation Starts the equation. K D { c /#º!-¾ KVyK T .5 y K G !- ) º º!: _ yKT02 Terminates the equation and /#º!- ) º º! displays the left end. { Checksum end length. / ) g (acceleration due to gravity) is included as a variable so you can change it for different units (98 m/s2 or 32.2 ft/s2 ). Calculate hove ran meters an object falls in 5 seconds, starting from rest.
f Retains 9.8 in G; prompts for T. # !/ ) Example: Solving the Ideal Gas Law Equation. The Ideal Gas Law describes the relationship between pressure, volume, temperature, and the amount (moles) of an ideal gas: P×V=N×R×T where P is pressure (in atmospheres or N/m2), V is volume (in liters), N is the number of moles of gas, R is the universal gas constant (0.0821 liter–atm mole–K or 8.314 J/mole–K), and T is temperature (Kelvins: K=°C + 273.1).
24 !@ ) Calculates T (Kelvins). 273.1 f #O / ) Stores 297.1 in T; solves for P in atmospheres. A 5–liter flask contains nitrogen gas. The pressure is 0.05 atmospheres when the temperature is 18°C. Calculate the density of the gas (N × 28/V, where 28 is the molecular weight of nitrogen). Keys: {G {N .05 f 5f f 18 273.1 f Display: Description: º#/ º º! Displays the equation. @ ) Solves for N; prompts for P. #@ ) Stores .05 in P; prompts for V.
When SOLVE evaluates an equation, it does it the same way W does — any "=" in the equation is treated as a " – " For example, the Ideal Gas Law equation is evaluated as P × V – (N × R × T). This ensures that an equality or assignment equation balances at the root, and that an expression equation equals zero at the root. Some equations are more difficult to solve than others. In some cases, you need to enter initial guesses in order to find a solution. (See "Choosing Initial Guesses for SOLVE," below.
root. If the X– and Y–register values are close together, and the Z–register value is close to zero, the estimate from the X–register may be an approximation to a root. Interrupting a SOLVE Calculation To halt a calculation, press or f. The current best estimate of the root is in the unknown variable; use { to view it without disturbing the stack. Choosing Initial Guesses for SOLVE The two initial guesses come from: The number currently stored in the unknown variable.
to enter guesses before solving for T because in the first part of that example you stored a value for T and solved for D. The value that was left in T was a good (realistic) one, so it was used as a guess when solving for T. If an equation does not allow certain values for the unknown, guesses can prevent these values from occurring. For example, y = t + log x results in an error if x ≤ 0 (messages 1 2 or 1 2 ).
If H is the height, then the length of the box is (80 – 2H) and the width is (40 – 2H). The volume V is: V = ( 80 – 2H ) × (40 – 2H ) × H which you can simplify and enter as V= ( 40 – H ) × ( 20 – H ) × 4 × H Type in the equation: Keys: Display: Description: Selects Equation mode and { G starts the equation. K V { c #/¾ { \ 40 K H { ] #/1 . 2¾ y { \ 20 . 2º1 . 2¾ KH{] y 4 y K H º1 . 2º º ¾ #/1 . 2º1 Terminates and displays the equation. { / Checksum and length.
{G {H 7500 f #/1 . 2º Displays current equation. #@value Solves for H; prompts for V. / ) Stores 7500 in V; solves for H. Now check the quality of this solution — that is, whether it returned an exact root — by looking at the value of the previous estimate of the root (in the Y–register) and the value of the equation at the root (in the Z–register). Keys: 9 Display: ) Description: This value from the Y–register is the estimate made just prior to the final result.
7500 _ (40 _ H ) (20 _ H ) 4 H 20,000 H _ 10 50 _ 10,000 For More Information This chapter gives you instructions for solving for unknowns or roots over a wide range of applications. Appendix C contains more detailed information about how the algorithm for SOLVE works, how to interpret results, what happens when no solution is found, and conditions that can cause incorrect results. Solving Equations File name 32sii-Manual-E-0424 Printed Date : 2003/4/24 Size : 17.7 x 25.
8 Integrating Equations Many problems in mathematics, science, and engineering require calculating the definite integral of a function– If the function is denoted by f(x) and the interval of integration is a to b, then the integral can be expressed mathematically as b I = ∫ f (x )dx a f (x) I a b x The quantity I can be interpreted geometrically as the area of a region bounded by the graph of the function f(x), the x–axis, and the limits x = a and x = b (provided that f(x) is nonnegative throughout th
) works only with real numbers. Integrating Equations ( ∫ FN) To Integrating Equations: To integrate an equation: 1. If the equation that defines the integrand's function isn't stored in the equation list, key it in (see "Entering Equations Into the Equation List" in chapter 6) and leave Equation mode. The equation usually contains just an expression. 2. Enter the limits of integration: key in the lower limit and press , then key in the upper limit. 3.
To integrate the same equation with different information: If you use the same limits of integration, press 9 9 move them into the X– and Y–registers. Then start at step 3 in the above list. If you want to use different limits, begin at step 2. To work another problem using a different equation, start over from step 1 with an equation that defines the integrated. Example: Bessel Function.
Leaves Equation mode. Now integrate this function with respect to t from zero to π ; x = 2. Keys: Display: Description: z { } 0 { M ) Selects Radians mode. Enters the limits of integration (lower limit first). {G {) 1%º 1!2 Displays the function. ∫ G_ Prompts for the variable of integration. T %@value 2 f ! ! x = 2. Starts integrating; calculates result for π ∫ / ) f (t ) Prompts for value of X. ∫0 {Mp The final result for ) J0 (2).
Example: Sine Integral. Certain problems in communications theory (for example, pulse transmission through idealized networks) require calculating an integral (sometimes called the sine integral) of the form t Si (t ) = ∫ ( 0 sin x )dx x Find Si (2). Enter the expression that defines the integrand's function: sin x x If the calculator attempted to evaluate this function at x = 0, the lower limit of integration, an error ( # & ) would result.
02 _ Enters limits of integration (lower first). {G {)X 1%2ª% Displays the current equation. ! ! Calculates the result for Si(2). ∫ / ) Accuracy of Integration Since the calculator cannot compute the value of an integral exactly, it approximates it. The accuracy of this approximation depends on the accuracy of the integrand's function itself, as calculated by your equation. This is affected by round–off error in the calculator and the accuracy of the empirical constants.
Interpreting Accuracy After calculating the integral, the calculator places the estimated uncertainty of that integral's result in the Y–register. Press Z to view the value of the uncertainty. For example, if the integral Si(2) is 1.6054 ± 0.0001, then 0.0001 is its uncertainty. Example: Specifying Accuracy. With the display format set to SCI 2, calculate the integral in the expression for Si(2) (from the previous example).
integration calculation decreases by a factor of ten for each additional digit, specified in the display format. Example: Changing the Accuracy. For the integral of Si(2) just calculated, specify that the result be accurate to four decimal places instead of only two. Keys: z { } 4 Display: Description: . Specifies accuracy to four decimal places. The uncertainty ) from the last example is still in the display.
For More Information This chapter gives you instructions for using integration in the HP 32SII over a wide range of applications. Appendix D contains more detailed information about how the algorithm for integration works, conditions that could cause incorrect results, conditions that prolong calculation time, and obtaining the current approximation to an integral. Integrating Equations File name 32sii-Manual-E-0424 Printed Date : 2003/4/24 Size : 17.7 x 25.
9 Operations with Comb Numbers The HP 32SII can use complex numbers in the form x + iy. It has operations for complex arithmetic (+, –, ×, ÷), complex trigonometry (sin, cos, tan), and the mathematics functions –z, 1/z, z1z2 , ln z, and e z. (where z1 and z2 are complex numbers). To enter a complex number: 1. Type the imaginary part. 2. Press . 3. Type the real part. Complex numbers in the HP 32SII are handled by entering each part (imaginary and real) of a complex number as a separate entry.
T t Z z x1 Y y iy2 X x iy1 Z1 Z2 x2 Real Stack Complex Stack Since the imaginary and real parts of a complex number are entered and stored separately, you can easily work with or alter either part by itself. Z1 y1 x1 Z2 Complex function y2 y imaginary part x2 x real part Complex input z or z1 and z2 Complex result, z Always enter the imaginary part (the y–part)of a number first. The real portion of the result (zx) is displayed; press Z to view the imaginary portion (zy).
Complex Operations Use the complex operations as you do real operations, but precede the operator with z F. To do an operation with one complex number: 1. Enter the complex number z, composed of x + i y, by keying in y x. 2. Select the complex function.
To do an arithmetic operation with two complex numbers: 1. Enter the first complex number, z1 (composed of x1 + i y1), by keying in y1 x1 . (For z1z2 , key in the base part, z1, first.) 2. Enter the second complex number, z2, by keying in y2 x2. (For z1z2 , key in the exponent, z2, second.) 3.
z1 × [1 ÷ (z2 + z3)] Keys: Display: 1 2 _ 3 _ 4 z F zF3 13 23 zFy Z ) Description: Add z2 + z3; displays real part. ) 1 ÷ (z2+z3). z1 ÷ (z2+z3). ) ) Result is 2.5 + i 9. Evaluate (4 – i 2/5) (3 – i 2/3). Do not use complex operations calculating just one part of a complex number. Keys: Display: 2 5 _ . ) when Description: Enters imaginary part of first complex number as a fraction. 4 ) Enters real part of first complex number. 23_ .
11 Intermediate result of 0 2 _ z (1 + i )–2 F0 zF* Z ) ) Real part of final results. Final result is . ) 0.8776 – i 0.4794. Using Complex Number in Polar Notation Many applications use real numbers in polar form or polar notation. These forms use pairs of numbers, as do complex numbers, so you can do arithmetic with these numbers by using the complex operations.
Add the following three loads. You will first need to convert the polar coordinates to rectangular coordinates. y L2 185 lb 143 o 170 lb 62 o L1 x L3 261 o 100 lb Keys: z { } 62 185 {r 143 170 { r zF 261 100 { r zF zq Display: Description: Sets Degrees mode. Enters L1 and converts it to ) . ) rectangular form. Eaters and converts L2. . ) Adds vectors. . ) Enters and converts L3. . ) Adds LI + L2 + L3.
10 Base Conversions and Arithmetic The BASE menu ( z w ) lets you change the number base used for entering numbers and other operations (including programming). Changing bases also converts the displayed number to the new base. BASE Menu Menu label Description { } Decimal mode. No annunciator. Converts numbers to base 10. Numbers have integer and fractional parts. { % } Hexadecimal mode. HEX annunciator on. Converts numbers to base 16; uses integers only. The top–row keys become digits through .
w { %} of the decimal number to base 16 and displays this value. z w { } z w { } z w { } Base 8. Base 2. Restores base 10; the original ) decimal value has been preserved, including its fractional part. Convert 24FF16 to binary base. The binary number will be more than 12 digits (the maximum display) long. Keys: Display: z w {HX} Description: Use the 6 key to type "F". _ 24FF z w { } The entire binary number does riot fit.
Arithmetic in bases 2, 8, and 16 is in 2's complement form and uses integers only: If a number has a fractional part, only the integer part is used for an arithmetic calculation. The result of an operation is always an integer (any fractional portion is truncated). Whereas conversions change only the displayed number and not the number in the X–register, arithmetic does alter the number in the X–register.
annunciator on. z w { } 1001100 Changes to base 2; BIN _ annunciator on. This terminates digit entry, so no is needed between the numbers. z w { %} z w { } Result in binary base. Result in hexadecimal base. Restores decimal base. 8 ) The Representation of Numbers Although the display of a number is converted when the base is changed, its stored form is not modified, so decimal numbers are not truncated — until they are used in arithmetic calculations.
546 z w { %} Enters a positive, decimal number; then converts it to hexadecimal. _ 2's complement (sign changed). z w { } Binary version; indicates more digits. << Displays the leftmost window; the number is negative since the highest bit is 1. z w { } . ) Negative decimal number.
If a number entered in decimal base is outside the range given above, then it produces the message ! in the other base modes. Any operation using ! causes an overflow condition, which substitutes the largest positive or negative number possible for the too–big number. Windows for Long Binary Numbers The longest binary number can have 36 digits–three times as many digits as fit in the display. Each 12–digit display of a long number is called a window.
())) ). Press { to view the digits obscured by the / … or @…label. Keys: z w { } Display: Description: _ Enters a large octal number. 123456712345 HA {A { (hold) z w { } /... Drops leftmost three digit's. Shows all digits. Restores Decimal mode. 8 8 8 ) Base Conversions and Arithmetic File name 32sii-Manual-E-0424 Printed Date : 2003/4/24 Size : 17.7 x 25.
