hp 33s scientific calculator user's guide H Edition 3 HP part number F2216-90001
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Contents Part 1. Basic Operation 1. Getting Started Important Preliminaries.......................................................1–1 Turning the Calculator On and Off.................................1–1 Adjusting Display Contrast ............................................1–1 Highlights of the Keyboard and Display ...............................1–2 Shifted Keys................................................................1–2 Alpha Keys.................................................................
Periods and Commas in Numbers................................ 1–18 Number of Decimal Places ......................................... 1–19 SHOWing Full 12–Digit Precision................................ 1–20 Fractions........................................................................ 1–21 Entering Fractions...................................................... 1–21 Displaying Fractions .................................................. 1–23 Messages .....................................................
3. Storing Data into Variables Storing and Recalling Numbers ...........................................3–2 Viewing a Variable without Recalling It.................................3–3 Reviewing Variables in the VAR Catalog ...............................3–3 Clearing Variables ............................................................3–4 Arithmetic with Stored Variables ..........................................3–4 Storage Arithmetic .......................................................
Factorial .................................................................. 4–14 Gamma................................................................... 4–14 Probability ............................................................... 4–14 Parts of Numbers ............................................................ 4–16 Names of Functions......................................................... 4–17 5. Fractions Entering Fractions .............................................................
Editing and Clearing Equations ...........................................6–7 Types of Equations.............................................................6–9 Evaluating Equations..........................................................6–9 Using ENTER for Evaluation ........................................6–11 Using XEQ for Evaluation ...........................................6–12 Responding to Equation Prompts ..................................6–12 The Syntax of Equations ..............................
Using Complex Numbers in Polar Notation........................... 9–5 10. Base Conversions and Arithmetic Arithmetic in Bases 2, 8, and 16....................................... 10–2 The Representation of Numbers......................................... 10–4 Negative Numbers.................................................... 10–4 Range of Numbers .................................................... 10–5 Windows for Long Binary Numbers ............................. 10–6 11.
Selecting a Mode......................................................12–3 Program Boundaries (LBL and RTN) ..............................12–3 Using RPN, ALG and Equations in Programs..................12–4 Data Input and Output ...............................................12–4 Entering a Program..........................................................12–5 Keys That Clear.........................................................12–6 Function Names in Programs.......................................
Selecting a Base Mode in a Program ......................... 12–22 Numbers Entered in Program Lines ............................ 12–23 Polynomial Expressions and Horner's Method ................... 12–23 13. Programming Techniques Routines in Programs ....................................................... 13–1 Calling Subroutines (XEQ, RTN) .................................. 13–2 Nested Subroutines ................................................... 13–3 Branching (GTO) ...................................
15. Mathematics Programs Vector Operations ...........................................................15–1 Solutions of Simultaneous Equations ................................. 15–12 Polynomial Root Finder ................................................... 15–20 Coordinate Transformations ............................................ 15–32 16. Statistics Programs Curve Fitting...................................................................16–1 Normal and Inverse–Normal Distributions ....................
Resetting the Calculator ..................................................... B–2 Clearing Memory ............................................................. B–3 The Status of Stack Lift ....................................................... B–4 Disabling Operations .................................................. B–4 Neutral Operations ..................................................... B–4 The Status of the LAST X Register ......................................... B–6 C. ALG: Summary About ALG ..
Underflow ......................................................................D–14 E. More about Integration How the Integral Is Evaluated.............................................. E–1 Conditions That Could Cause Incorrect Results ....................... E–2 Conditions That Prolong Calculation Time ............................. E–7 F. Messages G.
Part 1 Basic Operation
1 Getting Started v Watch for this symbol in the margin. It identifies examples or keystrokes that are shown in RPN mode and must be performed differently in ALG mode. Appendix C explains how to use your calculator in ALG mode. Important Preliminaries Turning the Calculator On and Off To turn the calculator on, press . ON is printed below the key. To turn the calculator off, press | . That is, press and release the | shift key, then press (which has OFF printed in purple above it).
Highlights of the Keyboard and Display Shifted Keys Each key has three functions: one printed on its face, a left–shifted function (Green), and a right–shifted function (Purple). The shifted function names are printed in green and purple above each key. Press the appropriate shift key ({ 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 { 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. Alpha Keys Right-shifted function Left-shifted function G Letter for alphabetic key Most keys have a letter written next to them, as shown above. Whenever you need to type a letter (for example, a variable or a program label), the A..
Silver Paint Keys Those eight silver paint keys have their specific pressure points marked in blue position in the illustration below. To use those keys, make sure to press down the corresponding position for the desired function. Backspacing and Clearing One of the first things you need to know is how to clear: how to correct numbers, clear the display, or start over.
Keys for Clearing Key b 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 1–7.) If the number is completed (no cursor), b 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, b erases the entire number.
Keys for Clearing (continued) Key {c Description The CLEAR menu ({º} {# } { } {´}) Contains options for clearing x (the number in the X–register), 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 { }.
Using Menus There is a lot more power to the HP 33s than what you see on the keyboard. This is because 14 of the keys are menu keys. There are 14 menus in all, which provide many more functions, or more options for more functions. HP 33s Menus Menu Name Menu Description Chapter Numeric Functions L.R. ˆ TPE º̂ ¸ Linear regression: curve fitting and linear estimation. 11 x, y º ¸ º· 11 Arithmetic mean of statistical x– and y–values; weighted mean of statistical x–values.
HP 33s Menus (continued) Menu Name Menu Description Chapter Other functio ns MEM # Memory status (bytes of memory available); catalog of variables; catalog of programs (program labels). 1, 3, 12 MODES * 8 Angular modes and ")" or "8" radix (decimal point) convention. 4, 1 DISPLAY % Fix, scientific, engineering, and ALL display formats.
Example: 6 ÷ 7 = 0.8571428571… Keys: 6 Display: % 7 q ({ }) ) ) . ( or Menus help you execute dozens of functions by guiding you to them with menu choices. You don't have to remember the names of 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.
RPN and ALG Keys The calculator can be set to perform arithmetic operations in either RPN (Reverse Polish Notation) or ALG (Algebraic) mode. In Reverse Polish Notation (RPN) mode, the intermediate results of calculations are stored automatically; hence, you do not have to use parentheses. In algebraic (ALG) mode, you perform addition, subtraction, multiplication, and division in the traditional way. To select RPN mode: Press { ¦ to set the calculator to RPN mode.
The Display and Annunciators First Line Second Line Annunciators The display comprises two lines and annunciators. The first line can display up to 255 characters. Entries with more than 14 characters will scroll to the left. However, if entries are more than 255 characters, the characters from the 256th onward are replaced with an ellipsis ()))). During inputting, the second line displays an entry; after calculating, it displays the result of a calculation.
HP 33s Annunciators Annunciator Meaning Chapter £ The "£ (Busy)" annunciator blinks while an operation, equation, or program is executing. c d When in Fraction–display mode (press { ), only one of the "c" or "d" halves of the "cd"' 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 "cd"' is on, the exact value of the fraction is being displayed. 5 ¡ ¢ Left shift is active.
HP 33s Annunciators (continued) Annunciator §,¨ Meaning Chapter The or keys are active to scroll the display, i.e. there are more digits to the left and right. (Equation–entry and Program–entry mode aren’t included) 1, 6 Use | to see the rest of a decimal number; use the left and right–cursor keys ( , ) to see the rest of an equation or binary number. Both these annunciators may appear simultaneously in the display, indicating that there are more characters to the left and to the right.
Keying in Numbers You can key in a number that has up to 12 digits plus a 3–digit exponent up to ±499. If you try to key in a number larger than this, digit entry halts and the ¤ annunciator briefly appears. If you make a mistake while keying in a number, press b to backspace and delete the last digit, or press to clear the whole number. Making Numbers Negative The ^ key changes the sign of a number. To key in a negative number, type the number, then press ^.
Keying in Exponents of Ten Use a (exponent) to key in numbers multiplied by powers of ten. For example, take Planck's constant, 6.6261 × 10–34: Key in the mantissa (the non–exponent part) of the number. If the mantissa is negative, press ^ after keying in its digits. 1. Keys: 6.6261 2. Press a Display: ) _ a. Notice that the cursor moves behind the : ) _ 3. Key in the exponent. (The largest possible exponent is ±499.
Keys: 123 Display: Description: Digit entry not terminated: the number is not complete. _ If you execute a function to calculate a result, the cursor disappears because the number is complete — digit entry has been terminated. # ) 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.
One–Number Functions To use a one–number function (such as , #, !, { @, { K, { , Q or ^) Key in the number. ( You don't need to press 1. $, | .) 2. Press the function key. (For a shifted function, press the appropriate | shift key first.) For example, calculate 1/32 and change its sign. Keys: 32 Description: Operand. Reciprocal of 32. ) # ! ^ 148.84 . Then square the last result and Display: _ 148.84 ) ) { or Square root of 148.84. Square of 12.2. .
For example, To calculate: Press: 3 3 12 3 z 12 3 85|T Display: 12 + 3 12 ) 12 – 3 12 ) 12 × 3 123 Percent change from 8 to 5 ) 8 ) . ) , The order of entry is important only for non–commutative functions such as , , , , , , , , q {F |D { \ { _ Q | T. If you type numbers in the wrong order, you can still get the correct answer (without re–typing them) by pressing [ 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 (the display menu). During some complicated internal calculations, the calculator uses 15–digit precision for intermediate results. The displayed number is rounded according to 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 103 (such as 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.
For example, in the number 14.8745632019, you see only "14.8746" when the display mode is set to FIX 4, but the last six digits ("632019") are present internally in the calculator. To temporarily display a number in full precision, press | . This shows you the mantissa (but no exponent) of the number for as long as you hold down . Keys: { %} 4 45 1.3 z Display: Description: Displays four decimal places. ) Four decimal places displayed.
2. Key in the fraction numerator and press separates the numerator from the denominator. again. The second 3. Key in the denominator, then press or a function key to terminate digit entry. The number or result is formatted according to the current display format. The a b/c symbol under the twice for fraction entry.
Displaying Fractions Press { to switch between Fraction–display mode and the current decimal display mode. Keys: Display: Description: 38 + _ Displays characters as you key them in. ) Terminates digit entry; displays the number in the current display format. { + Displays the number as a fraction.
Calculator Memory The HP 33s has 31KB of memory in which you can store any combination of data (variables, equations, or program lines). Checking Available Memory Pressing { Y displays the following menu: # 8 Where 8 is the number of bytes of memory available. Pressing the {# } menu key displays the catalog of variables (see "Reviewing Variables in the VAR Catalog" in chapter 3). Pressing the { } menu key displays the catalog of programs. 1.
2 RPN: The Automatic Memory Stack This chapter explains how calculations take place in the automatic memory stack in RPN mode. 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 Displayed X 0.0000 Displayed "Oldest" number The most "recent" number is in the X–register: this is the number you see in the second line of the display. In programming, the stack 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.
Reviewing the Stack R¶ (Roll Down) (roll down) key lets you review the entire contents of the stack by The "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.
Exchanging the X– and Y–Registers in the Stack Another key that manipulates the stack contents is [ (x exchange y). This key swaps the contents of the X– and Y–registers without affecting the rest of the stack. Pressing [ twice restores the original order of the X– and Y–register contents. The [ function is used primarily to swap the order of numbers in a calculation. For example, one way to calculate 9 ÷ (13 × 8): Press 13 8 z 9 [ q.
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. Because of the automatic movements of the stack, you do not need to clear the X–register before doing a new calculation. Most functions prepare the stack to lift its contents when the next number enters the X–register.
Using a Number Twice in a Row You can use the replicating feature of number to itself, press . to other advantages. To add a Filling the stack with a constant The replicating effect of together with the replicating effect of stack drop (from T into Z) allows you to fill the stack with a numeric constant for calculations. Example: Given bacterial culture with a constant growth rate of 50% per day, how large would a population of 100 be at the end of 3 days? Replicates T 1.5 T 1.5 1.5 1.5 1.