11 Statistical Operations The statistics menus in the HP 32SII provide functions to statistically analyze a set of one– or two–variable data: Mean, sample and population standard deviations. Linear regression and linear estimation ( x̂ and ŷ ). Weighted mean (x weighted by y). A Summation statistics: n, Σx, Σy, Σx2, Σy2, and Σxy. x y r s,σ x,y L.R.
Entering One–Variable Data 1. Press z b {Σ} to clear existing statistical data. 2. Key in each x–value and press 6. 3. The display shows n, the number of statistical data values now accumulated. Pressing 6 actually enters two variables into the statistics registers because the value already in the Y–register is accumulated as the y–value.
Correcting Errors in Data Entry If you make a mistake when entering statistical data, delete the incorrect data and add the correct data. Even if only one value of an x, y–pair is incorrect, you must delete and reenter both values. To correct statistical data: 1. Reenter the incorrect data, but instead of pressing 6, press z 4. This deletes the value(s) and decrements n. 2. Enter the correct value(s) using 6.
4 20 z 4 ) Deletes the first data pair. 5 20 6 Reenters the first data pair. ) There is still a. total of two data pairs in the statistics registers. Statistical Calculations Once you have entered your data, you can use the functions in the statistics menus. Statistics Menus Menu Key Description L.R. {, The linear–regression menu: linear ˆ } and curve–fitting {T} estimation { º̂ } { ¸ {P } {E }. See ''Linear Regression'' later in this chapter.
y–values as weights or frequencies. The weights can be integers or non–integers. Example: Mean (One Variable). Production supervisor May Kitt wants to determine the average time that a certain process takes. She randomly picks six people, observes each one as he or she carries out the process, and records the time required (in minutes): 15.5 9.25 10.0 12.5 12.0 8.5 Calculate the mean of the times. (Treat all data as x–values.) Keys: z b {´} 15.5 6 9.25 6 10 6 12.5 6 12 6 8.
1000 4.1 6 ) { / { º· } ) Calculates the mean price weighted for the quantity Four data pairs accumulated. purchased. Sample Standard Deviation Sample standard deviation is a measure of how dispersed the data values are about the mean. standard deviation assumes the data is a sampling of a larger, complete set of data, and is calculated using n – 1 as a divisor. Press { 2 {Uº } for the standard deviation of x–values. Press { 2 {U¸ } for the standard deviation of y–values.
Population Standard Deviation Population standard deviation is a measure of how dispersed the data values are about the mean. Population standard deviation assumes the data constitutes the complete set of data, and is calculated using n as a divisor. Press{ 2 {σ º } for the population standard deviation of the x–values. Press { 2 {σ¸ } for the population standard deviation of the y–values. Example: Population Standard Deviation. Grandma Tinkle has four grown sons with heights of 170, 173, 174, and 180 cm.
L.R. (Linear Regression) Menu Menu Label Description { º̂ } Estimates (predicts) x for a given hypothetical value of y, based on the line calculated to fit the data. ˆ} {¸ Estimates (predicts) y for a given hypothetical value of x, based on the line calculated to fit the data. {T} Correlation coefficient for the (x, y) data. The correlation coefficient is a. number in the range –1 through +1 that measures how closely the calculated line fits the data. {P} Slope of the calculated line.
data. 4.63 0 6 ) Enters data; displays n. 5.78 20 6 ) 6.61 40 6 ) 7.21 60 6 ) 7.78 80 6 ) Five data pairs entered. {, ˆ TPE º̂ ¸ Displays linear–regression menu. {T } ) Correction coefficient; data closely approximate a straight line. z , {P} z , {E} ) ) Slope of the line. y–intercept. Statistical Operations File name 32sii-Manual-E-0424 Printed Date : 2003/4/24 Size : 17.7 x 25.
y 8.50 X 7.50 (70, y) r = 0.9880 6.50 m = 0.0387 5.50 b = 4.8560 x 4.50 0 20 40 60 80 What if 70 kg of nitrogen fertilizer were applied to the rice field? Predict the grain yield based on the above statistics. Keys: 70 ˆ} { , {¸ Display: _ ) Description: Enters hypothetical x–value. The predicted yield in tons per hectare. Limitations on Precision of Data Since the calculator uses finite precision (12 to 15 digits), it follows that there are limitations to calculations due to rounding.
Normalizing Close, Large Numbers The calculator might be unable to correctly calculate the standard deviation and linear regression for a variable whose data values differ by a relatively small amount. To avoid this, normalize the data by entering each value as the difference from one central value (such as the mean). For normalized x–values, this difference must then be added back to the calculation of x and x̂ , and ŷ and b roust also be adjusted.
Press {º }, {¸ }, and {º¸ } to recall the sums of the squares and the sum of the products of the x and y — values that are of interest when performing other statistical calculations in addition to those provided by the calculator. If you've entered statistical data, you can see the contents of the statistics registers. Press z X {# }, then use z and z to view the statistics registers. Example: Viewing the Statistics Registers. Use 6 to store data pairs (1,2) and (3,4) in the statistics registers.
If not enough calculator memory is available to hold the statistics registers when you first press 6 (or 4 ), the calculator displays & " . You will rived to clear variables, equations, or programs (or a combination) to make room for the statistics registers before you can enter statistical data. Refer to "Managing Calculator Memory" in appendix B. Access to the Statistics Registers The statistics register assignments in the HP 32SII are shown in the following table.
Part 2 Programming Statistics Programs File name 32sii-Manual-E-0424Page: 14/162 Printed Date : 2003/4/24 Size : 17.7 x 25.
12 Simple Programming Part 1 of this manual introduced you to functions and operations that you can use manually, that is, by pressing a key for each individual operation. And you saw how you can use equations to repeat calculations without doing all of the keystrokes each time. In part 2, you'll learn how you can use programs for repetitive calculations —–calculations that may involve more input or output control or more intricate logic.
This very simple program assumes that the value for the radius is in the X– register (the display) when the program starts to run. It computes the area and leaves it in the X–register. To enter this program into program memory, do the following: Keys: Display: z b {ALL} {Y} zd Description: Clears memory. Activates Program–entry mode (PRGM annunciator on). zU z: {M y zd ! Resets program pointer to PRGM TOP. (Radius)2 º π Area = πx2 º Exits Program–entry mode.
Program Boundaries (LBL and RTN) If you want more than one program stored in program memory, then a program needs a label to mark its beginning (such as ) and a return to mark its end (such as ! ). Notice–that the line numbers acquire an to match their label. Program Labels Programs and segments of programs (called routines) should start with a label. To record a label, press: z letter–key The label is a single letter from A through Z.
Using RPN and Equations in Programs You can calculate in programs the same ways you calculate on the. keyboard: Using RPN operations (which work with the stack, as explained in chapter 2). Using equations (as explained in chapter 6). The previous example used a series of RPN operations to calculate the area of the circle. Instead, you could have used an equation in the program. (An example follows later in this chapter.) Many programs are a. combination of RPN and equations, using the strengths of both.
For output, you can display a variable with the VIEW instruction, you can display a message derived from an equation, or you can leave unmarked values on the stack. These are covered later in this chapter tinder "Entering and Displaying Data." Entering a Program Pressing z d toggles the calculator into and out of Program–entry mode — turns the PRGM annunciator on and off. Keystrokes in Program–entry mode are stored as program lines in memory.
5. End the program with a return instruction, which sets the program pointer back to ! after the program runs. Press { . 6. Press (or z d ) to cancel program entry. Numbers in program lines are stored as precisely as you entered them, and they're displayed using ALL or SCI format. (If a long number is shortened in the display, press { to view all digits.) To enter an equation in a program line: 1. Press { G to activate Equation–entry mode, The EQN annunciator turns on. 2.
Function Names in Programs Then name of function that is used in a program line is not necessarily the same as the function's name on its key, in its menu, or in an equation. The name that is used in a program is usually a fuller abbreviation than that which can fit on a key or in a menu. This fuller name appears briefly in the display whenever you execute a function — as long as you hold down the key, the name is displayed. Example: Entering a Labeled Program.
A different checksum means the program was not entered exactly as given here. Example: Entering a Program with an Equation. The following program calculates the area of a circle using an equation, rather than using RPN operation like the previous program. Keys: zdz U zE Display: ! Description: Activates Program–entry mode; sets pointer to top of memory. Labels this program routine E (for "equation").
Executing a Program (XEQ) Press W label to execute the program labeled with that letter. If there is only one program in memory, you can also execute it by pressing z U f (run/stop). The PRGM annunciator blinks on and off while the program is running. If necessary, enter the data before executing the program. Example: Run the programs labeled A and E to find the areas of three different circles with radii of 5, 2.5, and 2π. Remember to enter the radius before executing .A or E.
only program, you can press z U to move to its beginning.) 3. Press and hold z . This displays the current program line. When you release , the line is executed. The result of that execution is then displayed (it is in the X–register). To move to the preceding line, you can press z . No execution occurs. 4. The program pointer moves to the next line. Repeat step 3 until you find an error (an incorrect result occurs) or reach the end of the program.
Entering and Displaying Data The calculator's variables are used to store data input, intermediate results, and final results. (Variables, as explained in chapter 3, are identified by a letter from A through Z or i, but the variable names have nothing to do with program labels.) In a program, you can get data in these ways: From an INPUT instruction, which prompts for the value of a variable. (This is the most handy technique.) From the stack. (You can use STO to store the value in a variable for later use.
"R" is the variable's name, "?" is the prompt for information, and 0.0000 is the current value stored in the variable. Press f (run/stop) to resume the program. The value you keyed in then writes over the contents of the X–register and is stored in the given variable. If you have not changed the displayed value, then that value is retained in the X–register.
Thus the program should not assume that the X–, Y–, and Z–registers' contents will be the same before and after the INPUT instruction. If you collect, all the data in the beginning and then recall then when needed for calculation, then this prevents the stack's contents from being altered just, before a calculation. For example, see the "Coordinate Transformations" program in chapter 15.
Using VIEW for Displaying Data The programmed VIEW instruction { variable stops a running program and displays and identifies the contents of the given variable, such as / ) This is a display only, and does not copy the number to the X–register. If Fraction–display mode is active, the value is displayed as a fraction. Pressing copies this number to the X–register. If the number is wider than 10 characters, pressing { displays the entire number.
press { G to start the equation. Press number and math keys to get numbers and symbols. Press K before each letter. Press to end the equation. If flag 10 is set, equations are displayed instead of being evaluated. This means you can display any message you enter as are equation. (Flags are discussed in detail in chapter 13.) When the message is displayed, the program stops—.–press f to resume execution.
Keys: Display: Description: πº : º Checksum and length of equation. { / ) Store the volume in V. HV ! # Calculates the surface area. {G2 y { M y K R y {\KR KH{ ] ºπº º 1 Checksum and length of equation. { / ) Stores the surface area in S. HS ! Sets flag 10 to display equations. { x { } 0 Displays message in equations. {GK VKOKL o oKA KRKE K A # - Clears flag 10. { x { } 0 {V # $ # Displays volume.
Now find the volume and surface area–of a cylinder with a radius of 2 1/2 cm and a height of 8 cm. Keys: WC Display: @value Description: Starts executing C; prompts for R. (It displays whatever value happens to be in R.) 212 f 8f f f @value Enters 2 1/2 as a fraction. Prompts for H. # - #/ ) Message displayed. Volume in cm3. / ) Surface area in cm2.
Stopping or Interrupting a Program Programming a Stop or Pause (STOP, PSE) Pressing f (run/stop) during program entry inserts a STOP instruction. This will halt a running program until you resume it by pressing f from the keyboard. You can use STOP rather than RTN in order to end a program without returning the program pointer to the top of memory. Pressing { e during program entry inserts a PSE (pause) instruction.
Editing Program You can modify a program in program memory by inserting, deleting, and editing program lines. If a program line contains an equation, you can edit the equation—if any other program line requires even a minor change, you must delete the old line and insert a new one. To delete a program line: 1. Select the relevant program or routine ( z U label), activate program entry ( z d ), and press z or z ) to locate the program line that must be changed.
then enter the desired corrections. 4. Press to end the equation. Program Memory Viewing Program Memory Pressing z d toggles the calculator into and out of program entry (PRGM annunciator on, program lines displayed). When Program–entry mode is active, the contents of program memory are displayed. Program memory starts at ! . The list of program lines is circular, so you can wrap the program pointer froze the bottom to the top and reverse.
which use only 1.5 bytes. All other instructions use 1.5 bytes. Equations use 1.5 bytes, plus 1.5 bytes for each function, plus 9.5 or 1.5 bytes for each number. Each "(" and each ")" uses 1.5 bytes except "(" for prefix functions. If during program entry you encounter the message & " , then there is not enough room in program memory for the line you just tried to enter. You can make more room available by clearing programs or other data.
Clearing One or More Programs To clear a specific program from memory 1. Press z X { } and display (using z and z ) the label of the program. 2. Press z b. 3. Press to cancel the catalog or a to back out. To clear all programs from memory: 1. 2. 3. 4. Press z d to display program lines (PRGM annunciator on). Press z b { } to clear program memory. The message @ & prompts you for confirmation. Press {& }. Press z d to cancel program entry.
(hold) If your checksum does not match this number, then you have not entered this program correctly. You will see that all of the application programs provided in chapters 15 through 17 include checksum values with each labeled routine so that you can verify the accuracy of your program entry. In addition, each equation in a program has a checksum. See "To enter an equation in a program line" earlier in this chapter.
Selecting a Base Mode in a Program Insert a BIN, OCT, or HEX instruction into the beginning of the program. You should usually include a DEC instruction at the end of the program so that the calculator's setting will revert, to Decimal mode when the program is done. An instruction in a program to change the base mode will determine bow input is interpreted and how output looks during and after program execution, but it does not affect the program lines as you enter them.
Polynomial Expressions and Horner's Method Some expressions, such as polynomials, use the same variable several times for their solution. For example, the expression Ax4 + Bx3 + Cx2 + Dx + E uses the variable x four different times. A program to calculate such an expression using RPN operations could repeatedly recall a stored copy of x from a variable.
! 5 y º 2 ! 5x. - y º y º y º { ! z X { } ) 5x + 2. (5x + 2)x. (5x + 2)x2. (5x + 2)x3. Displays label P, which takes 19.5 bytes. z Checksum and length. / ) Cancels program entry. Now evaluate this polynomial x = 7. Keys: WP 7f Display: Prompts for x. %@value 8 ) Description: Result.
! º - º - º - º - ! Checksum and length: E93F 028.5 Simple Programming 12–27 File name 32sii-Manual-E-0424 Printed Date : 2003/4/24 Size : 17.7 x 25.
13 Programming Techniques Chapter 12 covered the basics of programming. This chapter explores more sophisticated but useful techniques: Using subroutines to simplify programs by separating and labeling portions of the program that are dedicated to particular tasks. The use of subroutines also shortens a program that must perform a series of steps more than once.
A routine typically starts with a label (LBL) and ends with an instruction that alters or stops program execution, such as RTN, GTO, or STOP, or perhaps another label. Calling Subroutines (XEQ, RTN) A subroutine is a routine that is called from (executed by) another routine and returns to that same routine when the subroutine is finished. The subroutine must start with a LBL and end with a RTN. A subroutine is itself a routine, and it can call other subroutines.
Starts here. "! % % ! # $ ! ! 1 2 Calls subroutine Q. Return here. Starts D again. . . . 1 Starts subroutine. 2 Returns to routines D. Nested Subroutines A subroutine can call another subroutine, and that subroutine can call yet another subroutine. This "nesting" of subroutines—the calling of a subroutine within another subroutine—is limited to a stack of subroutines seven levels deep (not counting the topmost program level).
Example: A Nested Subroutine. The following subroutine, labeled S, calculates the value of the expression a2 + b2 + c2 + d 2 as part of a larger calculation in a larger program. The subroutine calls upon another subroutine (a nested subroutine), labeled Q, to do the repetitive squaring and addition. This saves memory by keeping the program shorter than it would be without the subroutine. Starts subroutine here. "! Enters A. "! Enters B. "! Enters C. "! Enters D.
Branching (GTO) As we have seen with subroutines, it is often desirable to transfer execution to a part of the program other than the next line. This is called branching. Unconditional branching uses the GTO (go to) instruction to branch to a program label. It is not possible to branch to a specific line number during a program. A Programmed GTO Instruction The GTO label instruction (press z U label) transfers the execution of a running program to the program line containing that label, wherever it may be.
Can start here. . . . ! ' 1 Can start here. . . . ! ' Branches to Z. 1 Branches to Z. Can start here. . . . ! ' 1 Branches to Z. ' ' . . . 1 Branch to here. Using GTO from the Keyboard You can use z U to move the program pointer to a specified label or line number without starting program execution. To ! : z U . To a line number: z U label nn (nn < 100). For example, z U A05.
Conditional Instructions Another way to alter the sequence of program execution is by a conditional test, a true/false test that compares two numbers and skips the next program instruction if the proposition is false. For instance, if a conditional instruction on line A05 is º/ @ (that is, is x equal to zero?), then the program compares the contents of the X–register with zero. If the X–register does contain zero, then the program goes on to the next line.
Tests of Comparison (x?y, x?0) There are 12 comparisons available for programming. Pressing z l or { n displays a. menu for one of the two categories of tests: x?y for tests comparing x and y. x?0 for tests comparing x and 0. Remember that x refers to the number in the X–register, and y refers to the number in the Y–register. These do not compare the variables X and Y. Select the category of comparison, then press the menu key for the conditional instruction you want.
! º <¸@ ! ! ! ! % ! # $ % Tests to see if the correction is significant. Goes back to start of loop if correction is significant. Continues if correction is not significant. Displays the calculated value of X. Line T09 calculates the correction for Xguess. Line T13 compares the absolute value of the calculated correction with 0.0001. If the value is less than 0.0001 ("Do If True"), the program executes line T14; if the value is equal to or greater than 0.0001, the program skips to line T15.
tested. Flags 5 and 6 allow you to control overflow conditions that occur during a program. Setting flag 5 stops a program at the line just after the line that caused the overflow. By testing flag 6 in a program, you can alter the program's flow or change a result anytime an overflow occurs. Flags 7, 8, and 9 control the display of fractions. Flag 7 can also be controlled from the keyboard, When Fraction–display mode is toggled on or off by pressing z , flag 7 is set or cleared as well.
4. If the next program line is a PSE instruction, execution continues after a 1–second pause. The status of flag 10 is controlled only by execution of the SF and CF operations from the keyboard, or by SF and CF, statements in programs. Flag 11 controls prompting when executing equations in a program — it doesn't affect automatic prompting during keyboard execution: When flag 11 is clear (the default state), evaluation, SOLVE, and ∫ FN of equations in programs proceed without interruption.
Using Flags Pressing { x displays the FLAGS menu: { } { } { @} After selecting the function you want, you will be prompted for the flag number (0–11). For example, press { x { } 0 to set flag 0; press { x { } to set flag 10; press { x { } 1 to set flag 11. FLAGS Menu Menu Key Description { } n Set flag. Set flag n. { } n Clear flag. Clears flag n. { @ } n Is flag set? Tests the status of flag n.
Line L03 sets flag 0 so that line W07 takes the natural log of the X–input for a Logarithmic–model curve. Line E04 sets flag 1 so that line W11 takes the natural log of the Y–input for an Exponential–model curve. Lines P03 and P04 set both flags so that lines W07 and W11 take the natural logarithms of both the X– and Y–inputs for a Power–model curve. Note that lines S03, S04, L04, and E03 clear flags 0 and 1 to ensure that they will be set only as required for the four curve models. Program Lines: . . .
Example: Controlling the Fraction Display. The following program lets you exercise the calculator's fraction–display capability. The program prompts for and uses your inputs for a fractional number and a denominator (the /c value). The program also contains examples of how the three fraction–display flags (7, 8, and 9) and the "message–display" flag (10) are used. Messages in this program are listed a MESSAGE and are entered as equations: 1.
Program Lines: Description: ! Sets flag 8. ! Displays message, then shows the fraction. ! Sets flag 9. % Displays message, then shows the fraction. ! ! Goes to beginning of program. Checksum and length: 10C3 102.0 Use the above program to see the different forms of fraction display: Keys: WF Display: #@value Description: Executes label F; prompts for a fractional number (V). 2.
Keys: Display: c + Description: format (denominator is factor of 16), then shows the fraction. f % Message indicates the fraction format (denominator is 16), then c + shows the fraction. f{ ) x { } 0 Stops the program and clears flag 10 Loops Branching backwards — that is, to a label in a previous line — makes it possible to execute part of a program more than once. This is called looping.
Program lines: Description: "! "! Checksum and length: 6157 004.5 It is easier to recall A than to remember where it is in the stack. Calculates A – B. Replaces old A with new result. Recalls constant for comparison. Is B < new A? Yes: loops to repeat subtraction. No: displays new A. . ! º6¸@ ! # $ ! Checksum and length: 5FE1 013.
. . . %! variable A DSE instruction is like a FOR–NEXT loop with a negative increment. After pressing a shifted key for ISG or DSE ( z k or { m ), you will be prompted for a variable that will contain the loop–control number (described below). The Loop–Control Number The specified variable should contain a loop–control number ±ccccccc.fffii, where: ±ccccccc is the current counter value (1 to 12 digits). This value changes with loop execution. fff is the final counter value (must be three digits).
1 1 If current value > final value, continue loop. 1 1 If current value ≤ final value, continue loop. $ . . . $ $ $ . . . $ . . . $ $ $ . . . $ ! $ % % 2 2 If current value ≤ final value, exit loop. $ ! $ % % 2 2 If current value > final value, exit loop. For example, the loop–control number 0.050 for ISG means: start counting at zero, count up to 50, and increase the number by 1 each loop. The following program uses ISG to loop 10 times.
Indirectly Addressing Variables and Labels Indirect addressing is a technique used in advanced programming to specify a variable or label without specifying beforehand exactly which one. This is determined when the program runs, so it depends on the intermediate results (or input) of the program. Indirect addressing uses two different keys: (with ) and (with f ). The variable I has nothing to do with or the variable i.
The Indirect Address, (i) Many functions that use A through Z (as variables or labels) can use to refer to A through Z (variables or labels) or statistics registers indirectly. The function uses the value in variable i to determine which variable, label, or register to address. The following table shows how. If i contains: Then (i) will address: ±1 . . . ±26 variable A or label A . . .
STO(i) RCL(i) STO +, –,× ,÷, (i) RCL +, –,× ,÷, (i) XEQ(i) GTO(i) X<>(i) INPUT(i) VIEW(i) DSE(i) ISG (i) SOLVE(i) ∫ FN d(i) FN=(i) Program Control with (i) Since the contents of i can change each time a program runs–or even in different parts of the same program — a program instruction such as ! 6L5 can branch to a different label at different times. This maintains flexibility by leaving open (until the program runs) exactly which variable or program label will be needed. (See the first example below.
and line Y08 calls a different subroutine to compute increased by 6: & & & x̂ after i has been ! - L % 1L2 If i hold: Then XEQ(i) calls: 1 LBL A 2 LBL B 3 LBL C 4 7 LBL D LBL G 8 LBL H 9 LBL I 10 LBL J To: Compute model. Compute model. Compute model. Compute Compute model. Compute model. Compute model. Compute ŷ for straight–line ŷ for logarithmic ŷ for exponential ŷ x̂ for power model. for straight–line x̂ for logarithmic x̂ for exponential x̂ for power model.
! L Stores loop–control number in i. The next routine is L, a loop to collect all 12 known values for a 3x3 coefficient matrix (variables A – I) and the three constants (J – L) for the equations. Program Lines: "!1L2 L Description: This routine collects all known values in three equations. Prompts for and stores a number into the variable addressed by i. Adds 1 to i and repeats the loop until i reaches 13.012.
Disables equation prompting. ) Sets counter for 1 to 26. ! L Stores counter. Initializes sum. Checksum and length: EA5F 017.0 Program Lines: Description: Starts summation loop. 1L2: Equation to evaluate the ith square. (Press { G to start the equation.) Ckecksum and length of equation: 48AD 006.0 - Adds ith square to sum. L Tests for end of loop. ! Branches for next variable. Ends program.
14 Solving and Integrating Programs Solving a Program In chapter 7 you saw how you can enter an equation — it's added to the equation list — and then solve it for any variable. You can also, enter a program that calculates a function, and then solve it for any variable. This is especially useful if the equation you're solving changes for certain conditions or if it requires repeated calculations. To solve a programmed function: 1. Enter a program that defines the function.
2. Include an INPUT instruction for each variable, including the unknown. INPUT instructions enable you to solve for any variable in a multi–variable function. INPUT for the unknown is ignored by the calculator, so you need to write only one program that contains a separate INPUT instruction for every variable (including the unknown). If you include no INPUT instructions, the program uses the values stored in the variables or entered at equation prompts. 3. Enter the instructions to evaluate the function.