During program entry, b deletes the currently–displayed program line and cancels program entry. During digit entry, b backspaces over the displayed number. If the display shows a labeled number (such as / ) or b cancels that display and shows the X–register. When viewing an equation, to allow for editing. During equation entry, function at a time.
2. Reusing a number in a calculation. 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 { to retrieve the number so you can execute the correct function. (Press first if you want to clear the incorrect result from the stack.
Example: Suppose you made a mistake while calculating 16 × 19 = 304 There are three kinds of mistakes you could have made: Wrong Calculation: 16 19 19 z 16 18 z 15 Mistake: Correction: { {z Wrong first number 16 { z Wrong second number { q 19 z Wrong function Reusing Numbers with LAST X You can use { to reuse a number (such as a constant) in a calculation.
T t t t Z z z t 96.704 Y 96.7040 96.7040 z X 96.7040 52.3 947 149.0987 52.3947 52.3947 LAST X l l T t t Z z t Y 149.0987 z X 52.3947 2.8457 LAST X 52.3947 52.3947 Keys: { 96.704 52.3947 Display: ) Enters first number. ) Description: ) Intermediate result. Brings back display from before . q ) Final result. Example: Two close stellar neighbors of Earth are Rigel Centaurus (4.3 light–years away) and Sirius (8.7 light–years away).
9.5 a 15 z 8.7 ) { z Speed of light, c. ) _ Meters to R. Centaurus. ) Retrieves c. Meters to Sirius. ) Chain Calculations in RPN mode In RPN mode, the automatic lifting and dropping of the stack's contents let you retain intermediate results without storing or reentering them, and without using parentheses. Work from the Parentheses Out For example, solve (12 + 3) × 7.
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.) separate subsequent numbers and save intermediate results. The last result saved is the first one retrieved as needed to carry out the calculation. Calculate 2 ÷ (3 + 10): Keys: 10 2[q 3 Display: ) Description: Calculates (3 + 10) first. Puts 2 before 13 so the division is correct: 2 ÷ 13.
Exercises Calculate: (16.3805x 5) = 181.0000 0.05 Solution: 16.3805 5 z # .05 q Calculate: [(2 + 3) × (4 + 5)] + [(6 + 7) × (8 + 9)] = 21.5743 Solution: 2345z#6789z # Calculate: (10 – 5) ÷ [(17 – 12) × 4] = 0.2500 Solution: 17 or 10 12 5 4 17 z 10 5 12 4 [q zq 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.
This method takes one additional keystroke. Notice that the first intermediate result is still the innermost parentheses (7 × 3). The advantage to working a problem left–to–right is that you don't have to use [ to reposition operands for nomcommutaiive functions ( and q ). However, the first method (starting with the innermost parentheses) is often preferred because: It takes fewer keystrokes. It requires fewer registers in the stack.
A Solution: 14 12 18 12 z97 q Calculate: 232 – (13 × 9) + 1/7 = 412.1429 A Solution: 23 ! 13 9 z 7 Calculate: (5.4 × 0.8) ÷ (12.5 − 0.73 ) = 0.5961 Solution: 5.4 or 5.4 .8 z .7 3 12.5 [ .8 z 12.5 .7 3 q # q# Calculate: 8.33 × (4 − 5.2) ÷ [(8.33 − 7.46) × 0.32] = 4.5728 4.3 × (3.15 − 2.75) − (1.71× 2.01) A Solution: 4 5.2 8.33 z { 7.46 0.32 2.75 4.3 z 1.71 2.01 z q # z q 3.
3 Storing Data into Variables The HP 33s has 31KB 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.) 1. Cursor prompts for variable. 2. Indicates letter keys are active. 3. Letter keys.
Each black letter is associated with a key and a unique variable. The letter keys are automatically active when needed. (The A..Z annunciator in the display confirms this.) Note that the variables, X, Y, Z and T are different storage locations from the X–register, Y–register, Z–register, and T–register in the stack. Storing and Recalling Numbers Numbers are stored into and recalled from lettered variables with the I (store) and L (recall) functions.
Viewing a Variable without Recalling It The | function shows you the contents of a variable without putting that number in the X–register. The display is labeled for the variable, such as: / ) In Fraction–display mode ({ ), part of the integer may be dropped. This will be indicated by "…" at the left end of the integer. To see the full mantissa, press left of the radix ( ) or 8 ). | .
Clearing Variables Variables' values are retained by Continuous Memory until you replace them or clear them. Clearing a variable stores a zero there; a value of zero takes no memory. To clear a single variable: Store zero in it: Press 0 I variable. To clear selected variables: { Y {# } and use or to display the variable. { c. 3. Press to cancel the catalog. 1. Press 2. Press To clear all variables at once: Press { c {# }.
A 15 A 12 Result: 15 that is,A T t T t Z z Z z Y y Y y X 3 X 3 3 x Recall Arithmetic Recall arithmetic uses L , L , L z, or L q 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 L q A. Now x = 0.25, while 12 is still in A.
Keys: ID IE IF 1ID IEI F |D 1 2 3 |E |F b Display: ) ) ) ) Description: Stores the assumed values into the variable. Adds1 to D, E, and F. Displays the current value of D. / ) / ) / ) ) Clears the VIEW display; displays X-register again. Suppose the variables D, E, and F contain the values 2, 3, and 4 from the last example. Divide 3 by D, multiply it by E, and add F to the result.
|ZA ) |ZA ) Exchanges contents of the X–register and variable A. Exchanges 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 The Variable "i" There is a 27th variable 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. Quotient and Remainder of Divisions. Power functions. ( and ) Trigonometric functions. Hyperbolic functions. Percentage functions. Physics constants Conversion functions for coordinates, angles, and units.
To Calculate: Press: Natural logarithm (base e) Common logarithm (base 10) { Natural exponential Common exponential (antilogarithm) { Quotient and Remainder of Division You can use { F and | D to produce either the quotient or remainder of division operations involving two integers. 1. Key in the first integer. to separate the first number from the second. 3. Key in the second number. (Do not press .) 2. Press 4. Press the function key.
In RPN mode, to calculate a number y raised to a power x, key in y x, . (For y > 0, x can be any number; for y < 0, x must be an odd then press integer; for y = 0, x must be positive.) To Calculate: Press: Result: 152 15 10 6 6 { 54 5 4 ) 2 –1.4 2 1.4 ^ ) (–1.4) 3 1.4 196 196 # ) − 125 125 ^{@ . ) 3 ! ) 8 ^{$ 8 ) . ) In RPN mode, to calculate a root x of a number y (the xth root of y), key in y . For y < 0, x must be an integer.
Setting the Angular Mode The angular mode specifies which unit of measure to assume for angles used in trigonometric functions. The mode does not convert numbers already present (see "Conversion Functions" later in this chapter). 360 degrees = 2π radians = 400 grads To set an angular mode, press . A menu will be displayed from which you can select an option. Option Description Annunciator { } Sets Degrees mode (DEG). Uses decimal degrees, not degrees, minutes, and seconds.
Example: Show that cosine (5/7)π radians and cosine 128.57° are equal (to four significant digits). Keys: { } 57 |NzR { } 128.57 R Display: Description: Sets Radians mode; RAD annunciator on. ) 5/7 in decimal format. . ) Cos (5/7)π. . ) Switches to Degrees mode (no annunciator). . ) Calculates cos 128.57°, which is the same as cos (5/7)π.
Hyperbolic Functions With x in the display: To Calculate: Press: Hyperbolic sine of x (SINH). { O Hyperbolic cosine of x (COSH). { R Hyperbolic tangent of x (TANH). { U Hyperbolic arc sine of x (ASINH). { {M Hyperbolic arc cosine of x (ACOSH). { {P Hyperbolic arc tangent of x (ATANH).
) Total cost (base price + 6% tax). Suppose that the $15.76 item cost $16.12 last year. What is the percentage change from last year's price to this year's? Keys: 16.12 15.76 |T { % } 4 Note Display: Description: ) . ) This year's price dropped about 2.2% from last year's price. . ) Restores FIX 4 format. The order of the two numbers is important for the %CHG function. The order affects whether the percentage change is considered positive or negative.
Physics Constants There are 40 physics constants in the CONST menu. You can press to view the following items. | CONST Menu Items Description {F } Speed of light in vacuum {J } Standard acceleration of gravity { } Newtonian constant of gravitation Value 299792458 m s–1 9.80665 m s–2 6.673×10 –11 m3 kg– 1s–2 0.022413996 m3 mol–1 {#P } Molar volume of ideal gas { } { ∞ } Avogadro constant {H } Elementary charge 1.602176462×10–19 C {PH } Electron mass 9.
Items Description Value 2.817940285×10–15 m {TH } Classical electron radius {'µ } Characteristic impendence of vacuum {λ F } Compton wavelength 2.426310215×10–12 m {λ FQ } Neutron Compton wavelength 1.319590898×10–15 m {λ FR } Proton Compton wavelength 1.
Coordinate Conversions The function names for these conversions are y,xÆθ,r and θ,rÆy,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. A calculated result for θ will be between –180° and 180°, between –π and π radians, or between –200 and 200 grads. To convert between rectangular and polar coordinates: 1. Enter the coordinates (in rectangular or polar form) that you want to convert.
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 3 Keys: { } 10 | s [ 43{r [ 30 4 Display: Description: Sets Degrees mode. Calculates x. ) ) Displays y. ) Calculates hypotenuse (r). ) Displays θ. Example: Conversion with Vectors. Engineer P.C.
R θ _ 36.5 o R Xc 77.8 ohms C Keys: { } 36.5 ^ Display: Description: Sets Degrees mode. . ) 77.8 ) _ |s [ Enters r, ohms of total impedance. ) . ) Enters θ, degrees of voltage lag. Calculates x, ohms resistance, R. Displays y, ohms reactance, XC. For more sophisticated operations with vectors (addition, subtraction, cross product, and dot product), refer to the "Vector Operations" program in chapter 15, "Mathematics Programs".
|u { % } 4 ) Equals 8 minutes and 34.29 seconds. ) Restores FIX 4 display format. Angle Conversions When converting to radians, the number in the x–register is assumed to be degrees; when converting to degrees, the number in the x–register is assumed to be radians. To convert an angle between degrees and radians: 1. Key in the angle (in decimal degrees or radians) that you want to convert. 2. Press | w or { v. The result is displayed.
Probability Functions Factorial To calculate the factorial of a displayed non-negative integer x (0 ≤ x ≤ 253), press { (the left–shifted key). Gamma To calculate the gamma function of a noninteger x, Γ(x), key in (x – 1) and press { . The x! function calculates Γ(x + 1). The value for x cannot be a negative integer. Probability Combinations To calculate the number of possible sets of n items taken r at a time, enter n first, { \, then r (nonnegative integers only).
The RANDOM function uses a seed to generate a random number. Each random number generated becomes the seed for the next random number. Therefore, a sequence of random numbers can be repeated by starting with the same seed. You can store a new seed with the SEED function. If memory is cleared, the seed is reset to zero. A seed of zero will result in the calculator generating its own seed. Example: Combinations of People. A company employing 14 women and 10 men is forming a six–person safety committee.
Parts of Numbers These functions are primarily used in programming. Integer part To remove the fractional part of x and replace it with zeros, press example, the integer part of 14.2300 is 14.0000.) | ". (For Fractional part To remove the integer part of x and replace it with zeros, press example, the fractional part of 14.2300 is 0.2300) | ?. (For Absolute value To replace x with its absolute value, press { B. Sign value To indicate the sign of x, press | E. If the x value is negative, –1.
Names of Functions You might have noticed that the name of a function appears in the display when you press and hold the key to execute it. (The name remains displayed for as long as you hold the key down.) For instance, while pressing O, the display shows . "SIN" is the name of the function as it will appear in program lines (and usually in equations also).