R = The universal gas constant (0.0821 liter–atm/mole–K or 8.314 J/mole–K). T = Temperature (kelvins; K = °C + 273.1). To begin, put the calculator in Program mode; if necessary, position the program pointer to the top of program memory. Keys: Display: Description: zdz U ! Sets Program mode. Type in the program: Program Lines: Description: Identifies the programmed function. Stores P. "! Stores V. "! # Stores N. "! Stores R. "! Stores T.
unknown variable. {P 2f .005 f .0821 f 24 273.1 f #@value Selects P; prompts for V. @value Stores 2 in V; prompts for N. @value Stores .005 in N; prompts for R. !@value Stores .0821 in R; prompts for T. Calculates T. !@ ) # / ) Stores 297.1 in T; solves for P. Pressure is 0.0610 atm. Example: Program Using Equation. Write a program that uses an equation to solve the "Ideal Gas Law." Keys: zdz U Display: Description: Selects Program–entry mode.
Now calculate the change in pressure of the carbon dioxide if its temperature drops by 10 °C from the previous example. Keys: HL {VH Display: Description: ) Stores previous pressure. ) Enters the limits of integration (lower limit first). {P f f f 10 f @ ) Retains 2 in V; prompts for N. @ ) Retains .005 in N; prompts for R. !@ ) Retains .0821 in R; prompts for T. !@ ) Calculates new T. # / ) KL Selects variable P; prompts for V. #@ ) .
before displaying it). If you do want this result displayed, add a VIEW variable instruction after the SOLVE instruction. If no solution is found for the unknown variable, then the next program line is skipped (in accordance with the "Do if True" rule, explained in chapter 13). The program should then handle the case of not finding a root, such as by choosing new initial estimates or changing an input value. Example: SOLVE in a Program.
Integrating a Program In chapter 8 you saw how you can enter an equation (or expression) — it's added to the list of equations — and then integrate it with respect to any variable. You can also enter a program that calculates a function, and then integrate it with respect to any variable. This is especially useful if the function you're integrating changes for certain conditions or if it requires repeated calculations. To integrate a programmed function: 1.
is ignored by the calculator, so you need to write only one program that contains a separate INPUT instruction for every variable (including the variable of integration). If you include no INPUT instructions, the program uses the values stored in the variables or entered at equation prompts. 3. Enter the instructions to evaluate the function. A function programmed as a multi–line RPN sequence must calculate the function values you want to integrate.
z { } {VS 02 _ Selects Radians mode. Selects label S as the integrand. Enters lower and upper limits of integration. {)X Integrates function from 0 to 2; ! ! displays result. ) z { } ) Restores Degrees mode. Using Integration in a Program Integration can be executed from a program.
The e((D − M)÷S)2 ÷2 function is calculated by the routine labeled F. Other routines prompt for the known values and do the other calculations to find Q(D), the upper–tail area of a normal curve. The integration itself is set up and executed from routine Q: Recalls lower limit of integration. % Recalls upper limit of integration. (X = D.) / Specifies the function. ∫ G Integrates the normal function using the dummy variable D.
15 Mathematics Programs Vector Operations This program performs the basic vector operations of addition, subtraction, cross product, and dot (or scalar) product. The program uses three–dimensional vectors and provides input and output in rectangular or polar form. Angles between vectors can also be found. Z P R Y T X Mathematics Programs File name 32sii-Manual-E-0424 Printed Date : 2003/4/24 Size : 17.7 x 25.
This program uses the following equations.
Program Lines: Description Defines the beginning of the rectangular input/display routine. Displays or accepts input of X. "! % Displays or accepts input of Y. "! & Displays or accepts input of Z. "! ' Checksum and length: F8AB 006.0 Defines beginning of rectangular–to–polar conversion process. & % Calculates ¸8º´θ8T ( X2 + Y2 ) and arctan(Y/X). º65¸ ! ! Saves T = arctan(Y/X). Gets (X2 + Y2) back.
Program Listing: Program Lines: Description º65¸ ! & Saves Y = R sin(P) sin(T). ! Loops back for another display of polar form. Checksum and length: D518 022.5 Defines the beginning of the vector–enter routine. % Copies values in X , Y and Z to U, V and W respectively. ! " & ! # ' ! $ ! Loops back for polar conversion and display/input. Checksum and length: 1032 012.0 % % Defines beginning of vector–exchange routine.
Program Listing: Program Lines: Description ! % Saves X + U in X. # - & ! & Saves V + Y in Y. ' - $ ! ' Saves Z + W in Z. ! Loops back for polar conversion and display/input. Checksum and length: 641B 016.5 Defines the beginning of the vector–subtraction routine. Multiplies X, Y and Z by (–1) to change the sign. . ! º % ! º & ! º ' ! Goes to the vector–addition routine. Checksum and length: D051 017.
Program Listing: Program Lines: Description º # . ! ' Stores (XV – YU), which is the Z component. ¶ ! & Stores Y component. ¶ ! % Stores X component. ! Loops back for polar conversion and display/input. Checksum and length: FEB2 033.0 Defines beginning of dot–product and vector–angle routine. % º " & º # - ' º $ - ! Stores the dot product of XU + YV + ZW.
Program Listing: Program Lines: Description ¶ Divides previous result by the magnitude. ª Calculates angle. ! # $ Displays angle. ! Loops back for polar display/input. Checksum and length: 1DFC 040.5 Flags Used: None. Memory Required: 270 bytes: 182 for program, 88 for variables. Remarks: The length of routine S can be shortened by 6.5 bytes. The value –1 as shown uses 9.5 bytes. If it appears as 1 followed by +/– , it will require only 3 bytes.
3. Key in R and press f, key in T and press f, then key in P and press f Continue at step 5. 4. Key in X and press f, key in Y and press f, and key in Z and press f. 5. To key in a second vector, press W E (for enter), then go to step 2. 6. Perform desired vector operation: a. Add vectors by pressing W A; b. Subtract vector one from vector two by pressing W S; c. Compute the cross product by pressing W C; d. Compute the dot product by pressing W D and the angle between vectors by pressing f. 7.
rectangular to polar conversion capability to find the total distance and the direction to the transmitter. N (y) 7.3 Transmitter 15.7 Antenna E (x) W S Keys: Display: z { } WR %@value 7.3 f &@value Description: Sets Degrees mode. Starts rectangular input/display routine. 15.7 f '@value Sets X equal to 7.3. Sets Y equal to 15.7. .76 _ f @ ) f !@ ) f @ ) Calculates P, the angle from the z-axis. Sets Z equal to –0.76 and calculates R, the radius.
Example 2: What is the moment at the origin of the lever shown below? What is the component of force along the lever? What is the angle between the resultant of the force vectors and the lever? F 1 = 17 T = 215 o P = 17 o Z F 2 = 23 T = 80 o P = 74 o 1.07m 63 o Y 125 o X First, add the force vectors. Keys: WP 17 f 215 f 17 f WE 23 f 80 f Display: Description: @value Starts polar input routine. !@value Sets radius equal to 17. @value Sets T equal to 215. @ ) Sets P equal to 17.
74 f @ ) WA @ ) Sets P equal to 74. Adds the vectors and displays the resultant R. f f WE Displays T of resultant vector. @ ) Displays P of resultant vector. @ ) Enters resultant vector. !@ ) Since the moment equals the cross product of the radius vector and the force vector (r × F), key in the vector representing the lever and take the cross product. Keys: Display: Description: 1.07 f !@ 125 f @ ) Sets T equal to 125.
WD f / ) / ) Calculates dot product. Calculates angle between resultant force vector and lever. f @ ) Gets back to input routine. Solutions of Simultaneous Equations This program solves simultaneous linear equations in two or three unknowns. It does this through matrix inversion and matrix multiplication. A system of three linear equations AX + DY + GZ = J BX + EY + HZ = K CX + FY + IZ = L can be represented by the matrix equation below.
Program Listing: Program Lines: ) ! L Description Starting point for input of coefficients. Loop–control value: loops from I to 12, one at a time. Stores control value in index variable. Checksum and length: 9F76 012.5 Starts the input loop. "!1L2 Prompts for and stores the variable addressed by i. Adds one to i. L If i is less than 13, goes back to LBL L and gets the ! next value. Returns to LBL A to review values.
Program Lines: º . ! ' º º . ! L º º . ! º º . º º . ! ¶ ! º º . Description Calculates H' × determinant = BG – AH. Calculates I' × determinant = AE – BD.
Program Lines: Description º º . ! ¶ ! L Calculates G', × determinant = DH – EG. Stores D'. Stores I'. ! % Stores E'. ! % Stores F'. ! ' Stores H'. ! Sets index value to point to last element of matrix. ! L Recalls value of determinant. $ Checksum and length: 4C14 105.0 This routine completes inverse by dividing by determinant. ! ª1L2 Divides element.
Program Lines: % Description Sets index value to point to last element in second row. % Sets index value to point to last element in third row. Checksum and length: C1D3 009.0 This routine calculates product of column vector and row pointed to by index value. Saves index value in i. ! L Recalls J from column vector. Recalls K from column vector. Recalls L from column vector. º1L2 Multiplies by last element in row.
Program Lines: Description Checksum and length: 4E79 012.0 This routine calculates the determinant. º Calculates A × E × I. º º º Calculates (A × E × I) + (D × H × C). - º º Calculates (A × E × I) + (D × H × C) + (G × F × B). - º º (A × E × I) + (D × H × C) + (G × F × B) – (G × E × . C).
Flags Used: None. Memory Required: 348 bytes: 212 for program, 136 for variables. Program Instructions: 1. Key in the program routines; press when done. 2. Press W A to input coefficients of matrix and column vector. 3. Key in coefficient or vector value (A through L) at each prompt and press f. 4. Optional: press W D to compute determinant of 3 × 3 system. 5. Press W I to compute inverse of 3 × 3 matrix. 6. Optional: press W A and repeatedly press f to review the values of the inverted matrix. 7.
Example: For the system below, compute the inverse and the system solution. Review the inverted matrix. Invert the matrix again and review the result to make sure that the original matrix is returned. 23X + 15Y + 17Z = 31 8X + 11Y – 6Z = 17 4X + 15Y + 12Z = 14 Keys: WA 23 f Display: Description: @value Starts input routine. @value Sets first coefficient, A, equal to 23. 8f @value Sets B equal to 8. 4f @value Sets C equal to 4. 15 f . . . 14 f @value . . .
f f f WI @. ) Displays next value. @ ) Displays next value. @ ) Displays next value. ) Inverts inverse to produce original matrix. WA f @ ) . . . . . . @ ) Begins review of inverted matrix. Displays next value, ...... and so on. Polynomial Root Finder This program finds the roots of a polynomial of order 2 through 5 with real coefficients. It calculates both real and complex roots. For this program, a general polynomial has the form xn + an–1xn–1 + ...
b0 = a0(4a2 – a32) – a12. Let y0 be the largest real root of the above cubic. Then the fourth–order polynomial is reduced to two quadratic polynomials: x2 + (J + L)× + (K + M) = 0 x2 + (J – L)x + (K – M) = 0 where J = a3/2 K = y0 /2 L= J 2 − a2 + y0 M= K 2 − a2 × (the sign of JK – a1/2) Roots of the fourth degree polynomial are found by solving these two quadratic polynomials.
Program Lines: Description ! 1L2 Starts root finding routine. Checksum and length: CE86 010.5 Evaluates polynomials using Horner's method, and synthetically reduces the order of the polynomial using the root. ! L Uses pointer to polynomial as index. Starting value for Horner's method. Checksum and length: B85F 006.0 Starts the Horner's method loop. ! Saves synthetic division coefficient. º % Multiplies current sum by next power of x.
Program Lines: ª -+. ! ! ! º µ . º6 @ ! Description a1/2. –a1/2. Saves – a1/2. Stores real part if complex root. (a1/2)2. a0. (a1/2)2 – ao. Initializes flag 0. Discriminant (d) < 0 Sets flag 0 if d < 0 (complex roots). d d ! Stores imaginary part if complex root. Complex roots? @ Returns if complex roots. ! ! .
Program Lines: Description % Solves remaining second–order polynomial and stores roots. # $ % Displays real root of cubic. ! Displays remaining roots. Checksum and length: CCF5 010.5 Starts fifth–order solution routine. Indicates fifth–order polynomial to be solved. % Solves for one real root and puts three synthetic division coefficients for fourth–order polynomial on stack. Discards polynomial function value. ¶ ! Stores coefficient.
Program Lines: Description b2= –a2. -+. ! Stores b2. a3. º a3 a1. º 4a0. b1 = a3a1 – 4a0. . ! Stores b1. To enter lines D21 and D22 Press 4 { 3. % ª Creates 7.004 as a pointer to the cubic coefficients. - % Solves for real root and puts a0 and a1 for second–order polynomial on stack. Discards polynomial function value. ¶ % Solves for remaining roots of cubic and stores roots.
Program Lines: Description ! ª K = y0/2 % Creates 10–9 as a lower bound for M2 +º K K2. º . M2 = K2 –a0. º6¸@ If M2 < 10 –9, use 0 for M2. º ! M = K 2 − a0 ! Stores M. J. º JK. a1. a1/2 ª JK – a1/2. . º/ @ Use 1 if JK – a1/2 = 0 ! Stores 1 or JK – a1/2. ! ª Calculates sign of C. J. J2 º . J2 -– a2.
Program Lines: Description polynomial. J. . J – L. K. . K – M. Checksum and length: 9133 061.5 ! ! Starts routine to calculate and display two roots. ! % Uses quadratic routine to calculate two roots. Checksum and length: 0019 003.0 Starts routine to display two real roots or two roots. Gets the first real root. ! % Stores the first real root. # $ % Displays real root or real part of complex root.
Flags Used: Flag 0 is used to remember if the root is real or complex (that is, to remember the sign of d). If d is negative, then flag 0 is set. Flag 0 is tested later in the program to assure that both the real and imaginary parts are displayed if necessary. Memory Required: 382.0 bytes: 268.5 for programs, 33.5 for SOLVE, 80 for variables. Remarks: The program accommodates polynomials of order 2, 3, 4, and 5. It does not check if the order you enter is valid.
2. 3. 4. 5. Key in the program routines; press when done. Press W P to start the polynomial root finder. Key in F, the order of the polynomial, and press f At each prompt, key in the coefficient and press f. You're not prompted for the highest–order coefficient — it's assumed to be 1. You must enter 0 for coefficients that are 0. Coefficient A must not be 0. Terms mid Coefficients Order 5 4 3 2 x5 1 x4 E 1 x3 D D 1 x2 C C C 1 x B B B B Constant A A A A 6.
Exampl e 1: Find the roots of x5 – x4 – 101x3 +101x2 + 100x – 100 = 0. Keys: WP Display: @value Description: Starts the polynomial root finder; prompts for order. 5f @value Stores 5 its F; prompts for E. 1_f @value Stores –1 in E; prompts for D. 101 f @value Store –101 in D. prompts for C. 101 f @value Stores 101 in C; prompts for B. 100 f @value Stores 100 in B; prompts for A. 100 _ f %/ ) Stores –100 in A; calculates the first root. f f f f %/ ) %/ ) %/.
22 @value 4pf %/ ) Stores –10/4 in B; prompts for A. Stores 22/4 in A; calculates the first root. f f %/ ) %/. ) Calculates the second root. Displays the real part of the third root. f %/ ) Displays the imaginary part of the third root. f %/. ) Displays the real part of the fourth root. f L/. ) Displays the imaginary part of the fourth root. The third and fourth roots are –1.00 ± 1.00 i.
The following formulas are used to convert a point P from the Cartesian coordinate pair (x, y) in the old system to the pair (u, v) in the new, translated, rotated system. u = (x – m) cosθ + (y – n) sinθ v = (y – n) cos θ – (y – n) sinθ The inverse transformation is accomplished with the formulas below. x = u cosθ – v sinθ + m y = u sinθ + v cosθ + n The HP 32SII complex and polar–to–rectangular functions make these computations straightforward.
y y' x Old coordinate system P u y [0, 0] [ m, n ] v x' x θ New coordinate system Program Listing: Program Lines: Description This routine defines the new coordinate system. "! Prompts for and stores M, the new origin's x–coordinate. "! Prompts for and stores N, the new origin's y–coordinate. "! ! Prompts for and stores T, the angle θ. ! Loops for review of inputs. Checksum and length: 2ED3 007.
Program Lines: Description "! % Prompts for and stores X, the old x–coordinate. "! & Prompts for and stores Y, the old y–coordinate. % Pushes Y up and recalls X to the X–register. Pushes X and Y up and recalls N to the X–register. Pushes N, X, and Y up and recalls M. %. Calculates (X – M) and (Y – N). ! Pushes (X – M) and (Y – N) up and recalls T. Charges the sign of T because sin(–T) equals –sin(T). -+. Sets radius to 1 for computation of cos(T) and –sin(T).
Program Lines: Description ! % Stores the x–coordinate in variable X. º65¸ Swaps the positions of the coordinates. ! & Stores the y–coordinate in variable Y. º65¸ Swaps the positions of the coordinates back. # $ % Halts the program to display X. # $ & Halts the program to display Y. ! Goes back for another calculation. Checksum and length: 7C14 027.0 Flags Used: None. Memory Required: 119 bytes: 63 for program, 56 for variables. Program Instructions: 1.
13. Key in U (the x–coordinate in the new system) and press f. 14. Key in V (the y–coordinate in the new system) and press f to see X. 15. Press f to see Y. 16. For another new–to–old transformation, press f and go to step 13. For an old–to–new transformation, go to step 7. Variables Used: M N T X Y U V The x–coordinate of the origin of the new system. The y–coordinate of the origin of the new system. The rotation angle, θ, between the old and new systems. The x–coordinate f a point in the old system.
y y' P 3 (6, 8) P 1 ( _ 9, 7) x P 2 ( _ 5, _ 4) T (M, N) P' 4 (2.7, _ 3.6) ( M , N ) = (7, _ 4) T = 27 o Keys: Display: z { } Description: Sets Degrees mode since T is given in degrees. WD @value Starts the routine that defines the transformation. 7f @value Store 7 in M. 4_f !@value Store –4 in N. 27 f @ ) WN %@value Stores 27 in T. Starts the old–to–new routine. Mathematics Programs 15–37 File name 32sii-Manual-E-0424 Printed Date : 2003/4/24 Size : 17.7 x 25.
9_f &@value 7f "/. ) Stores 7 in Y and calculates U. f f #/ ) Stores –9 in X. Calculates V. Resumes the old–to–new routine %@. ) for next problem. 5_f &@ ) 4_f "/. ) Stores –4 in Y. f f #/ ) Calculates V. %@. ) Resumes the old–to–new routine Stores –5 in X. for next problem. 6f &@. ) Stores 6 in X . 8f "/ ) Stores 8 in Y and calculates U. f WO 2.7 f 3.6 _ f f #/ ) Calculates V. "@ ) Starts the new–to–old routine.
16 Statistics Programs Curve Fitting This program can be used to fit one of four models of equations to your data. These models are the straight line, the logarithmic curve, the exponential curve and the power curve. The program accepts two or more (x, y) data pairs and then calculates the correlation coefficient, r, and the two regression coefficients, m and b. The program includes a routine to calculate the estimates x̂ and ŷ . (For definitions of these values, see "Linear Regression" in chapter 11.
Exponential Curve Fit E Straight Line Fit S y y y = B _ Mx y = Be Mx x Logarithmic Curve Fit L y x Power Curve Fit P y = B + MIn x x y y = Bx M x To fit logarithmic curves, values of x must be positive. To fit exponential curves, values of y must be positive. To fit power curves, both x and y must be positive. A 1 2 error will occur if a negative number is entered for these cases.
Program Listing: Program Lines: Description This routine set, the status for the straight–line model. Enters index value for later storage in i (for indirect addressing). Clears flag 0, the indicator for ln X. Clears flag 1, the indicator for In Y. ! ' Branches to common entry point Z. Checksum and length: EBD2 007.5 This routine sets the status fog the logarithmic model. Enters index value for later storage in i (for indirect addressing).
Program Lines: Description ' ! L Stores the index value in i for indirect addressing. Sets the loop counter to zero for the first input. ' Checksum and length: 8C2F 006.0 $ Defines the beginning of the input loop. Adjusts the loop counter by one to prompt for input. - ! % Stores loop counter in X so that it will appear with the prompt for X. Displays counter with prompt and stores X input. $ "! % $ @ If flag 0 is set . . . . . . takes the natural log of the X–input.
Program Lines: Description @ If flag 1 is seta takes the natural antilog of b. H % ! Stores b in B. Displays value, # $ Calculates coefficient m. P ! Stores m in M. Displays value. # $ Checksum aril length: EBF3 018.0 & & Defines the beginning of the estimation (projection) loop. Displays, prompts for, and, if changed, stores x–value & "! % in X. Calls subroutine to compute ŷ . & % 1L2 & ! & Stores ŷ –value in Y.
Program Lines: Description Restores index value to its original value. ! . L & . Calculates x̂ =(Y – B) ÷ M. ª ! Returns to the calling routine. Checksum and length: 0D3F 009.0 This subroutine calculates model. ŷ for the logarithmic % º Calculates ŷ = M In X + B. - Returns to the calling routine. Checksum and length: 7AB7 009.0 This subroutine calculates x̂ for the logarithmic model.
Program Lines: Description This subroutine calculates x̂ for the exponential model. Restores index value to its original value. ! . L & ª Calculates x̂ = (ln (Y ÷ B)) ÷ M. ª ! Returns to the calling routine. Checksum and length: 7D3B 010.5 This subroutine calculates ŷ for the power model. % ¸ % Calculates Y= B(XM). º ! Returns to the calling routine. Checksum and length: 30CD 009.
Memory Required: 270 bytes: 174 for program, 96 for data (statistic. registers 48). Program instructions: 1. Key in the program routines; press when done. 2. Press W and select the type of curve you wish to fit by pressing: S for a straight line; L for a logarithmic curvy.; E for an exponential curve; or P for a power curve. 3. Key in x–value and press f. 4. Key in y–value and press f. 5. Repeat steps 3 and 4 for each data pair.
also used for scratch. Regression coefficient (slope of a straight line). Correlation coefficient; also used for scratch. The x–value of a data pair when entering data; the hypothetical x when projecting ŷ ; or x̂ (x–estimate) when given a hypothetical y. The y–value of a data pair when entering data; the hypothetical y when projecting x̂ ; or ŷ (y–estimate) when given a hypothetical x. Index variable used to indirectly address the correct x̂ –, ŷ –projection equation.
f WU %@ ) Retrieves %@ prompt. %@ ) Deletes the last pair. Now proceed with the correct data entry. 37.9 f &@ ) 100 f %@ ) 36.2 f &@ 97.5 f %@ ) 35.1 f &@ 95.5 f %@ ) 34.6 f &@ ) 94 f %@ ) WR / ) Enters correct x–value of data pair. Enters y–value of data pair. Enters x–value of data pair. ) ) Enters y–value of data pair. Enters x–value of data pair. Enters y–value of data pair. Enters x–valise of data pair. Enters y–value of data pair.
Logarithmic Exponential Power To start: WL WE WP R 0.9965 0.9945 0.9959 M –139.0088 51.1312 8.9730 B 65.8446 0.0177 0.6640 Y ( ŷ when X=37) 98.7508 98.5870 98.6845 X ( x̂ when Y=101) 38.2857 38.3628 38.3151 Normal and Inverse–Normal Distributions Normal distribution is frequently used to model the behavior of random variation about a mean.
Q(x ) = 0.5 − 1 σ 2π x ∫x 2 e −(( x − x )÷σ ) ÷2dx This program uses the built–in integration feature of the HP 32SIl to integrate the equation of the normal frequency curve. The inverse is obtained using Newton's method to iteratively search for a value of x which yields the given probability Q(x). Program Lines: Description This routine initializes the standard–deviation program. Stores default value for mean. ! Prompts for and stores mean, M.
Program Lines: ! ! ! ! ! ! ! ! ! ! ! ! Description . % ! ¶ % Calculates the derivative at Xguess. ª ! Calculates the correction for Xguess ª ! - % Adds the correction to yield a new Xguess. ) º6¸@ Tests to see if the correction is significant. ! ! Goes back to start of loop if correction is significant. Continues if correction is not significant. ! % ! # $ % Displays the calculated value of X. ! ! Loops to calculate another X.
Program Lines: Description ! Returns to the calling routine. Checksum and length: F79E 032.0 the integrand for the normal This subroutine calculates 2 function e −(( X − M)÷S) ÷2 . ª º ª -+. H % ! Returns to the calling routine. Checksum and length: 3DC2 015.0 Flags Used: None. Memory Required: 155.5 bytes: 107.5 for program, 48 for variables. Remarks: The accuracy of this program is dependent on the display setting.
Yom do riot need to key in the inverse routine (in routines I and T) if you are not interested in the inverse capability. Program Instructions: 1. Key in the program routines; press when done. 2. Press W S. 3. After the prompt for M, key in the population mean and press f. (If the mean is zero, just press f.) 4. After the prompt for S, key in the population standard deviation and press f. (If the standard deviation is 1, just press f ) 5. To calculate X given Q(X), skip to step 9 of these instructions. 6.