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/ , press 5 8 or 5 8. 8 To turn Fraction–display mode on and off, press { . 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.
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. You can type fractions only if the number base is 10 — the normal number base. See chapter 10 for information about changing the number base.
Entered Value Internal Value Displayed Fraction 2 3/8 2.37500000000 + 14 15/32 14.4687500000 + 54/ 4.50000000000 + 6 18/5 9.60000000000 + 34/ 12 2.83333333333 + 15/ 8192 0.00183105469 12 T S + 12345678 12345/3 (Illegal entry) ¤ 16 3/16384 (Illegal entry) ¤ Accuracy Indicators The accuracy of a displayed fraction is indicated by the c and d annunciators at the right of the display.
This is especially important if you change the rules about how fractions are displayed. (See "Changing the Fraction Display" later.) For example, if you force all fractions to have 5 as the denominator, then 2/3 is displayed as + c 3.3333 because the exact fraction is approximately /5, "a little above" 3/5. 2 Similarly, – /3 is displayed as . + c because the true numerator is "a little above" 3. Sometimes an annunciator is lit when you wouldn't expect it to be.
You can select one of three fraction formats. The next few topics show how to change the fraction display. Setting the Maximum Denominator For any fraction, the denominator is selected based on a value stored in the calculator. If you think of fractions as a b/c, then /c corresponds to the value that controls the denominator.
To select a fraction format, you must change the states of two flags. Each flag can be "set" or "clear," and in one case the state of flag 9 doesn't matter. To Get This Fraction Format: Change These Flags: 8 9 Clear — Factors of denominator Set Clear Fixed denominator Set Set Most precise You can change flags 8 and 9 to set the fraction format using the steps listed here. (Because flags are especially useful in programs, their use is covered in detail in chapter 13.) 1.
Fraction Format ¼ Number Entered and Fraction Displayed 2 2 2/3 2.5 2.9999 216/25 Most precise 2 2 1/2 2 2/3S 3T 2 9/14T Factors of denominator 2 2 1/2 2 11/16T 3T 2 5/8S Fixed denominator 2 0/16 2 8/16 2 11/16T 3 0/16T 2 10/16S ¼ For a /c value of 16. Example: Suppose a stock has a current value of 48 1/4.
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. How wide is each section, assuming you can conveniently measure 1/ –inch increments? What's the cumulative roundoff error? 16 Keys: 16 | 34ID 6q 56 {J 6z LD | y { } 8 { Display: Description: Sets up fraction format for 1/ –inch increments.
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. When you're running a program, displayed values are shown using Fraction–display mode if it's active. If you're prompted for values by INPUT instructions, you may enter fractions, regardless of the display mode.
6 Entering and Evaluating Equations How You Can Use Equations You can use equations on the HP 33s in several ways: 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 = .
L V |d ¾ Begins a new equation, turning on the "¾ " equation–entry cursor. L turns on the A..Z annunciator so you can enter a variable name. #/¾ L V types # and moves the cursor to the right. .25 #/ ) _ Digit entry uses the "_" digit–entry cursor. z|Nz #/ ) ºπº¾ z ends the number and restores the "¾ " cursor. 2 LD zLL #/ ) ºπº : _ #/ ) ºπº : º Terminates and displays the equation.
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. They're described in more detail later. Key Operation |H 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.
Entering Equations into the Equation List The equation list is a collection of equations you enter. The list is saved in the calculator's memory. Each equation you enter is automatically saved in the equation list. 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 | H.
Numbers in Equations You can enter any valid number in an equation except fractions and numbers that aren't base 10 numbers. Numbers are always shown using ALL display format, which displays up to 12 characters. To enter a number in an equation, you can use the standard number–entry keys, including , ^, and a. 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.
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)+25 Keys: Display: Description: |H #/ ) ºπº : º Shows the last equation used in the equation list. LR|d /¾ Starts a new equation with variable R.
! ! 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 or 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. Display the equation in the equation list, as described above. If it's more than 14 characters long, only 14 characters are shown.
To edit an equation you're typing: 1. Press b repeatedly until you delete the unwanted number or function. If you're typing a decimal number and the "_" digit–entry cursor is on, b deletes only the rightmost character. If you delete all characters in the number, the calculator switches back to the "¾ " equation–entry cursor. If the "¾ " equation–entry cursor is on, pressing b deletes the entire rightmost number or function. 2. Retype the rest of the equation. 3.
Keys: Display: Description: |H / º º 1!. 2 Shows the current equation in the equation list. b º 1!. 2- ¾ Turns on Equation–entry mode and shows the "¾ " cursor at the end of the equation. bb / º º 1!. 2¾ Deletes the number 25. / º º 1!. 2 Shows the end of edited equation in the equation list. Leaves Equation mode. Types of Equations The HP 33s works with three types of equations: Equalities.
Because many equations have two sides separated by "=", the basic value of an equation is the difference between the values of the two sides. For this calculation, "=" in an equation essentially treated as "ಥ". The value is a measure of how well the equation balances. The HP 33s has two keys for evaluating equations: and actions differ only in how they evaluate assignment equations: X. Their X returns the value of the equation, regardless of the type of equation.
The evaluation of an equation takes no values from the stack — it uses only numbers in the equation and variable values. The value of the equation is returned to the X–register. The LAST X register isn't affected. Using ENTER for Evaluation If an equation is displayed in the equation list, you can press to evaluate the equation. (If you're in the process of typing the equation, pressing only ends the equation — it doesn't evaluate it.
a6q Changes cubic millimeters to liters (but doesn't change V). ) Using XEQ for Evaluation If an equation is displayed in the equation list, you can press X 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 changed to 35.5 millimeters.
To change the number, type the new number and press g. 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 g. For example, you can press 2 5 g. To calculate with the displayed number, press typing another number. before To cancel the prompt, press . The current value for the variable remains in the X–register.
Order Operation Example 1 Functions and Parentheses 2 Power ( 3 Unary Minus (^) . 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. Examples: 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!- ( .
Equation Functions The following table lists the functions that are valid in equations. Appendix G, "Operation Index" also gives this information.
0 1.%(. 2 0 1%(1.&22 Eleven of the equation functions have names that differ from their equivalent operations: Operation Equation function x2 SQ x SQRT ex EXP 10 x ALOG 1/x INV y XROOT yx ^ INT÷ IDIV Rmdr RMDR x3 CB X 3 x CBRT Example: Perimeter of a Trapezoid. The following equation calculates the perimeter of a trapezoid.
Parentheses used to group items P=A+B+Hx(1ΊSIN(T)+1ΊSIN(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 .) / - - º1 #1 1!22- #1 1 222 Example: Area of a Polygon.
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. You have to edit the equation to correct the error. (See "Editing and Clearing Equations" earlier in this chapter.) By not checking equation syntax until evaluation, the HP 33s lets you create "equations" that might actually be messages.
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.
If the displayed value is the one you want, press g. If you want a different value, type or calculate the value and press (For details, see "Responding to Equation Prompts" in chapter 6.) You can halt a running calculation by pressing g. or g. When the root is found, it's stored in the unknown variable, and the variable value is VIEWed in the display.
/#º!- ) º º!: Terminates the equation and displays the left end. | / / Checksum and length. g (acceleration due to gravity) is included as a variable so you can change it for different units (9.8 m/s2 or 32.2 ft/s2 ). Calculate how many meters an object falls in 5 seconds, starting from rest. Since Equation mode is turned on and the desired equation is already in the display, you can start solving for D: Keys: Display: Description: # _ D Prompts for unknown variable.
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).
g Stores 297.1 in T; solves for P in atmospheres. #O / ) 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: |H N .05 5 g g g 18 273.1 g 28 z LVq Display: Description: º#/ º º! Displays the equation. @ ) Solves for N; prompts for P. #@ ) Stores .05 in P; prompts for V. @ ) Stores 5 in V; prompts for R.
When SOLVE evaluates an equation, it does it the same way X 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.
Interrupting a SOLVE Calculation To halt a calculation, press or g. 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. The number in the X–register (the display). These sources are used for guesses whether you enter guesses or not.
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 (message ! ). In the following example, the equation has more than one root, but guesses help find the desired root. Example: Using Guesses to Find a Root. Using a rectangular piece of sheet metal 40 cm by 80 cm, form an open–top box having a volume of 7500 cm3.
Type in the equation: Keys: Display: | H LV|d #/¾ | ] 40 LH|` z | ] 20 |` z4zLH #/1 . 2¾ Description: Selects Equation mode and starts the equation. LH 1 . 2º1 . 2¾ 2º1 . 2º º ¾ | #/1 . 2º1 . Terminates and displays the equation. / / Checksum and length. It seems reasonable that either a tall, narrow box or a short, flat box could be formed having the desired volume. Because the taller box is preferred, larger initial estimates of the height are reasonable.
Keys: Display: Description: This value from the Y–register is the estimate made just prior to the final result. Since it is the same as the solution, the solution is an exact root. ) ) This value from the Z–register shows the equation equals zero at the root. The dimensions of the desired box are 50 × 10 × 15 cm. If you ignored the upper limit on the height (20 cm) and used initial estimates of 30 and 40 cm, you would obtain a height of 42.0256 cm — a root that is physically meaningless.
For More Information This chapter gives you instructions for solving for unknowns or roots over a wide range of applications. Appendix D 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.
8 Integrating Equations Many problems in mathematics, science, and engineering require calculating the definite integral of a function.
Integrating Equations ( ³ FN) 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 key in the upper limit. , then 3.
Find the Bessel function for x–values of 2 and 3. Enter the expression that defines the integrand's function: cos (x sin t ) Keys: { c { } Display: Description: Clears memory. Current equation or Selects Equation mode. {& } |H ! ! RL zO LT |`|` 1%¾ 1%º 1!22 Terminates the expression and displays its left end. | / / Checksum and length. Leaves Equation mode. X Types the equation.
Now calculate J0(3) with the same limits of integration. You must respecify the limits of integration (0, π) since they were pushed off the stack by the subsequent division by π. Keys: 0 |N Display: Description: Enters the limits of integration (lower limit first). ) |H | 1%º 1!22 Displays the current equation. ³ G_ Prompts for the variable of integration. T %@ ) 3 g Prompts for value of X. ! ! ³ / . ) |Nq . ) x = 3.
Keys: |H Display: The current equation or ! ! Description: Selects Equation mode. OLX |` 1%¾ Starts the equation. 1%2¾ The closing right parenthesis is required in this case. qLX | 1%2ª%¾ 1%2ª% Terminates the equation. / / Checksum and length. Leaves Equation mode. Now integrate this function with respect to x (that is, X) from zero to 2 (t = 2). Keys: { } 02 |H | X Display: Description: Selects Radians mode.
Specifying Accuracy The display format's setting (FIX, SCI, ENG, or ALL) determines the precision of the integration calculation: the greater the number of digits displayed, the greater the precision of the calculated integral (and the greater the time required to calculate it). The fewer the number of digits displayed, the faster the calculation, but the calculator will presume that the function is accurate to the only number of digits specified in the display format.
| X ! ! ³ / ) The integral approximated to two decimal places. [ ) . The uncertainty of the approximation of the integral. The integral is 1.61±0.0161. Since the uncertainty would not affect the approximation until its third decimal place, you can consider all the displayed digits in this approximation to be accurate.
{ } ) Restores Degrees mode. This uncertainty indicates that the result might be correct to only three decimal places. In reality, this result is accurate to seven decimal places when compared with the actual value of this integral. Since the uncertainty of a result is calculated conservatively, the calculator's approximation in most cases is more accurate than its uncertainty indicates.
9 Operations with Complex Numbers The HP 33s 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, z1z 2 , 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 33s are handled by entering each part (imaginary and real) of a complex number as a separate entry.