Example 1: Your good friend informs you that your blind date has "3σ" intelligence. You interpret this to mean that this person is more intelligent than the local population except for people more than three standard deviations above the mean. Suppose that you intuit that the local population contains 10,000 possible blind dates. How many people fall into the "3σ" band? Since this problem is stated in terms of standard deviations, use the default value of zero for M and 1 for S.
f 2f %@ ) / ) Resumes program. Enters X–value of 2 and calculates Q(X). 10000 y ) Multiplies by the population for the revised estimate. Example 2: The mean of a set of test scores is 55. The standard deviation is 15.3.
0.8 f %/ ) Stores 0.8 (100 percent minus 20 percent) in Q(X) and calculates X. Grouped Standard Deviation The standard deviation of grouped data, Sxy, is the standard deviation of data points x1, x2, ... , xn, occurring at positive integer frequencies f1, f2, ... , fn. (∑ xif i)2 ∑ xi − ∑ fi Sxg = (∑ fi ) − 1 2 This program allows you to input data, correct entries, and calculate the standard deviation and weighted mean of the grouped data.
Program Lines: Description Updates ∑ fi in register 28. ! -1L2 º % xifi ! L Stores index for register 29. ¶ Updates ∑ xifi in register 29. ! -1L2 2 º % xi f ! L Stores index for register 31. ¶ xi 2fi in register 31. Updates ! -1L2 º65¸ Gets 1 (or –1). ! - Increments (or decrements) N. # $ Displays current number of data pairs. ! Goes to label I for next data input. Checksum and length: 214E 030.
Flags Used: None. Memory Required: 143 bytes: 71 for programs, 72 for data. Program Instructions: 1. 2. 3. 4. 5. 6. Key in the program routines; press when done. Press W S to start entering new data. Key in xi–value (data point) and press f. Key in f i–value (frequency) and press f. Press f after VIEWing the number of points entered. Repeat steps 3 through 5 for each data point.
i Register 28 Register 29 Register 31 Index variable used to indirectly address the correct statistics register. Summation Σ fi. Summation Σ xifi. Summation Σ xi2fi. Exampl e: Enter the following data and calculate the grouped standard deviation. Group xi fi 1 5 17 Keys: WS 5f 17 f 2 8 26 3 13 37 4 15 43 Display: 5 22 73 6 37 115 Description: %@value Prompts for the first xi. @value Stores 5 in X; prompts for first fi. / ) Stores 17 in F; displays the counter.
Keys: f f 15 f 43 f f 22 f 73 f f 37 f 115 f WG Display: / ) Description: Displays the counter. %@ ) Prompts for the fourth x i. @ ) Prompts for the fourth fi. / ) Displays the counter. %@ ) Prompts for the fifth x1. @ ) Prompts for the fifth fi. / ) Displays the counter. %@ ) Prompts for the sixth xi. @ ) Prompts for the sixth fi. / ) / ) Displays the counter.
17 Miscellaneous Programs and Equations Time Value of Money Given any four of the five values in the "Time–Value–of–Money equation" (TVM), you can solve for the fifth value. This equation is useful in a wide variety of financial applications such as consumer and home loans and savings accounts.
problem can he viewed from two perspectives. The lender and the borrower view the same problem with reversed signs. Equation Entry: Key in this equation: º º1 .1 - ª 2:. 2ª - º1 - ª Keys: Display: {G ! ! 2:. - Description: Selects Equation mode. or current equation K P y 100 y{\1 y{\1 K I p 100 {]0 KN{] pKIKFy {\1KI p 100 { ] 0KN KB { (hold) _ º º º Starts entering equation. º1 .¾ º1 .1 -¾ .1 - ª .1 - ª - ª _ 2:¾ 2:. 2¾ 2:.
Remarks: The TVM equation requires that I must be non–zero to avoid a # & error. If you're solving for I and aren't sure of its current value, press 1 H I before you begin the SOLVE calculation ( { I ). The order in which you're prompted for values depends upon the variable you're solving for. SOLVE instructions: 1. If your first TVM calculation is to solve for interest rate, I, press 1 H I. 2. Press { G.
Variables Used: N I The number of compounding periods. The periodic interest rate as a percentage. (For example, if the annual interest rate is 15% and there are 12 payments per year, the periodic interest rate, i, is 15÷12=1.25%.) The initial balance of loan or savings account. The periodic payment. The future value of a savings account or balance of a loan. B P F Example: Part 1. You are financing the purchase of a car with a 3–year (36–montld) loan at 10.5% annual interest compounded monthly.
36 f @value Stores 36 in N; prompts for F. 0f @value Stores 0 in F; prompts for D. 7250 @ 8 ) Calculates B, the beginning loan balance. 1500 f Stores 5750 in B; calculates # /. ) monthly payment, P. The answer is negative since the loan has been viewed from the borrower's perspective. Money received by the borrower (the beginning balance) is positive, while money paid out is negative. Part 2.
Note that the interest rate, I, from part 2 is not zero, so you won't get a # & error when you calculate the new I. Keys: Display: {G Rº {F f f 24 f f R@. Description: Displays leftmost part of the TVM º1 .1 - equation. Selects F; prompts for P. ) @ ) Retains P; prompts for I. @ ) Retains 0.56 in I; prompts for N. @ 8 ) Stores 24 in N; prompts for B. # Retains 5750 in B; calculates F, the future balance. Again, the sign is /.
LB L Y V IEW Prim e N ote: x is t he value in the X-regis ter. LB L Z P + 2 →x Start LB L P x→ P 3→ D LB L X FP [ P / D ] → x yes x = 0? no yes D >√ P ? no D + 2 →D Miscellaneous Programs and Equations File name 32sii-Manual-E-0424 Printed Date : 2003/4/24 Size : 17.7 x 25.
Program Listing: Program Lines: Description & & This routine displays prime number P. & # $ Checksum and length: 5D0B 003.0 ' ' This routine adds 2 to P. ' ' - Checksum and length: 0C68 004.5 This routine stores the input value for P. ! ª º/¸@ Tests for even input. ! - Increments P if input an even number. ! Stores 3 in test divisor, D. Checksum and length: 40BA 016.
Program Lines: Description % ! & If all factors have been tried, branches to the display routine. Calculates the next possible factor, D + 2. % % ! - % ! % Branches to test potential prime with new factor. Checksum and length: 061F 021.0 Flags Used: None. Memory Required: 61 bytes: 45 for program, 16 for variables. Program Instructions: 1. 2. 3. 4. Key in the program routines; press when done. Key in a positive integer greater than 3. Press W P to run program.
789 W P / ) Calculates next prime number after 789. f / ) Calculates next prime number after 797. 17–10 Miscellaneous Programs and Equations File name 32sii-Manual-E-0424 Printed Date : 2003/4/24 Size : 17.7 x 25.
Part 3 Appendixes and Reference File name 32sii-Manual-E-0424 Printed Date : 2003/4/24 Size : 17.7 x 25.
A Support, Batteries, and Service Calculator Support You can obtain answers to questions about using your calculator from our Calculator Support Department. Our experience shows that many customers have similar questions about our products, so we have provided the following section, "Answers to Common Questions." If you don't find an answer to your question, contact us at the address or phone number listed on the inside back cover.
A: Exponent of ten; that is, 2.51 × 10–13. Q: The calculator has displayed the message & " . What should I do? A: You must clear a portion of memory before proceeding. (See appendix B.) Q: Why does calculating the sine (or tangent) of π radians display a very small number instead of 0? A: π cannot be represented exactly with the 12–digit precision of the calculator.
Changing the Batteries Replace the batteries as soon as possible when the low battery annunciator ( ¤ ) appears. If the battery annunciator is on, and the display dims, you may lose data. If data is lost, the & message is displayed. Once you've removed the batteries, replace them within 2 minutes to avoid losing stored information. (Have the new batteries readily at hand before you open the battery compartment.) Use any brand of fresh I.E.
Testing Calculator Operation Use the following guidelines to determine if the calculator is working properly. Test the calculator after every step to see if its operation has been restored. If your calculator requires service, refer to page A–7. The calculator won't turn on (steps 1–4) or doesn't respond when you press the keys (steps 1–3): 1. Reset the calculator. Hold down the key and press -. It may be necessary to repeat these reset keystrokes several times. 2. Erase memory.
The Self–Test If the display can be turned on, but the calculator does not seem to be operating properly, do the following diagnostic self–test. 1. Hold down the key, then press 0, at the same time. 2. Press any key eight times and watch the various patterns displayed. After you've pressed the key eight times, the calculator displays the copyright message ) 8 and then the message . 3. Starting at the upper left corner ( < ) and moving from left to right, press each key in the top row.
Limited One–Year Warranty What Is Covered The calculator (except for the batteries, or damage caused by the batteries) is warranted by Hewlett–Packard against defects in materials and workmanship for one year from the dale of original purchase. If you sell your unit or give it as a gift, the warranty is automatically transferred to the new owner and remains in effect for the original one–year period.
Products are sold on the basis of specifications applicable at the time of manufacture. Hewlett–Packard shall have no obligation to modify or update products once sold. Consumer Transaction in the United Kingdom This warranty shall not apply to consumer transactions and shall not affect the statutory rights of a consumer. In relation to such transactions, the rights and obligations of Seller and Buyer shall be determined by statute.
All shipping, reimportation arrangements, and customs costs are your responsibility. Service Charge There is a standard repair charge for out–of–warranty service. The Calculator Service Center (listed on the inside of the back cover) can tell you how much this charge is. The full charge is subject to the customer's local sales or value–added tax wherever applicable. Calculator products damaged by accident or misuse are not covered by the fixed service charges.
Service Agreements In the U.S., a support agreement is available for repair and service. Refer to the form that was packaged with the manual. For additional information, contact the Calculator Service Center (see the inside of the back cover). Regulatory Information U.S.A. The HP 32SII generates and uses radio frequency energy and may interfere with radio and television reception.
B User Memory and the Stack This appendix covers The allocation and requirements of user memory, How to reset the calculator without affecting memory, How to clear (purge) all of user memory and reset the system defaults, and Which operations affect stack lift. Managing Calculator Memory The HP 32SII has 384 bytes of user memory available to you for any combination of stored data (variables, equations, or program lines). SOLVE, ∫ FN, and statistical calculations also require user memory.
Memory Requirements Data or Operation Variables Instructions in program lines Numbers in program lines Operations in equations Numbers in equations Statistics data SOLVE calculations ∫ FN (integration) calculations Amount of Memory Used 8 bytes per non–zero value. (No bytes for zero values.) 1.5 bytes. Integers 0 through 254: 1.5 bytes. All other numbers: 9.5 bytes. 1.5 bytes. Integers 0 through 254: 1.5 bytes. All other numbers: 9.5 bytes. 48 bytes maximum (8 bytes for each non–zero summation register).
1. Display the program line containing the equation. 2. Press { to see the checksum and length. For example, / ) . To manually deallocate the memory allocated for a SOLVE or ∫ FN calculation that has been interrupted, press { . This deallocation is done automatically whenever you execute a program or another SOLVE or ∫ FN calculation. Resetting the Calculator If the calculator doesn't respond to keystrokes or if it is otherwise behaving unusually, attempt to reset it.
1. Press and hold down the key. 2. Press and hold down <. 3. Press 6. (You will be pressing three keys simultaneously). When you release all three keys, the display shows & if the operation is successful.
All functions except those in the following two lists will enable stack lift. Disabling Operations The four operations ENTER, Σ+, Σ–, and CLx disable stack lift. A number keyed in after one of these disabling operations writes over the number currently in the X–register. The Y–, Z– and T–registers remain unchanged. In addition, when and @ act like CLx, they also disable stack lift.
The Status of the LAST X Register The following operations save x in the LAST X register: +, –, × , ÷ LN, LOG x̂ , ŷ SINH, COSH, TANH %, %CHG y,xθ,r θ,ry, x Cn,r Pn,r CMPLX +.
C More about Solving This appendix provides information about the SOLVE operation beyond that given in chapter 7. How SOLVE Finds a Root SOLVE is an iterative operation; that is, it repetitively executes the specified equation. The value returned by the equation is a function f(x) of the unknown variable x. (f(x) is mathematical shorthand for a function defined in terms of the unknown variable x.
If f(x) has one or more local minima or minima, each occurs singly between adjacent roots off f(x) (figure d, below). f (x) f (x) x x b a f (x) f (x) x x d c Function Whose Roots Can Be Found In most situations, the calculated root is an accurate estimate of the theoretical, infinitely precise root of the equation. An "ideal" solution is one for which f(x) = 0.
Interpreting Results The SOLVE operation will produce a solution under either of the. following conditions: If it finds an estimate for which f(x) equals zero. (See figure a, below.) If it finds an estimate where f(x) is not equal to zero, but the calculated root is a 12–digit number adjacent to the place where the function's graph crosses the x–axis (see figure b, below).
Keys: {G 2 _ y KX03 4 y K X 0 2 6 y K X 8 { Display: Description: Select Equation mode. Enters the equation. . º%: - %: . Clecksum and length. ) / Cancels Equation mode. Now, salve the equation to find the root: Keys: Display: Description: 0 H X 10 _ {G . º%: - º%: . Selects Equation mode; displays the left end of the Initial guesses for the root. equation. {X # %/ ) 9 ) Solves for X; displays the result.
Keys: Display: Description: Selects Equation mode. {G Enters the equation. KX02 K X 6 %: -%. Checksum and length. { / ) Cancels Equation mode. Now, solve the equation to find its positive and negative roots: Keys: 0 H X 10 Display: Description: Your initial guesses for the _ positive root. {G Selects Equation mode; %: -%. displays the equation. {X %/ ) 9 Calculates the positive root # ) using guesses 0 an 10. Final two estimates are they same.
between two neighboring values of x, it returns the possible root. However, the value for f(x) will be relatively large. If the pole occurs at a value of x that is exactly represented with 12 digits, then that value would cause the calculation to halt with an error message. f (x) f (x) x x a b Special Case: A Discontinuity and a Pole Example: Discontinuous Function. Find the root of the equation: IP(x) = 1.5 Enter the equation: Keys: zG z [PARTS] { } KX{]{ 1.
Cancels Equation mode. Now, solve to find the root: Keys: 0HX5 Display: Description: Your initial guesses for the _ root. {G 1%2/ ) Selects Equation mode; displays the equation. {X Finds a root with guesses 0 # %/ ) and 5. { ) Shows root, to 11 decimal places. 9{ ) The previous estimate is slightly bigger. 9 . ) f(x) is relatively large. Note the difference between the last two estimates, as well as the relatively large value for f(x).
K X p {\KX 026 {]1 { Enters the equation. %ª1%: . 22. / Checksum and length. ) Cancels Equation mode. Now, solve to find the root. Keys: Display: 2.3 H X 2.7 ) _ {G Description: Your initial guesses for the root. %ª1%: . 22. Selects Equation mode; displays the equation. {X # %/ ) 99 8 8 8 Calculates the root using guesses that bracket 6. f(x) is relatively large. ) There is a pole between the final estimates.
The search halts because SOLVE is working on a horizontal asymptote—an area where f(x) is essentially constant for a wide range of x (see figure b, below). The ending value of f(x) is the value of the potential asymptote. The search is concentrated in a local "flat" region of the function (see figure c, below). The ending value of f(x) is the value of the function in this region.
Example: A Relative Minimum. Calculate the root of this parabolic equation: x2 – 6x + 13 = 0. It has a minimum at x = 3. Enter the equation as an expression: Keys: Display: Description: Selects Equation mode. {G Enters the equation. KX02 6 y K X 13 %: . º%- Checksum and length. { Cancels Equation mode. / ) Now, solve to find the root: Keys: Display: Description: 0 H X 10 _ {G %: . º%- Selects Equation mode; displays the equation.
10 − 1 =0 X Enter the equation as an expression. Keys: {G 10 3 K X {] { .005 H X 5 {G Display: Description: Selects Equation mode. Enters the equation. . #1%2 Checksum and length. ) / Cancels Equation mode. _ . #1%2 Your positive guesses for the root. {X %/ ) Selects Equation mode; displays the equation. 9 ) Solves for x using guesses 0.005 and 5. 9{ Previous estimate is the same.
It's apparent from inspecting the equation that if x is a negative number, the smallest that f(x) can be is 10. f(x) approaches 10 as x becomes a negative number of large magnitude. Example: A Math Error. Find the root of the equation: [x ÷ (x + 0.3)] − 0.5 = 0 Enter the equation as an expression: Keys: Display: Description: {G
Keys: Display: Description: 0 H X 10 _ . _ {G Selects Equation mode; displays !1%ª1%- ) the left end of the equation. {X !1 2 Math error. Clears error message; cancels Equation mode. {X %/. ) Displays the final estimate of x. Example : A Local "Flat" Region. Find the root of the function f(x) = x + 2 if x< –1, f(x) = 1 for –1 ≤ x ≤ 1 (a local flat region), f(x) = –x + 2 if x >1. Enter the function as the program: .
Solve for X using initial guesses of 10–8 and –10–8. Keys: Display: Description: Enters guesses. ` 8 _ H X . . _ 1_`8_ {VJ . ) . Selects program "J" as the function. {X ! No root found using very small guesses near zero (thereby restricting the search to the flat region of the function). @ 9 9 ) ) ) . The last two estimates are far apart, and the final value of f(x) is large.
function never changes sign SOLVE returns the message ! . However, the final estimate of x (press @ to see it) is the best possible 12–digit approximation of the root when the routine quits. Underflow Underflow occurs when the magnitude of a number is smaller than the calculator can represent, so it substitutes zero. This can affect SOLVE results. For example, consider the equation 1 x2 whose root is infinite in value. Because of underflow, SOLVE returns a very large value as a root.
D More about Integration This appendix provides information about integration beyond that given in chapter 8. How the Integral Is Evaluated The algorithm used by the integration operation, ∫ Gº, calculates the integral of a function f(x) by computing a weighted average of the function's values at many values of x (known as sample points) within the interval of integration.
As explained in chapter 8, the uncertainty of the final approximation is a number derived from the display format, which specifies the uncertainty for the function. At the end of each iteration, the algorithm compares the approximation calculated during that iteration with the approximations calculated during two previous iterations.
showing (over a portion of the interval of integration) three functions whose graphs include the many sample points in common. f (x) x With this number of sample pints, the algorithm will calculate the same approximation for the integral of any of the functions shown. The actual integrals of the functions shown with solid blue and black lines are about the same, so the approximation will be fairly accurate if f(x) is one of these functions.
∞ ∫0 xe −x dx Since you're evaluating this integral numerically, you might think that you should represent the upper limit of integration as 10499, which is virtually the largest cumber you ears key into the calculator. Try it and what happens. Enter the function f(x) = xe–x. Keys: {G KXy* KX{] { Display: Description: Select equation mode. %º % 1¾ Enter the equation. %º % 1.%2 End of the equation. / Checksum and length. ) Cancels Equation mode.
f (x) x The graph is a spike very close to the origin. Because no sample point happened to discover the spike, the algorithm assumed that f(x) was identically equal to zero throughout the interval of integration. Even if you increased the number of sample points by calculating the integral in SCI 11 or ALL format, none of the additional sample points would discover the spike when this particular function is integrated over this particular interval.
fluctuations can be better characterized by its samples when these variations are spread out over most of the interval of integration than if they are confined to only a small fraction of the interval. (These two situations are shown in the following two illustrations.
f (x) Calculated integral of this function will be accurate. x a b f (x) Calculated integral of this function may be accurate. x a b In many cases you will be familiar enough with the function you want to integrate that you will know whether the function has any quick wiggles relative to the interval of integration. If you're not familiar with the function, More about Integration File name 32sii-Manual-E-0424 Printed Date : 2003/4/24 Size : 17.7 x 25.
and you suspect that it may cause problems, you can quickly plot a few points by evaluating the function using the equation or program you wrote for that purpose. If, for any reason, after obtaining an approximation to an integral, you suspect its validity, there's a simple procedure to verify it: subdivide the interval of integration into two or more adjacent subintervals, integrate the function over each subinterval, then add the resulting approximations.
Z ) . Uncertainty of approximation. This is the correct answer, but it took a very long time. To understand why, compare the graph of the function between x = 0 and x = 103, which looks about the same as that shown in the previous example, with the graph of the function between x = 0 and x = 10: f (x) x 0 10 You can see that this function is "interesting" only at small values of x.
calculation of the integral of any function will be prolonged if the interval of integration includes mostly regions where the function is not interesting. Fortunately, if you must calculate such an integral, you can modify the problem so that the calculation time is considerably reduced. Two such techniques are subdividing the interval of integration and transformation of variables.
E Messages The calculator responds to certain conditions or keystrokes by displaying a message. The £ symbol comes on to call your attention to the message. For significant conditions, the message remains until you clear it. Pressing or @ clears the message; pressing am other key clears the message and executes that key's function. ∫ ! # A running program attempted t select a program label ( /label) while an integration calculation was running.
The calculator is calculating the integral of an ! ! equation or program. This might take a while. A running SOLVE or ∫ FN operation was interrupted ! " ! by pressing or f. Data error: # ! Attempted to calculate combinations or permutations with r >n, with non–integer r or n, or with n ≥1012. Attempted to use a trigonometric or hyperbolic function with an illegal argument: T with x an odd multiple of 90°. O or L with x< –1 or x > 1. 7 R with x≤ –1; or x ≥ 1. 7 O with x < 1.
Attempted to refer to a nonexistent program label (or % ! ! line number) with U,U , W, or { }. Note that the error % ! ! can mean you explicitly (from the keyboard) called a program label that does not exist; or the program that you called referred to another label, which does not exist. The catalog of programs ( z X { } ) indicates no program labels stored. ! SOLVE cannot find the root of the equation using the current initial guesses (see page C–8).
while a SOLVE operation was running. The calculator is solving an equation or program for # its root. This might take a while. ! 1 2 Attempted to calculate the square root of a negative number. ! ! Statistics error: Attempted to do a statistics calculation with n = 0. Attempted to calculate sx sy, with n = 1. x̂ , ŷ , m, r, or b Attempted to calculate r, x̂ or xw with x–data only (all y–values equal to zero). Attempted to calculate x–values equal.
F Operation Index This section is a quick reference for all functions and operations and their formulas, where appropriate. The listing is in alphabetical order by the function's name. This name is the one used in program lines. For example, the function named FIX n is executed as z { %} n. Nonprogrammable functions have their names in key boxes. For example, a.
Name 1/x 10x % %CHG π Σ+ Σ– Σx Σx2 Σxy Σy Σy2 σx Keys and Description Page to next equation in equation list; moves program pointer to next line (during program entry); executes the current program line (not during program entry). 3 Reciprocal. z ( Common exponential. Returns 10 raised to the × power. { P Percent. Returns (y × x) ÷ 100. { S Percent change. Returns (x – y)(100 ÷ y). { M Returns the approximation 3.14159265359 (12 digits). 6 Accumulates (y, x) into statistics registers.
Name σy Keys and Description { 2 {σ¸} Page 11–7 1 Returns population standard deviation of y–values: ∑ (yi − y )2 ÷ n θ, ry,x ∫ FN d variable ( ) A through Z ABS ACOS ACOSH ALOG ALL ASIN { r 4–7 Polar to rectangular coordinates. Converts (r, θ) to (x, y). { ) { ∫ G _} variable Integrates the displayed equation or the program selected by FN=, using lower limit of the variable of integration in the Y–register and upper limit of the variable if integration in the X–register.
Name Keys and Description Page Returns sin –1 x. ASINH Hyperbolic arc sine. Returns sinh –1 x. z R Arc tangent. Returns tan –1 x. ATAN ATANH b zw BIN z7zR Hyperbolic arc tangent. Returns tanh –1 x. { , {E} Returns the y–intercept of the regression line: y – m x . Displays the base–conversion menu. z w { } Selects Binary (base 2) mode.
Name z b { } CLΣ CLVARS CLx CM zF CMPLX +/– CMPLX + CMPLX – CMPLX × CMPLX ÷ CMPLX1/x CMPLXCOS CMPLXex Keys and Description Clears the displayed equation (calculator in Program mode). z b { ´} Clears statistics registers. z b {# } Clears all variables to zero. z b {º } Clears x (the X-register) to zero. z Converts inches to centimeters. Displays the CMPLX_ prefix for complex functions. z F _ Complex change sign. Returns –(zx + i zy). z F Complex addition.
Name CMPLXSIN CMPLXTAN CMPLXyx Keys and Description z F N Complex sine. Returns sin (zy + i zy). z F T Complex tangent. Returns tan (zx + i zy). z F 0 Complex power. Returns COS COSH DEC DEG DEG z DSE variable ` ENG n Combinations of n items taken r at a time. Returns n! ÷ (r! (n – r)!). Q Cosine. Returns cos x. z 7 Q Hyperbolic cosine. Returns cosh x. z w { } Selects Decimal mode. z { } Selects Degrees angular mode. z u Radians to degrees. Returns (360/2π) x.