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. y1 Z1 x1 Z2 Complex function y2 (displayed) y imaginary part x2 (displayed) x real part Complex input z or z 1and z 2 Complex result, z Always enter the imaginary part (the y–part) of a number first. The real portion of the result (zx) is displayed on the second line; the imaginary portion (zy) is displayed on the first line.
Functions for One Complex Number, z To Calculate: Press: Change sign, –z {G^ Inverse, 1/z {G Natural log, ln z {G Natural antilog, ez {G Sin z {GO Cos z {GR Tan z {GU 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 z1z 2 , key in the exponent, z2, second.) 3.
Examples: Here are some examples of trigonometry and arithmetic with complex numbers: Evaluate sin (2 + i 3) Keys: 2 {GO 3 Display: . ) ) Description: Result is 9.1545 – i 4.1689. Evaluate the expression z 1 ÷ (z2 + z3), where z1 = 23 + i 13, z2 = –2 + i z3 = 4 – i 3 Since the stack can retain only two complex numbers at a time, perform the calculation as z1 × [1 ÷ (z2 + z3)] Keys: 2 ^ ^ 4 { G 1 3 Display: . ) ) {G 23 {Gz 13 ) ) Add z2 + z3; displays real part.
23^ 3 {Gz Enters imaginary part of second complex number as a fraction. . ) ) Completes entry of second number and then multiplies the two complex numbers. Result is 11.7333 – i 3.8667. . ) . ) Evaluate e z −2 , where z = (1 + i ). Use enter –2 as –2 + i 0. Keys: Display: 1 2 ^ { G . ) ) {G . ) ) 1 0 to evaluate z–2; {G Description: Intermediate result of (1 + i )–2 Final result is 0.8776 – i 0.4794.
imaginar y (a, b) r θ real Example: Vector Addition. Add the following three loads. You will first need to convert the polar coordinates to rectangular coordinates. y L2 170 lb 185 lb 143 o 62 o L1 x L3 100 lb 261 o Keys: { } 185 | s 62 Display: Description: Sets Degrees mode. ) Enters L1 and converts it to rectangular form. ) 143 170 | s {G 261 9–6 100 | s ) . ) Enters and converts L2. ) . ) Adds vectors. . ) .
{G ) . ) Adds L1 + L2 + L3.
10 Base Conversions and Arithmetic The BASE menu ( { x ) 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.
{ x { } { x { } 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: { x { % } Use the _ 24FF { x { } Description: ! key to type "F". The entire binary number does not fit. The § annunciator indicates that the number continues to the left. Displays the rest of the number.
If the result of an operation cannot be represented in 36 bits, the display shows # $ and then shows the largest positive or negative number possible. Example: Here are some examples of arithmetic in Hexadecimal, Octal, and Binary modes: 12F16 + E9A16 = ? Keys: Display: { x { % } 12F Description: Sets base 16; HEX annunciator on. E9A Result. 77608 – 43268 =? { x { ! } 7760 Sets base 8; OCT annunciator on. Converts displayed number to octal. 4326 Result.
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. When a number appears in hexadecimal, octal, or binary base, it is shown as a right–justified integer with up to 36 bits (12 octal digits or 9 hexadecimal digits). Leading zeros are not displayed, but they are important because they indicate a positive number.
Range of Numbers The 36-bit word size determines the range of numbers that can be represented in hexadecimal (9 digits), octal (12 digits), and binary bases (36 digits), and the range of decimal numbers (11 digits) that can be converted to these other bases.
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. 36 - bit number Highest window Lowest window (displayed) When a binary number is larger than the 12 digits, the § or ¨ annunciator (or both) appears, indicating in which direction the additional digits lie. Press the indicated key ( or ) to view the obscured window.
11 Statistical Operations The statistics menus in the HP 33s 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). Summation statistics: n, Σx, Σy, Σx2, Σy2, and Σxy. Entering Statistical Data One– and two–variable statistical data are entered (or deleted) in similar fashion using the (or { ) key.
Entering One–Variable Data { c {Σ} to clear existing statistical data. 2. Key in each x–value and press . 1. Press 3. The display shows n, the number of statistical data values now accumulated. Pressing actually enters two variables into the statistics registers because the value already in the Y–register is accumulated as the y–value.
1. Reenter the incorrect data, but instead of pressing deletes the value(s) and decrements n. 2. Enter the correct value(s) using , press { . This . If the incorrect values were the ones just entered, press { to retrieve them, then press { to delete them. (The incorrect y–value was still in the Y–register, and its x–value was saved in the LAST X register.
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 estimation { º̂ } { ¸ ˆ } and curve–fitting {T } {P } {E }. See ''Linear Regression'' later in this chapter. x ,y | The mean menu: { º } { ¸ } { º · }. See "Mean" below. s,σ | The standard–deviation menu: {Uº } {U¸ } {σº } {σ¸ }.
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: { c {´} Display: Clears the statistics registers. ) 9.25 10 12.5 12 8.5 ) 15.5 | {º} Description: Enters the first time. Enters the remaining data; six data points accumulated. º ¸ º· ) Calculates the mean time to complete the process. Example: Weighted Mean (Two Variables). A manufacturing company purchases a certain part four times a year.
Sample Standard Deviation Sample standard deviation is a measure of how dispersed the data values are about the mean sample standard deviation assumes the data is a sampling of a larger, complete set of data, and is calculated using n – 1 as a divisor. | {Uº } for the standard deviation of x–values. Press | {U¸ } for the standard deviation of y–values. Press The {σº } and {σ¸ } keys in this menu are described in the next section, "Population Standard Deviation.
Example: Population Standard Deviation. Grandma Hinkle has four grown sons with heights of 170, 173, 174, and 180 cm. Find the population standard deviation of their heights. Keys: Display: { c {´} 173 180 | {σº } 170 174 Description: Clears the statistics registers. Enters data. Four data points accumulated. ) σ σ Uº U¸ º ¸ Calculates the population standard deviation. ) Linear Regression Linear regression, L.R.
To find an estimated value for x (or y), key in a given hypothetical value for y (or x), then press | { º̂ } (or | {¸ ˆ }). To find the values that define the line that best fits your data, press | followed by {T }, {P }, or {E }. Example: Curve Fitting. The yield of a new variety of rice depends on its rate of fertilization with nitrogen. For the following data, determine the linear relationship: the correlation coefficient, the slope, and the y–intercept. X, Nitrogen Applied (kg per hectare) 0.
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 Display: ) Description: Enters hypothetical x–value. _ | {¸ ˆ} º̂ ¸ˆ T P E ) The predicted yield in tons per hectare.
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 must also be adjusted.
If you've entered statistical data, you can see the contents of the statistics registers. Press { Y {# }, then use and to view the statistics registers. Example: Viewing the Statistics Registers. Use to store data pairs (1,2) and (3,4) in the statistics registers. Then view the stored statistical values. Keys: { c {´} 1 2 Display: Description: Clears the statistics registers. ) ) Stores the first data pair (1,2). 3 ) ) Stores the second data pair (3,4).
Statistics Registers Register Number Description n 28 Number of accumulated data pairs. Σx 29 Sum of accumulated x–values. Σy 30 Sum of accumulated y–values. Σx2 31 Sum of squares of accumulated x–values. Σy2 32 Sum of squares of accumulated y–values. Σxy 33 Sum of products of accumulated x– and y–values. You can load a statistics register with a summation by storing the number (28 through 33) of the register you want in i (number I ) and then storing the summation (value I ).
Part 2 Programming
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.
RPN mode ALG mode º º π º º π ! 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. In RPN mode, to enter this program into program memory, do the following: Keys: (In RPN mode) Display: Description: { c { } {& } {e Clears memory. Activates Program–entry mode (PRGM annunciator on).
Designing a Program The following topics show what instructions you can put in a program. What you put in a program affects how it appears when you view it and how it works when you run it. Selecting a Mode Programs created and saved in RPN mode can only be edited and executed in RPN mode, and programs or steps created and saved in ALG mode can only be edited and executed in ALG mode. You can ensure that your program executes in the correct mode by making RPN or ALG the first instruction in the program.
When a program finishes running, the last RTN instruction returns the program pointer to ! , the top of program memory. Using RPN, ALG 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 ALG operations (as explained in appendix C). Using equations (as explained in chapter 6).
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 under "Entering and Displaying Data." Entering a Program Pressing { e 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 { e ) 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 | turns on. H to activate Equation–entry mode. The EQN annunciator 2.
Function Names in Programs The name of a 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.
Example: Entering a Program with an Equation. The following program calculates the area of a circle using an equation, rather than using RPN operations like the previous program. Keys: (In RPN mode) Display: Description: {e{ V ! Activates Program–entry mode; sets pointer to top of memory. {E Labels this program routine E (for "equation"). IR ! Stores radius in variable R.
Running a Program To run or execute a program, program entry cannot be active (no program–line numbers displayed; PRGM off). Pressing will cancel Program–entry mode. Executing a Program (XEQ) Press X label to execute the program labeled with that letter. If there is only one program in memory, you can also execute it by pressing { V g (run/stop). If necessary, enter the data before executing the program.
2. Press { V label to set the program pointer to the start of the program (that is, at its LBL instruction). The ! instruction moves the program pointer without starting execution. (If the program is the first or only program, you can press { V to move to its beginning.) 3. Press and hold . 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 .
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.
Press g (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. The area–of–a–circle program with an INPUT instruction looks like this: RPN mode "! º π º ! ALG mode "! º º π ! ! To use the INPUT function in a program: 1.
For example, see the "Coordinate Transformations" program in chapter 15. Routine D collects all the necessary input for the variables M, N, and T (lines D0002 through D0004) that define the x and y coordinates and angle θ of a new system. To respond to a prompt: When you run the program, it will stop at each INPUT and prompt you for that variable, such as @ ) . The value displayed (and the contents of the X–register) will be the current contents of R. To leave the number unchanged, just press g.
Pressing Press { c clears the contents of the displayed variable. g to continue the program, If you don't want the program to stop, see "Displaying Information without Stopping" below. For example, see the program for "Normal and Inverse–Normal Distributions" in chapter 16. Lines T0015 and T0016 at the end of the T routine display the result for X. Note also that this VIEW instruction in this program is preceded by a RCL instruction.
V = πR2H S = 2π R2 + 2π RH = 2π R ( R + H ) Keys: (In RPN mode) Display: Description: {e{ V {C {R {H ! Program, entry; sets pointer to top of memory. Labels program. "! "! |H| NzLR 2zLH | / / Checksum and length of equation. IV |H2 z | N z L R z |]LR LH| ` | Store the volume in V. / / Checksum and length of equation.
Keys: (In RPN mode) Display: Description: |V |S | { Y { } # $ # Displays volume. # $ Displays surface area. ! Ends program. / Displays label C and the length of the program in bytes. | / / Checksum and length of program. Cancels program entry. 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: (In RPN mode) XC Display: Description: Starts executing C; prompts for R.
The display is cleared by other display operations, and by the RND operation if flag 7 is set (rounding to a fraction). Press | f to enter PSE in a program. The VIEW and PSE lines — or the equation and PSE lines — are treated as one operation when you execute a program one line at a time. Stopping or Interrupting a Program Programming a Stop or Pause (STOP, PSE) Pressing g (run/stop) during program entry inserts a STOP instruction.
To see the line in the program containing the error–causing instruction, press { e. The program will have stopped at that point. (For instance, it might be a ÷ instruction, which caused an illegal division by zero.) Editing a 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.
2. Press b. This turns on the "¾ " editing cursor, but does not delete anything in the equation. 3. Press b as required to delete the function or number you want to change, then enter the desired corrections. 4. Press to end the equation. Program Memory Viewing Program Memory Pressing { e 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 ! .
Memory Usage 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. See "Clearing One or More Programs" below, or "Managing Calculator Memory" in appendix B. The Catalog of Programs (MEM) The catalog of programs is a list of all program labels with the number of bytes of memory used by each label and the lines associated with it.