Name ENTER {G ex EXP °F z FIX n {x FN = label FP FS? n GAL Keys and Description Page digits following the first digit (n = 0 through 11). Separates two numbers keyed in sequentially; completes equation entry; evaluates the displayed equation (and stores result if appropriate). 1–11 6–4 6–12 2–5 Copies x into the Y–register, lifts y into the Z–register, lifts z into the T–register, and loses t. Activates or cancels (toggles) Equation–entry mode. * Natural exponential.
Name Keys and Description z { } GRAD GTO label zU label nn zU HEX z7 HMS Sets Grads angular mode. z U label Sets the program pointer to the beginning of program label in program memory. Sets program pointer to line nn of program label. Sets program pointer to PRGM TOP. z w { %} Selects Hexadecimal (base :16) mode. Displays the HYP_ prefix for hyperbolic functions. z t Page 4–3 13–5 13–16 12–20 12–20 10–1 4–5 4–9 1 4–9 1 6–5 2 6–5 13–21 2 4–11 1 Hours to hours, minutes, seconds.
Name Keys and Description L input in the variable. (Used only in programs.) 3 Reciprocal of argument. { [PARTS] { } Integer part of x. z k variable Increment, Skip if Greater. For control number ccccccc.fffii stored in variable, adds ii (increment value) to ccccccc (counter value) and, if the result > fff (final value), skips the next program line. z } Converts pounds to kilograms. z Converts gallons to liters.
Name z n OCT or z { { [PARTS] Pn,r zd { [PROB] PSE r Keys and Description Page Displays menu to set Angular modes and the radix (• or , ). z 5 {Q} Returns the number of sets of data points. z w { } Selects Octal (base 8) mode. Turns the calculator off. 1–14 4–3 11–11 Displays the menu for selecting parts of numbers. { [PROB] { Q8T} Permutations of n items taken r at a time. Returns n!÷(n – r)!. Activates or cancels (toggles) Program–entry mode. Displays the menu for probability functions.
Name RANDOM RCL variable RCL+ variable RCL– variable RCLx variable RCL÷ variable RND RTN R¶ Rµ {2 Keys and Description Selects the period as the radix mark (decimal point). { [PROB] { } Executes the RANDOM function. Returns a random number in the range 0 through 1. K variable Recall. Copies variable into the X–register. K variable Returns x + variable. K variable. Returns x – variable. K y variable. Returns x × variable. K p Round. Returns x ÷ variable. z I Round.
Name z { } n SCI n { [SCRL] SEED SF n { SIN SINH SOLVE variable o SQ SQRT STO variable STO + variable STO – variable STO × variable STO ÷ variable F–12 Keys and Description Selects Scientific display with n decimal places. (n = 0 through 11.) Scroll. Enables and disables scrolling of equations in Equation and Program modes. { [PROB] { } Restarts the random–number sequence with the seed x . z x { } n Sets flag n (n – 0 through 11).
Name STOP {5 sx Keys and Description Stores variable ÷ x into variable. f Run/stop. Begins program execution at the current program line; stops a running program and displays the X–register. Displays the summation menu. { 2 {Uº} Returns sample standard deviation of x–values: Page 12–18 11–4 11–6 1 11–6 1 4–4 4–5 1 1 ∑ (xi − x )2 ÷ (n − 1) { 2 {U¸} sy Returns sample standard deviation of y–values: ∑ (yi − y )2 ÷ (n − 1) TAN TANH VIEW variable W XEQ label x2 X y x x̂ T Tangent.
Name x! X ROOT xw {/ x<> variable x<>y zl x≠y x≤y? xy? x≥y? x=y? {n F–14 Keys and Description returns the x–estimate based on the regression line: x̂ = (y – b) ÷ m. z 1 Factorial (or gamma). Returns (x)(x – 1) ... (2)(1), or Γ (x + 1). z . The argument1 root of argument2. Returns weighted mean of x values: (Σyixi) ÷ Σyi. Displays the mean (arithmetic average) menu. { Y x exchange. Exchanges x with a variable. Z x exchange y. Moves x to the Y–register and y to the X–register.
Name Keys and Description Page menu. x≠0? x≤0? x<0? x>0? x≥0? x=0? y ŷ y,xθ,r yx z n {≠} If x≠0, executes next program line; if x=0, skips the next program line. z n {≤} If x≤0, executes next program line; if x>0, skips next program line. z n {<} If x<0, executes next program line; if x≥0, skips the next program line. z n {>} If x>0, executes next program line; if x≤0, skips the next program line. z n {≥} If x≥0, executes next program line; if x<0, skips the next program line.
Index £, 1-21 @. See backspace key ALL format. See display format in equations, 6-6 in programs, 12-6 Setting, 1-17 ¤ annunciator, 1-1, A-2 alpha characters, 1-2 annunciators angles between vectors, 15-1 converting format, 4-11 converting units, 4-11 implied units, 4-3, A-2 Special characters binary numbers, 10-7 equations, 6-8, 12-7, 12-16 _. See equation-entry cursor ¾.
converting to, 10-1 range of, 10-6 scrolling, 10-7 typing, 10-1 viewing all digits, 3-4, 10-7 A..
polynomial roots, 15-22 viewing, 9-2 cash flows, 17-1 catalogs leaving, 1-3 program, 1-21, 12-22 using, 1-21 variable, 1-21, 3-4 conditional tests, 13-6, 13-7, 13-8, 13-11, 13-16, 14-6 constant (filling stack), 2-7 Continuous Memory, 1-1 chain calculations, 2-13 change-percentage function, 4-6 changing sign of numbers, 1-11, 1-14, 9-3 checksums equations, 6-21, 12-7, 12-24 programs, 12-22, 12-23 %CHG arguments, 4-7 clearing equations, 6-10 general information, 1-3 memory, 1-22, A-1 messages, 1-21 numbers
denominators controlling, 5-6, 13-9, 13-13 range of, 1-19, 5-1, 5-3 setting maxim urn, 5-5 digit-entry cursor backspacing, 1-3, 6-9, 12-7 in equations, 6-6 in programs, 12-7 meaning, 1-12 discontinuities of functions, C-6 duplicating numbers, 2-6 ending equations, 6-5, 6-9, 6-10, 12-6 evaluating equations, 6-12, 6-13 separating numbers, 1-13, 1-15, 2-6 stack operation, 2-6 EQN annunciator in equation list, 6-5, 6-8 in Program mode, 12-6 display adjusting contrast, 1-1 annunciators, 1-8 function names in,
deleting in programs, 12-7, 12-20 displaying, 6-8 displaying in programs, 12-15, 12-18, 13-10 editing, 1-3, 6-9, 6-10 editing the programs, 12-7, 12-20 entering, 6-5, 6-9 entering in programs, 12-6 evaluating, 6-12, 6-13, 6-14, 7-6, 12-4, 13-10 functions, 6-6, 6-17, F-1 in programs, 12-4, 12-6, 12-7, 12-24, 13-10 integrating, 8-2 lengths, 6-21, 12-7, H-2 list of.
equation prompting, 13-10 fraction display, 5-6, 13-9 meanings, 13-8 operations, 13-11 overflow, 13-9 setting, 13-11 testing, 13-8, 13-11 unassigned, 13-9 FLAGS menu, 13-11 flow diagrams, 13-2 ∫ FN.
limits of, 8-2, 14-7, D-7 memory usage, 8-2, 12-22, B-2, B-3 purpose, 8-1 restrictions, 14-10 results on stack, 8-2, 8-7 resuming, 14-7 stopping, 8-2, 14-7 subintervals, D-7, D-9 time required, 8-6, D-7 transforming variables, D-9 uncertainty of result, 8-2, 8-6, 8-7, D-2 using, 8-2 variable of, 8-2 numbers HEX annunciator, 10-1 hex numbers.
variable catalog, 1-21, 3-4 lender (finance), 17-1 length conversions, 4-12 letter keys, 1-2 limits of integration, 8-2, 14-7 linear regression (estimation), 11-8, 16-1 linear-regression menu, 11-8 logarithmic curve fitting, 16-1 logarithmic functions, 4-2, 9-3 loop counter, 13-16, 13-17, 13-21 looping, 13-15, 13-16 Łukasiewicz, 2-1 M mantissa, 1-12, 1-18 mass conversions, 4-12 math complex-number, 9-1, 9-4 general procedure, 1-14 intermediate results, 2-13 long calculations, 2-13 order of calculation, 2-
negative, 1-11, 9-3, 10-5 order in calculations, 1-15 periods and commas in, 1-16, A-1 precision, 1-16, C-16 prime, 17-7 range of, 1-13, 10-6 real, 4-1, 8-1 recalling, 3-2 reusing, 2-6, 2-11 rounding, 4-15 showing all digits, 1-18, 10-8 storing, 3-2 truncating, 10-5 typing, 1-11, 1-12, 10-1 minimum of function, C-9 modes. See angular mode, base mode, Equation mode, Fraction-display mode, Program-entry mode MODES menu angular mode, 4-4 setting radix, 1-1.
in equations, 6-6, 6-7, 6-16 memory usage, 12-22 PARTS menu, 4-15 pause.
entering, 12-5 equation evaluation, 13-10 equation prompting, 13-10 equations in, 12-4, 12-6 errors in, 12-19 executing, 12-10 flags, 13-8, 13-11 for integration, 14-7 for SOLVE, 14-1, C-1 fractions with, 5-10, 12-15, 13-9 functions not allowed, 12-24 indirect addressing, 13-19, 13-20, 13-21 inserting lines, 12-6, 12-20 interrupting, 12-19 lengths, 12-22, 12-23, B-3 line numbers, 12-3, 12-20, 12-21 loop counter, 13-16, 13-17 looping, 13-15, 13-16 memory usage, 12-22, B-2 messages in, 12-15, 1.
12-4 in programs, 12-4 origins, 2-1 real part (complex numbers), 9-1, 9-2 recall arithmetic, 3-6, B-8 rectangular-to-polar coordinate conversion, 4-8, 9-6, 15-1 f ending prompts, 6-13, 6-15, 7-2, 12-14 interrupting programs, 12-19 resuming programs, 12-15, 12-16, 12-19 running programs, 12-22 stopping integration, 8-2, 14-7 stopping SOLVE, 7-7, 14-1 regression (linear), 11-8, 16-1 repair service, A-7 resetting the calculator, A-4, B-3 return (program). See programs Reverse Polish Notation.
variable digits, 3-3, 3-4, 10-8, 12-15 sign conventions (finance), 17-1 sign (of numbers), 1-11, 1-14, 9-3, 10-5 simultaneous equations, 15-13 sine (trig), 4-4, 9-3, A-2 single-step execution, 12-10 slope (curve-fit), 11-8, 16-1 SOLVE asymptotes, C-9 base mode, 12-25, 14-10 checking results, 7-6, C-3 discontinuity, C-6 evaluating equations, 7-1, 7-6 evaluating programs, 14-1 flat regions, C-9 how it works, 7-6, C-1 initial guesses, 7-2, 7-6, 7-7, 7-10, 14-5 in programs, 14-5 interrupting, 8-3 memory usage,
entering, 11-1 initializing, 11-2 memory usage, 12-22, B-2 one-variable, 11-2 precision, 11-11 sums of variables, 11-12 two-variable, 11-2 statistics calculating, 11-4 curve fitting, 11-8, 16-1 distributions, 16-12 grouped data, 16-19 one-variable data, 11-2 operations, 11-1 two-variable data, 11-2 T tangent (trig), 4-4, 9-3, A-2 temperatures converting units, 4-12 limits for calculator, A-2 testing the calculator, .
clearing while viewing, 12-15 default, B-5 exchanging with X, 3-8 indirect addressing, 13-19, 13-20 in equations, 6-5, 7-1 in programs, 12-12, 14-1, 14-7 memory usage:, 12-22, B-2 names, 3-1 number storage, 3-1 of integration, 8-2, 14-7 polynomials, 12-26 program input, 12-13 program output, 12-14, 12-18 recalling, 3-2, 3-4 separate from stack, 3-2 showing all digits, 3-3, 3-4, 10-8, 12-15 solving for, 7-2, 14-1, 14-5, C-1 storing, 3-2 storing from equation, 6-13 typing name, 1-2 viewing, 3-3, 12-14, 12-18
Batteries are delivered with this product, when empty do not throw them away but correct as small chemical waste. Bij dit produkt zijn batterijen. Wanneer deze leeg zijn, moet u ze niet weggooien maar inleveren aIs KCA. File name 32sii-Manual-E-0424Page: 16/376 Printed Date : 2003/4/24 Size : 17.7 x 25.