To clear all programs from memory: { e to display program lines (PRGM annunciator on). 2. Press { c { } to clear program memory. 1. Press 3. The message @ & prompts you for confirmation. Press {& }. 4. Press { e to cancel program entry. Clearing all of memory ({ c { }) also clears all programs. The Checksum The checksum is a unique hexadecimal value given to each program label and its associated lines (until the next label).
Nonprogrammable Functions The following functions of the HP 33s are not programmable: { c { } { c { } b , , , {e { h, { j {V { V label nnnn {Y | |H { Programming with BASE You can program instructions to change the base mode using { x. These settings work in programs just as they do as functions executed from the keyboard. This allows you to write programs that accept numbers in any of the four bases, do arithmetic in any base, and display results in any base.
Numbers Entered in Program Lines Before starting program entry, set the base mode. The current setting for the base mode determines the base of the numbers that are entered into program lines. The display of these numbers changes when you change the base mode. Program line numbers always appear in base 10. An annunciator tells you which base is the current setting. Compare the program lines below in the left and right columns. All non–decimal numbers are right–justified in the calculator's display.
Keys: (In ALG mode) Display: {e{ V {A { X ! 5 z LX "! % º % ¸º Description: 5 5x. 5x4 4 - 2 z LX º 5x4 + 2x 5x4 + 2x3 5x4 + 5x4 + 2 % ¸º 3 | { Y { } ! ! / Displays label A, which takes 93 bytes. | / / Checksum and length. Cancels program entry. Now evaluate this polynomial for x = 7.
A more general form of this program for any equation Ax4 + Bx3 + Cx2 + Dx + E would be: "! "! "! "! "! "! % % h - h % - h % - h % - ! ! Checksum and length: E41A 54 Simple Programming 12–25
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. Using conditional instructions (comparisons and flags) to determine which instructions or subroutines should be used.
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. XEQ must branch to a label (LBL) for the subroutine. (It cannot branch to a line number.) At the very next RTN encountered, program execution returns to the line after the originating XEQ.
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). The operation of nested subroutines is as shown below: MAIN program (top level) End of program Attempting to execute a subroutine nested more than seven levels deep causes an % # $ error.
In RPN mode, Starts subroutine here. "! Enters A. "! Enters B. "! Enters C. "! Enters D. Recalls the data. º % % % º ! N P R NPR º65¸ º ! M O Q A2. A2 + B2. A2 + B2 + C2 A2 + B2 + C2+ D2 A 2 + B2 + C 2 + D 2 Returns to main routine. MOQ Nested subroutine Adds x2. Returns to subroutine S.
A Programmed GTO Instruction The GTO label instruction (press { V label) transfers the execution of a running program to the program line containing that label, wherever it may be. The program continues running from the new location, and never automatically returns to its point of origination, so GTO is not used for subroutines. For example, consider the "Curve Fitting" program in chapter 16.
{ V . To a line number: { V label nnnn (nnnn < 10000). For example, { V A0005. To a label: { V label —but only if program entry is not active (no program lines displayed; PRGM off). For example, { V A. To ! : 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.
Flag tests. These check the status of flags, which can be either set or clear. Loop counters. These are usually used to loop a specified number of times. Tests of Comparison (x?y, x?0) There are 12 comparisons available for programming. Pressing | o displays a menu for one of the two categories of tests: { n or 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.
Example: The "Normal and Inverse–Normal Distributions" program in chapter 16 uses the x
Flags 0, 1, 2, 3, and 4 have no preassigned meanings. That is, their states will mean whatever you define them to mean in a given program. (See the example below.) Flag 5, when set, will interrupt a program when an overflow occurs within the program, displaying # $ and ¤. An overflow occurs when a result exceeds the largest number that the calculator can handle. The largest possible number is substituted for the overflow result.
Flag 10 controls program execution of equations: When flag 10 is clear (the default state), equations in running programs are evaluated and the result put on the stack. When flag 10 is set, equations in running programs are displayed as messages, causing them to behave like a VIEW statement: 1. Program execution halts. 2. The program pointer moves to the next program line. 3. The equation is displayed without affecting the stack. You can clear the display by pressing b or .
Annunciators for Set Flags Flags 0, 1, 2, 3 and 4 have annunciators in the display that turn on when the corresponding flag is set. The presence or absence of 0 , 1 , 2 , 3 or 4 lets you know at any time whether any of these five flags is set or not. However, there is no such indication for the status of flags 5 through 11. The statuses of these flags can be determined by executing the FS? instruction from the keyboard. (See "Using Flags" below.
Example: Using Flags. The "Curve Fitting" program in chapter 16 uses flags 0 and 1 to determine whether to take the natural logarithm of the X– and Y–inputs: Lines S0003 and S0004 clear both of these flags so that lines W0007 and W0011 (in the input loop routine) do not take the natural logarithms of the X– and Y–inputs for a Straight–line model curve. Line L0003 sets flag 0 so that line W0007 takes the natural log of the X–input for a Logarithmic–model curve.
Program Lines: (In RPN mode) Description: . . . Clears flag 0, the indicator for In X. Clears flag 1, the indicator for In Y. . . . Sets flag 0, the indicator for In X. Clears flag 1, the indicator for In Y. . . . Clears flag 0, the indicator for In X. Sets flag 1, the indicator for In Y. . . . Sets flag 0, the indicator for ln X. Sets flag 1, the indicator for In Y. . . . $ @ If flag 0 is set ... $ ...
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 as MESSAGE and are entered as equations: 1. Set Equation–entry mode by pressing on). 2.
Program Lines: (In ALG mode) Description: Begins the fraction program. Clears three fraction flags. Displays messages. Selects decimal base. "! # Prompts for a number. "! Prompts for denominator (2 – 4095). # Displays message, then shows the decimal number.
Use the above program to see the different forms of fraction display: Keys: (In ALG mode) XF Display: Description: #@ value Executes label F; prompts for a fractional number (V). @ value Stores 2.53 in V; prompts for denominator (D). ) Stores 16 as the /c value. Displays message, then the decimal number. g ! + d Message indicates the fraction format (denominator is no greater than 16), then shows the fraction.
This routine (taken from the "Coordinate Transformations" program on page 15–32 in chapter 15) is an example of an infinite loop. It is used to collect the initial data prior to the coordinate transformation. After entering the three values, it is up to the user to manually interrupt this loop by selecting the transformation to be performed (pressing X N for the old–to–new system or X O for the new–to–old system).
Loops with Counters (DSE, ISG) When you want to execute a loop a specific number of times, use the { l (increment; skip if greater than) or | m (decrement; skip if less than or equal to) conditional function keys. Each time a loop function is executed in a program, it automatically decrements or increments a counter value stored in a variable. It compares the current counter value to a final counter value, then continues or exits the loop depending on the result.
Given the loop–control number ccccccc.fffii, ISG increments ccccccc to ccccccc + ii, compares the new ccccccc with fff, and makes program execution skip the next program line if this ccccccc > fff. M If current value > final value, continue loop. If current value ≤ final value, continue loop. $ . . . $ $ M $ % % M $ . . . $ . . . $ $ $ . . . % % M N ! $ N If current value ≤ final value, exit loop.
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 ). 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 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) ³ 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 ! 1 1 L2 2 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.
& & & ! - L % 1 1 L2 2 If i holds: Then XEQ(i) calls: To: 1 LBL A Compute ŷ for straight–line model. 2 LBL B Compute ŷ for logarithmic model. 3 LBL C Compute ŷ for exponential model. 4 LBL D Compute ŷ for power model. 7 LBL G Compute 8 LBL H Compute 9 LBL I Compute 10 LBL J Compute x̂ x̂ x̂ x̂ for straight–line model. for logarithmic model. for exponential model. for power model. Example: Loop Control With (i).
Program Lines: (In RPN mode) Description: This routine collects all known values in three equations. "!1 1 L2 2 Prompts for and stores a number into the variable addressed by i. L Adds 1 to i and repeats the loop until i reaches 13.012. ! ! When i exceeds the final counter value, execution branches back to A. Label J is a loop that completes the inversion of the 3 × 3 matrix.
Program Lines: (In RPN mode) Description: Begins the program. Sets equations for execution. Disables equation prompting. ) Sets counter for 1 to 26. ! L Stores counter. Initializes sum. Checksum and length: AEC5 42 Starts summation loop. 1 L2 2 : Equation to evaluate the ith square. (Press | H to start the equation.) Ckecksum and length of equation: F09C 5 - Adds ith square to sum. L Tests for end of loop.
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: (In ALG mode) {e{ V Display: ! Description: Sets Program mode. Type in the program: Program Lines: (In ALG mode) Description: Identifies the programmed function. "! Stores P. "! # Stores V.
Keys: (In ALG mode) Display: Description: | W G Selects "G" — the program. SOLVE evaluates to find the value of the unknown variable. P #@ value Selects P; prompts for V. g @ value Stores 2 in V; prompts for N. @ value Stores .005 in N; prompts for R. !@ value Stores .0821 in R; prompts for T. 24 273.1 !@ ) Calculates T. g # / ) 2 .005 g .0821 g Stores 297.1 in T; solves for P. Pressure is 0.0610 atm. Example: Program Using Equation.
| ) ! Ends the program. Cancels Program–entry mode. Checksum and length of program: 36FF 21 Now calculate the change in pressure of the carbon dioxide if its temperature drops by 10 °C from the previous example. Keys: (In RPN mode) IL |WH P Display: Description: ) Stores previous pressure. ) Selects program “H.” #@ ) Selects variable P; prompts for V. g @ ) Retains 2 in V; prompts for N. g @ ) Retains .005 in N; prompts for R.
Using SOLVE in a Program You can use the SOLVE operation as part of a program. If appropriate, include or prompt for initial guesses (into the unknown variable and into the X–register) before executing the SOLVE variable instruction.
Program Lines: (In RPN mode) Description: % % Setup for X. % Index for X. % ! Branches to main routine. Checksum and length: 4800 21 & & Setup for Y. & Index for Y. & ! Branches to main routine. Checksum and length: C5E1 21 Main routine. Stores index in i. / Defines program to solve. Solves for appropriate variable. # $1 1 L2 2 ! L # 1 1 L2 2 Displays solution. Ends program.
2. Select the program that defines the function to integrate: press | W label. (You can skip this step if you're reintegrating the same program.) 3. Enter the limits of integration: key in the lower limit and press key in the upper limit. , then 4. Select the variable of integration and start the calculation: press variable. | Notice that FN= is required if you're integrating a programmed function, but not if you're integrating an equation from the equation list.
Example: Program Using Equation. The sine integral function in the example in chapter 8 is Si(t) = sin x t ³ 0 ( x )dx This function can be evaluated by integrating a program that defines the integrand: Defines the function. The function as an expression. (Checksum and length: 0EE0 8). 1%2ª% ! Ends the subroutine Checksum and length of program: BDE3 17 Enter this program and integrate the sine integral function with respect to x from 0 to 2 (t = 2).
³ G variable The programmed ³ FN instruction does not produce a labeled display ( ³ = value) since this might not be the significant output for your program (that is, you might want to do further calculations with this number before displaying it). If you do want this result displayed, add a PSE ( | f ) or STOP (g) instruction to display the result in the X–register after the ³ FN instruction.
Restrictions on Solving and Integrating The SOLVE variable and ³ FN d variable instructions cannot call a routine that contains another SOLVE or ³ FN instruction. That is, neither of these instructions can be used recursively. For example, attempting to calculate a multiple integral will result in an ³ 1 ³ 2 error. Also, SOLVE and ³ FN cannot call a routine that contains an /label instruction; if attempted, a # ! # or ³ ! # error will be returned.
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 This program uses the following equations.
Vector addition and subtraction: v 1 + v 2 = (X + U)i + (Y + V)j + (Z + W)k v 2 – v 1 = (U – X)i + (V – Y)j + (W – Z)k Cross product: v 1 × v 2 = (YW – ZV )i + (ZU – XW)j + (XV – YU)k Dot Product: D = XU + YV + ZW Angle between vectors (γ): G = arccos D R1 × R2 where v1 = X i + Y j + Z k and v 2=U i + V j + W k The vector displayed by the input routines (LBL P and LBL R) is V1.
Program Listing: Program Lines: (In ALG mode) 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: 8E7D 12 & º65¸ % ¸8º ´θ 8T Defines beginning of rectangular–to–polar conversion process. Calculates ( X2 + Y2 ) and arctan(Y/X).
Program Lines: (In ALG mode) ! ' Description Stores Z = R cos(P). º65¸ θ8T ´¸8º ! Calculates R sin(P) cos(T) and R sin(P) sin(T). Saves X = R sin(P) cos(T). º65¸ ! % ! & ! Saves Y = R sin(P) sin(T). Loops back for another display of polar form. Checksum and length: 5F1D 48 Defines the beginning of the vector–enter routine. % Copies values in X, Y and Z to U, V and W respectively.
Program Lines: (In ALG mode) % - " # ! % 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: 6ED7 33 . 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.
Program Lines: (In ALG mode) ! ! % º # . & º " ! ! ' ! % ! ! & Description Calculates (ZU – WX), which is the Y component. Stores (XV – YU), which is the Z component. Stores X component. Stores Y component. Loops back for polar conversion and display/input.
Program Lines: (In ALG mode) Description $ ¸8º ´ θ8T ! 1 ª Divides the dot product by the magnitude of the X–, Y–, Z–vector. ª Divides previous result by the magnitude. 2 ! # $ Displays angle. ! Loops back for polar display/input. Calculates the magnitude of the U, V, W vector. Calculates angle. Checksum and length: 0548 90 Flags Used: None.
3. Key in R and press g, key in T and press g. Continue at step 5. 4. Key in X and press g. g, then key in P and press g, key in Y and press g, and key in Z and press 5. To key in a second vector, press X E (for enter), then go to step 2. 6. Perform desired vector operation: a. Add vectors by pressing X A; b. Subtract vector one from vector two by pressing X S; c. Compute the cross product by pressing X C; d. Compute the dot product by pressing vectors by pressing g. 7.
N (y) 7.3 Transmitter 15.7 Antenna E (x) W S Keys: (In ALG mode) { } X R 7.3 g 15.7 .76 g ^ g Display: Description: Sets Degrees mode. %@ value Starts rectangular input/display routine. &@ value Sets X equal to 7.3. '@ value Sets Y equal to 15.7. @ ) Sets Z equal to –0.76 and calculates R, the radius. g !@ ) g @ ) Calculates T, the angle in the x/y plane. Calculates P, the angle from the z–axis.
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 X o First, add the force vectors. Keys: (In ALG mode) XP Display: Description: @ value Starts polar input routine. !@ value Sets radius equal to 17. @ value Sets T equal to 215. g @ ) Sets P equal to 17. XE @ ) Enters vector by copying it into v 2. 17 g 215 17 23 g g Sets radius of v 1 equal to 23. !@ . ) 80 g @ ) 74 g @ ) Sets T equal to 80. Sets P equal to 74.
g @ ) Displays P of resultant vector. XE @ ) 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: (In ALG mode) 1.07 125 63 g g g XC Display: Description: Sets R equal to 1.07. !@ ) @ ) Sets T equal to 125. @ ) Sets P equal to 63. @ ) Calculates cross product and displays R of result.
125 63 g g XD @ ) Sets T equal to 125. @ ) Sets P equal to 63. / ) g / ) g @ ) Calculates dot product. Calculates angle between resultant force vector and lever. 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.
Program Listing: Program Lines: (In RPN mode) Description Starting point for input of coefficients. ) Loop–control value: loops from 1 to 12, one at a time. Stores control value in index variable. ! L Checksum and length: 35E7 21 Starts the input loop. "!1 1 L2 2 Prompts for and stores the variable addressed by i. L Adds one to i. ! If i is less than 13, goes back to LBL L and gets the next value.
Program Lines: (In RPN mode) º . º º ! L º º . º º . º º . ! ' Description Calculates H' × determinant = BG – AH. . ! Calculates I' × determinant = AE – BD.
Program Lines: (In RPN mode) º º Description . ! Calculates G' × determinant = DH – EG. ¶ ! Stores D'. L % ! & ! ! ' ! ! L $ Stores I'. Stores E'. Stores F'. Stores H'. Sets index value to point to last element of matrix. Recalls value of determinant.
Program Lines: (In RPN mode) Description row. % Sets index value to point to last element in third row. Checksum and length: DA21 54 This routine calculates product of column vector and row pointed to by index value. Saves index value in i. Recalls J from column vector. Recalls K from column vector. Recalls L from column vector. ! L º1 1 L2 2 Multiplies by last element in row.
Program Lines: (In RPN mode) º º º º - Description Calculates A × E × I. Calculates (A × E × I) + (D × H × C). º º - º º . º º . º º . ( A × E × I) + ( D × H × C ) + ( G × F × B ) – ( G × E × C ) – (A × F × H) – (D × B × I).
Program Instructions: 1. Key in the program routines; press 2. Press when done. X A to input coefficients of matrix and column vector. 3. Key in coefficient or vector value (A through L) at each prompt and press g. X D to compute determinant of 3 × 3 system. X I to compute inverse of 3 × 3 matrix. 6. Optional: press X A and repeatedly press g to review the values of the 4. Optional: press 5. Press inverted matrix. 7.
Keys: (In RPN mode) Display: Description: XA @ value Starts input routine. g @ value Sets first coefficient, A, equal to 23. 23 8 g @ value Sets B equal to 8. 4 g @ value Sets C equal to 4. @ value . . . @ ) Sets D equal to 15. 15 . . . 14 g g Continues entry for E through L. Returns to first coefficient entered. XI 8 XM %/ ) g &/ ) Calculates and displays Y. g '/ . ) Calculates and displays Z.
g g g @ ) @ ) XI ) XA @ ) g . . . Displays next value. @ . ) @ ) . . . Displays next value. Displays next value. Inverts inverse to produce original matrix. 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)x + (K + M) = 0 x2 + (J – L)x + (K – M) = 0 where J = a3/2 K = y0 /2 L= M= J 2 − a2 + y 0 × (the sign of JK – a1/2) K 2 − a0 Roots of the fourth degree polynomial are found by solving these two quadratic polynomials.
Program Listing: Program Lines: (In RPN mode) Description Defines the beginning of the polynomial root finder routine. "! Prompts for and stores the order of the polynomial. Uses order as loop counter. ! L Checksum and length: 5CC4 9 Starts prompting routine. "!1 1 L2 2 Prompts for a coefficient. L Counts down the input loop. ! Repeats until done.
Program Lines: (In RPN mode) Description ! % First initial guess. Second initial guess. -+. / # % ! Specifies routine to solve. Solves for a real root. Gets synthetic division coefficients for next lower order polynomial. Generates DIVIDE BY 0 error if no real root found. ª Checksum and length: 15FE 54 Starts quadratic solution routine. º65¸ Exchanges a0 and a1. ª a1/2. -+. –a1/2.
Program Lines: (In RPN mode) Description ! Checksum and length: B9A7 81 Starts second–order solution routine. Gets L. Gets M. ! ! Calculates and displays two roots. Checksum and length: DE6F 12 Starts third–order solution routine. Indicates cubic polynomial to be solved. % ¶ Discards polynomial function value. % Solves remaining second–order polynomial and stores roots.
Program Lines: (In RPN mode) Description Checksum and length: C7A6 51 Starts fourth–order solution routine. º 4a2. a3. a32 . º . º 4a2 – a32. ao(4a2 – a32). a1. º a12. . b0 =a0(4a0 – a32) – a12. Stores b0. -+. b2= –a2. Stores b2. a3. º a3 a1. º .
Program Lines: (In RPN mode) Description Complex roots? @ ! Calculate four roots of remaining fourth–order polynomial. If not complex roots, determine largest real root (y0) º6¸@ º65¸ º6¸@ º65¸ ! Stores largest real root of cubic. Checksum and length: C8B3 180 ! ª ! ª Starts fourth–order solution routine. J = a3/2. K = y0/2.
Program Lines: (In RPN mode) ! Description Stores 1 or JK – a1/2. J. º J2 . J2 -– a2. - - J. - J + L. K. - K + M. % ! Calculate and display two roots of the fourth–order polynomial. J. . J – L. K. . ! ª Calculates sign of C. J2 -– a2 +y0.
Program Lines: (In RPN mode) ! " Description Displays complex roots if any. Stores second real root. ! % # $ % Displays second real root. ! Returns to calling routine. Checksum and length: 96DA 30 " " Starts routine to display complex roots. " Stores the imaginary part of the first complex root. " # $ L Displays the imaginary part of the first complex root. " # $ % Displays the real part of the second complex root.
Because of round–off error in numerical computations, the program may produce values that are not true roots of the polynomial. The only way to confirm the roots is to evaluate the polynomial manually to see if it is zero at the roots. For a third– or higher–order polynomial, if SOLVE cannot find a real root, the error # & is displayed. You can save time and memory by omitting routines you don't need. If you're not solving fifth–order polynomials, you can omit routine E.
A through E Coefficients of polynomial; scratch. F Order of polynomial; scratch. G Scratch. H Pointer to polynomial coefficients. X The value of a real root, or the real part of complex root i The imaginary part of a complex root; also used as an index variable. Example 1: Find the roots of x5 – x4 – 101x3 +101x2 + 100x – 100 = 0. Keys: (In RPN mode) XP Display: Description: @ value Starts the polynomial root finder; prompts for order. 5 g @ value Stores 5 in F; prompts for E.
Example 2: Find the roots of 4x4 – 8x3 – 13x2 – 10x + 22 = 0. Because the coefficient of the highest–order term must be 1, divide that coefficient into each of the other coefficients. Keys: (In RPN mode) XP Display: Description: @ value Starts the polynomial root finder; prompts for order. @ value Stores 4 in F; prompts for D. 8 ^4 qg @ value Stores –8/4 in D; prompts for C. 13 ^4 qg @ value Stores –13/4 in C. prompts for B.
Example 3: Find the roots of the following quadratic polynomial: x2 + x – 6 = 0 Keys: (In RPN mode) XP Display: Description: @ value Starts the polynomial root finder; prompts for order. 2 g @ value Stores 2 in F; prompts for B. 1 g @ value Stores 1 in B; prompts for A. 6 ^g %/ . ) Stores –6 in A; calculates the first root. g %/ ) Calculates the second root. Coordinate Transformations This program provides two–dimensional coordinate translation and rotation.
y y' x Old coordinate system P u y [0, 0] [ m, n ] v x' x θ New coordinate system Mathematics Programs 15–33
Program Listing: Program Lines: (In RPN mode) 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: 1EDA 15 This routine converts from the old system to the new system.
Program Lines: (In RPN mode) Description "! # Prompts for and stores V. " Pushes V up and recalls U. ! Pushes U and V up and recalls T. Sets radius to 1 for the computation of sin(T) and cos(T). θ8T ´¸8º Calculates cos(T) and sin(T). %º Calculates U cos(T) –V sin(T) and U sin(T) + V cos(T). Pushes up previous results and recalls N. Pushes up results and recalls M.
X N to start the old–to–new transformation routine. g. 9. Key in Y, press g, and see the x–coordinate, U, in the new system. 10. Press g and see the y–coordinate, V, in the new system. 11. For another old–to–new transformation, press g and go to step 8. For a 7. Press 8. Key in X and press new–to–old transformation, continue with step 12. X O to start the new–to–old transformation routine. g. 14. Key in V (the y–coordinate in the new system) and press g to see X. 15. Press g to see Y. 16.
y y' P 1 ( _ 9, 7) P 3 (6, 8) x P 2 ( _ 5, _ 4) (M, N) T P' 4 (2.7, _ 3.6) ( M , N ) = (7, _ 4) T = 27 o Keys: (In RPN mode) Display: Description: { } Sets Degrees mode since T is given in degrees. XD @ value Starts the routine that defines the transformation. 7 g @ value Stores 7 in M. 4 ^g !@ value Stores –4 in U. @ ) Stores 27 in T. 27 g XN %@ value Starts the old–to–new routine. 9 ^g &@ value Stores –9 in X. 7 g "/ .
g 5 4 ^g ^g %@ . ) Stores –5 in X. &@ ) "/ . ) Stores –4 in Y. g #/ ) g %@ . ) &@ . ) 6 8 g g "/ ) Resumes the old–to–new routine for next problem. Calculates V. Resumes the old–to–new routine for next problem. Stores 6 in X . Stores 8 in Y and calculates U. g #/ ) Calculates V. XO "@ ) Starts the new–to–old routine. 2.7 g #@ ) Stores 2.7 in U. 3.6 ^g %/ ) Stores –3.6 in V and calculates X. &/ .
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 C urve Fit E Straight Line Fit S y y y = Be Mx y = B + Mx x Logarithmic Curve Fit L y x Power Curve Fit P y y = Bx M y = B + MIn x x 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: (In RPN mode) Description This routine sets, 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: E3F5 27 This routine sets the status for the logarithmic model.
Program Lines: (In RPN mode) ' Description Sets the loop counter to zero for the first input. Checksum and length: 5AB9 24 $ $ 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: (In RPN mode) ! Description Stores b in B. # $ Displays value. P Calculates coefficient m. ! Stores m in M. # $ Displays value. Checksum and length: 9CC9 36 & & Defines the beginning of the estimation (projection) loop. & "! % Displays, prompts for, and, if changed, stores x–value in X.
Program Lines: (In RPN mode) % º - ! Description Calculates ŷ = M In X + B. Returns to the calling routine. Checksum and length: A5BB 18 x̂ This subroutine calculates Restores index value to its original value. & . ª ! . L x̂ for the logarithmic model. = e(Y – B) ÷ M H % Calculates ! Returns to the calling routine.
Program Lines: (In RPN mode) Description ! ! ! ¸ % ! º ! ! ! Calculates Y= B(XM). Returns to the calling routine. Checksum and length: 018C 18 x̂ This subroutine calculates Restores index value to its original value. & ª +º ¸ % Calculates ! Returns to the calling routine. ! . L for the power model.
5. Repeat steps 3 and 4 for each data pair. If you discover that you have made an error after you have pressed g in step 3 (with the &@value prompt still visible), press g again (displaying the %@value prompt) and press X U to undo (remove) the last data pair. If you discover that you made an error after step 4, press X U. In either case, continue at step 3. 6. After all data are keyed in, press X R to see the correlation coefficient, R. g to see the regression coefficient B.
Example 1: Fit a straight line to the data below. Make an intentional error when keying in the third data pair and correct it with the undo routine. Also, estimate y for an x value of 37. Estimate x for a y value of 101. X 40.5 38.6 37.9 36.2 35.1 34.6 Y 104.5 102 100 97.5 95.5 94 Keys: (In RPN mode) XS 40.5 g 104.5 38.6 102 g g g Display: Description: Starts straight–line routine. %@ ) &@ value Enters x–value of data pair. %@ ) Enters y–value of data pair.
100 g 36.2 97.5 g g &@ ) 95.5 g %@ ) 94 g Enters x–value of data pair. Enters y–value of data pair. %@ ) g g &@ ) 35.1 34.6 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. %@ ) XR / ) Calculates the correlation coefficient. g / ) Calculates regression coefficient B. g / ) Calculates regression coefficient M.
Y ( ŷ Logarithmic Exponential Power To start: XL XE XP R 0.9965 0.9945 0.9959 M –139.0088 51.1312 8.9730 B 65.8446 0.0177 0.6640 98.7508 98.5870 98.6845 38.2857 38.3628 38.3151 when X=37) X ( x̂ when Y=101) Normal and Inverse–Normal Distributions Normal distribution is frequently used to model the behavior of random variation about a mean.
Program Listing: Program Lines: (In RPN mode) Description This routine initializes the normal distribution program. Stores default value for mean. ! "! Prompts for and stores mean, M. Stores default value for standard deviation. ! "! Prompts for and stores standard deviation, S. ! Stops displaying value of standard deviation. Checksum and length: D72F 48 This routine calculates Q(X) given X. "! % Prompts for and stores X.
Program Lines: (In RPN mode) ! - % Description 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. ) Checksum and length: 0E12 63 This subroutine calculates the upper–tail area Q(x).
Program Lines: (In RPN mode) ª º ª -+. H % ! Description Returns to the calling routine. Checksum and length: 1981 42 Flags Used: None. Remarks: The accuracy of this program is dependent on the display setting. For inputs in the area between ±3 standard deviations, a display of four or more significant figures is adequate for most applications. At full precision, the input limit becomes ±5 standard deviations.
6. To calculate Q(X) given X, 7. X D. After the prompt, key in the value of X and press displayed. g. The result, Q(X), is 8. To calculate Q(X) for a new X with the same mean and standard deviation, press g and go to step 7. 9. To calculate X given Q(X), press X I. 10. After the prompt, key in the value of Q(X) and press displayed. g. The result, X, is 11. To calculate X for a new Q(X) with the same mean and standard deviation, press g and go to step 10.
XD 3 g 10000 z %@ value Starts the distribution program and prompts for X. / ) Enters 3 for X and starts computation of Q(X). Displays the ratio of the population smarter than everyone within three standard deviations of the mean. ) Multiplies by the population. Displays the approximate number of blind dates in the local population that meet the criteria. Since your friend has been known to exaggerate from time to time, you decide to see how rare a "2σ" date might be.
55 g 15.3 g XD 90 g Stores 55 for the mean. @ ) ) Stores 15.3 for the standard deviation. %@ value Starts the distribution program and prompts for X. / ) Enters 90 for X and calculates Q(X). Thus, we would expect that only about 1 percent of the students would do better than score 90. Keys: (In RPN mode) XI 0.1 g g 0.8 g Display: Description: Starts the inverse routine. @ ) %/ ) @ ) Stores 0.1 (10 percent) in Q(X) and calculates X.
Program Listing: Program Lines: (In ALG mode) Description Start grouped standard deviation program. ; Clears statistics registers (28 through 33). ! Clears the count N. Checksum and length: EF85 24 Input statistical data points. "! % Stores data point in X. "! Stores data–point frequency in F. Enters increment for N. ! Recalls data–point frequency fi.
Program Lines: (In ALG mode) ! -1L2 Description Updates ¦x 2 i i f in register 31. ! - ! # $ Displays current number of data pairs. ! Goes to label I for next data input. Increments (or decrements) N. Checksum and length: 3080 117 Calculates statistics for grouped data. Uº Grouped standard deviation. ! # $ Displays grouped standard deviation.
Program Instructions: 1. Key in the program routines; press 2. Press when done. X S to start entering new data. 3. Key in xi –value (data point) and press g. 4. Key in fi –value (frequency) and press g. 5. Press g after VIEWing the number of points entered. 6. Repeat steps 3 through 5 for each data point. If you discover that you have made a data-entry error (xi or fi) after you have pressed g in step 4, press X U and then press g again. Then go back to step 3 to enter the correct data. 7.
Group 1 2 3 4 5 6 xi 5 8 13 15 22 37 fi 17 26 37 43 73 115 Keys: (In ALG mode) Display: Description: XS %@ value Prompts for the first xi. g @ value Stores 5 in X; prompts for first fi. 5 17 g g 8 g 26 g g 14 37 g g / ) %@ ) Prompts for the second xi. Prompts for second fi. @ ) Displays the counter. / ) %@ ) Prompts for the third xi. Prompts for the third fi. @ ) / ) Stores 17 in F; displays the counter.
g 15 43 g g g 22 73 g g g 37 g 115 g Prompts for the fourth xi. %@ ) @ ) / ) Prompts for the fourth fi. Displays the counter. Prompts for the fifth xi. %@ ) @ ) / ) Prompts for the fifth fi. Displays the counter. Prompts for the sixth xi. %@ ) Prompts for the sixth fi. @ ) / ) Displays the counter. XG / ) Calculates and displays the grouped standard deviation (sx) of the six data points.
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.
Equation Entry: Key in this equation: º º1 .1 - ª 2:. 2ª - º1 - ª Keys: (In RPN mode) Display: Description: |H ! ! or current equation L P z 100 º z|]1 |]1 L I q 100 |` LN|` qLILFz |]1LI q 100 | ` LN LB º º1 .¾ º º1 .1 -¾ | (hold) / / _ Selects Equation mode. Starts entering equation. _ º1 .1 - ª 1 .1 - ª 1 - ª 2:. - 2:¾ 2:. 2¾ 2:. 2ª - º¾ :. 2ª - º1 - ¾ - º1 - ª º1 - ª - ª º 2¾ 2:. ¾ 2:. - ¾ º1 .
SOLVE instructions: 1. If your first TVM calculation is to solve for interest rate, I, press 1 2. Press | H. If necessary, press or equation list until you come to the TVM equation. I I. to scroll through the 3. Do one of the following five operations: a. Press b. Press N to calculate the number of compounding periods. I to calculate periodic interest. For monthly payments, the result returned for I is the monthly interest rate, i; press 12 z to see the annual interest rate.
B = 7,250 _ 1,500 I = 10.5% p er year N = 36 month s F=0 P=? Keys: (In RPN mode) { % } 2 | H ( as Display: needed ) P 10.5 12 q g 36 0 g g 7250 g 1500 Selects FIX 2 display format. º Description: º1 .1 - ª Displays the leftmost part of the TVM equation. @ value Selects P; prompts for I. @ ) Converts your annual interest rate input to the equivalent monthly rate. @ value Stores 0.88 in I; prompts for N. @ value Stores 36 in N; prompts for F.
Part 2. What interest rate would reduce the monthly payment by $10? Keys: (In RPN mode) Display: |H º I @ . ) º1 .1 - ª Displays the leftmost hart of the TVM equation. {J @ . ) @ . ) 10 g Description: @ ) Selects I; prompts for P. Rounds the payment to two decimal places. Calculates new payment. Stores –176,89 in P; prompts for N. g @ ) Retains 36 in N; prompts for F. g @ 8 ) Retains 0 in F; prompts for B.
g @ ) g @ ) 24 g Retains P; prompts for I. Retains 0.56 in I; prompts for N. @ 8 ) g { % } 4 Stores 24 in N; prompts for B. # / . 8 ) Retains 5750 in B; calculates F, the future balance. Again, the sign is negative, indicating that you must, pay out this money. Sets FIX 4 display format. Prime Number Generator This program accepts any positive integer greater than 3.
LBL Y VIEW Prime Note: x is the value in the X-register.
Program Listing: Program Lines: (In ALG mode) & & & # $ Description This routine displays prime number P. Checksum and length: AA7A ' ' ' ' - 6 This routine adds 2 to P. Checksum and length: 8696 21 ª ! This routine stores the input value for P. ! º65¸ º/¸@ Tests for even input. ! - Increments P if input an even number. Stores 3 in test divisor, D.
Program Lines: (In ALG mode) Description % % º >¸@ Tests to see whether all possible factors have been tried. % ! & 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: 161E 57 Flags Used: None. Program Instructions: 1. Key in the program routines; press when done. 2.
Keys: (In ALG mode) 789 XP g Display: Description: ) Calculates next prime number after 789. ) Calculates next prime number after 797.
Part 3 Appendixes and Reference
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 the Calculator Support Department listed on page A–7.
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. Q: Why do I get incorrect answers when I use the trigonometric functions? A: You must make sure the calculator is using the correct angular mode ( { }, { }, or { } ).
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.) To install batteries: 1. Have two fresh button–cell batteries at hand. Avoid touching the battery terminals — handle batteries only by their edges. 2. Make sure the calculator is OFF. Do not press ON ( ) again until the entire battery–changing procedure is completed.
Warning Do not mutilate, puncture, or dispose of batteries in fire. The batteries can burst or explode, releasing hazardous chemicals. 5. Insert a new CR2032 lithium battery, making sure that the positive sign (+) is facing outward. Replace the plate and push it into its original place. 6. Remove and insert the other battery as in step 4~5. Make sure that the positive sign (+) on each battery is facing outward. 7. Replace the battery compartment cover. 8. Press .
If the calculator responds to keystrokes but you suspect that it is malfunctioning: 1. Do the self–test described in the next section. If the calculator fails the self test, it requires service. 2. If the calculator passes the self–test, you may have made a mistake operating the calculator. Reread portions of the manual and check "Answers to Common Questions" (page A–1). 3. Contact the Calculator Support Department listed on page A–7.
Warranty HP 33s Scientific Calculator; Warranty period: 12 months 1. HP warrants to you, the end-user customer, that HP hardware, accessories and supplies will be free from defects in materials and workmanship after the date of purchase, for the period specified above. If HP receives notice of such defects during the warranty period, HP will, at its option, either repair or replace products which prove to be defective. Replacement products may be either new or like-new. 2.
7. TO THE EXTENT ALLOWED BY LOCAL LAW, THE REMEDIES IN THIS WARRANTY STATEMENT ARE YOUR SOLE AND EXCLUSIVE REMEDIES. EXCEPT AS INDICATED ABOVE, IN NO EVENT WILL HP OR ITS SUPPLIERS BE LIABLE FOR LOSS OF DATA OR FOR DIRECT, SPECIAL, INCIDENTAL, CONSEQUENTIAL (INCLUDING LOST PROFIT OR DATA), OR OTHER DAMAGE, WHETHER BASED IN CONTRACT, TORT, OR OTHERWISE.
Asia Pacific L.
N.America Country : Telephone numbers USA 1800-HP INVENT Canada (905)206-4663 or 800-HP INVENT ROTC = Rest of the country Please logon to http://www.hp.com for the latest service and support information. Regulatory Information This section contains information that shows how the HP 33s scientific calculator complies with regulations in certain regions. Any modifications to the calculator not expressly approved by Hewlett-Packard could void the authority to operate the 33s in these regions.
Japan この装置は、情報処理装置等電波障害自主規制協議会(VCCI)の基準 に基づく第二情報技術装置です。この装置は、家庭環境で使用することを目的としていま すが、この装置がラジオやテレビジョン受信機に近接して使用されると、受信障害を引き 起こすことがあります。 取扱説明書に従って正しい取り扱いをしてください。 Noise Declaration. In the operator position under normal operation (per ISO 7779): LpA<70dB. Disposal of Waste Equipment by Users in Private Household in the European Union This symbol on the product or on its packaging indicates that this product must not be disposed of with your other household waste.
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 33s has 31KB of user memory available to you for any combination of stored data (variables, equations, or program lines). SOLVE, ³ FN, and statistical calculations also require user memory.
2. If necessary, scroll through the equation list (press or ) until you see the desired equation. 3. Press | to see the checksum (hexadecimal) and length (in bytes) of the equation. For example, / / . To see the total memory requirements of specific programs: 1. Press { Y { } to display the first label in the program list. until you see the desired 2. Scroll through the program list (press or program label and size). For example, / . 3.
Clearing Memory The usual way to clear user memory is to press { c { }. However, there is also a more powerful clearing procedure that resets additional information and is useful if the keyboard is not functioning properly. If the calculator fails to respond to keystrokes, and you are unable to restore operation by resetting it or changing the batteries, try the following MEMORY CLEAR procedure.
Memory may inadvertently be cleared if the calculator is dropped or if power is interrupted. The Status of Stack Lift The four stack registers are always present, and the stack always has a stack–lift status. That is to say, the stack lift is always enabled or disabled regarding its behavior when the next number is placed in the X–register. (Refer to chapter 2, "The Automatic Memory Stack.") All functions except those in the following two lists will enable stack lift.
DEG, RAD, GRAD FIX, SCI, ENG, ALL DEC, HEX, OCT, BIN CLVARS PSE SHOW RADIX . RADIX , CLΣ g and STOP and * and b* Y {# }** Y { }** V V label nnnn EQN FDISP Errors e and program entry Switching binary windows Digit entry ¼ Except when used like CLx. ¼¼ Including all operations performed while the catalog is displayed except {# } and { } X, which enable stack lift.
The Status of the LAST X Register The following operations save x in the LAST X register: x , x2, X y +, –, × , ÷ 3 x , x3 ex, 10x LN, LOG yx, SIN, COS, TAN ASIN, ACOS, ATAN SINH, COSH, TANH ASINH, ACOSH, ATANH IP, FP, SGN, INTG, RND, ABS %, %CHG Σ+, Σ– RCL+, –, ×, ÷ y,xθ,r θ,ry, x HR, HMS DEG, RAD nCr nPr x! CMPLX +/– CMPLX +, –, × ,÷ CMPLX ex, LN, yx, 1/x CMPLX SIN, COS, TAN kg, lb l, gal °C, °F cm, in I/x, INT÷, Rmdr Notice that /c does not affect the LAST X reg
C ALG: Summary About ALG This appendix summarizes some features unique to ALG mode, including, Two–number arithmetic Chain calculation Reviewing the stack Coordinate conversions Operations with complex numbers Integrating an equation Arithmetic in bases 2, 8, and 16 Entering statistical two–variable data Press | to set the calculator to ALG mode. When the calculator is in ALG mode, the ALG annunciator is on. In ALG mode, operations are performed in the following order. 1.
Doing Two–number Arithmetic in ALG This discussion of arithmetic using ALG replaces the following parts that are affected by ALG mode. One-number functions (such as #) work the same in ALG and RPN modes. Two–number arithmetic operations are affected by ALG mode: Simple arithmetic Power functions ( , ) Percentage calculations (Q or | T) Permutations and Combinations ({ \, { _) Quotient and Remainder of Division ({ F, | D) Simple Arithmetic Here are some examples of simple arithmetic.
To Calculate: Press: 123 12 641/3 (cube root) 3 Display: 3 64 : / 8 ) º / ) Percentage Calculations The Percent Function. The Q key divides a number by 100. Combined with , it adds or subtracts percentages. or To Calculate: Press: Display: 27% of 200 200 z 27 Q º 0/ ) 200 less 27% 200 27 Q . 0/ ) 12% greater than 25 25 12 Q - 0/ ) To Calculate: Press: x% of y zxQ y|Tx y Percentage change from y to x.
Example: Suppose that the $15.76 item cost $16.12 last year. What is the percentage change from last year's price to this year's? Keys: 16.12 15.76 |T Display: ) 0 ) . ) Description: This year's price dropped / about 2.2% from last year's price. Permutations and Combinations Example: Combinations of People. A company employing 14 women and 10 men is forming a six–person safety committee.
Parentheses Calculations In ALG mode, you can use parentheses up to 13 levels. For example, suppose you want to calculate: 30 ×9 85 − 12 If you were to key in 30 ¯ 85 Ã, the calculator would calculate the intermediate result, 0.3529. However, that’s not what you want. To delay the division until you’ve subtracted 12 from 85, use parentheses: Keys: Display: Description: 30 ¯ º y 85 Ã No calculation is done. 12 º| Calculates 85 − 12.
z 12 q 360 750 or 750 z 12 q 360 In the second case, the q key acts like the key by displaying the result of 750 × 12. Here’s a longer chain calculation: 456 − 75 68 × 18.5 1.9 This calculation can be written as: 456 75 q 18.5 z 68 q 1.9 . Watch what happens in the display as you key it in: Keys: 456 Display: 75 q 18.5 z 68 q 1.9 .
You can press or (or of the stack and recall them. and | ) to review the entire contents However, in normal operation in ALG mode, the stack in ALG mode differs from the one in RPN mode. (Because when you press , the result is not placed into X1, X2 etc.) Only after evaluating equations, programs, or integrating equations, the values of the four registers will be the same as in RPN mode. Coordinate Conversions To convert between rectangular and polar coordinates: 1.
8 ´¸8º &/ ) Displays y. If you want to perform a coordinate conversion as part of a chain calculation, you need to use parentheses to impose the required order of operations. Example: If r = 4.5, θ = 2 π , what are x, y ? 3 Keys: { } |]2q3z |N|` Display: Description: Sets Radians mode. 1 ª ºπ2 ) Use parentheses to impose the required order of operations. [ 4.5 | s ) 8 ) Calculates x. %/. ) ) 8 ) Displays y.
Operations with Complex Numbers To enter a complex number웛 x + iy. 1. Type the real part, x, then the function key. 2. Type the imaginary part, y, then press Fox example, to do 2 + i 4, press 2 { G. 4 { G. To view the result of complex operations웛 After keying in the complex number, press to calculate. Then the real portion of the result is displayed; press to view the imaginary portion.
Examples: Evaluate sin (2워3i ) Keys: | ] 2 3 { G | ` Display: 1 워 L2 / ) O Description: 1 워 L2 / ) 1 워 L2 /. ) Result is 9.1545 – i 4.1689 Examples: Evaluate the expression z 1 ÷ (z2 + z3), where z1 = 23 + i 13, z2 = –2 + i z3 = 4 – i 3 Keys: | ] 23 13 {G|` q|]2^ 1{G4 3{G |` Display: 1 워 L2ª1. - / ) C–10 ALG: Summary Real part of result. 1 워 L2ª1. - / ) Description: Result is 2.5000 + i 9.
Examples: Evaluate (4－i 2/5)(3－i 2/3) Keys: ºy4ÃË2 Ë5¹cº |ºy3ÃË 2Ë3¹c º|Ï Display: Description: Real part of result. Ø Result is 11.7333 – i 3.8667 Arithmetic in Bases 2, 8, and 16 In ALG mode, if the current expression in the first line does not fit in the display, the rightmost digits are replaced with an ellipsis () to indicate it is too long to be displayed.
1008 ÷ 58=? 100 ¯ 5Ï Integer part of result. 5A016 + 100110002 =? ¹ ¶ {} 5A0 Ù Set base 16; HEX annunciator on. ¹ ¶ {} Changes to base 2; BIN annunciator on. 10011000 Ï ... Result in binary base. ¹ ¶ {} ... Result in hexadecimal base. ¹ ¶ {} _ Restores decimal base.
Keys: { c {´} 4 [ 20 6 [ 400 Display: Clears existing statistical data. Enters the first new data pair. 8 Q/ ) 8 Q/ ) Display shows n, the number of data pairs you entered. Brings back last x–value. Last y is still in Y–register. { !º ) { 8 Q/ ) 8 Q/ ) 6 [ 40 Description: 4 [ 20 { 8 Q/ ) 5 [ 20 8 Q/ ) Deletes the last data pair. Reenters the last data pair. Deletes the first data pair. Reenters the first data pair.
D More about Solving This appendix provides information about the SOLVE operation beyond that given in chapter 7. How SOLVE Finds a Root SOLVE first attempts to solve the equation directly for the unknown variable. If the attempt fails, SOLVE changes to an iterative(repetitive) procedure. The iterative operation is to execute repetitively the specified equation. The value returned by the equation is a function f(x) of the unknown variable x.
f (x) f (x) x x b a f (x) f (x) x x c d 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. However, a very small non–zero value for f(x) is often acceptable because it might result from approximating numbers with limited (12–digit) precision.
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: Display: Description: |H 2 ^ z 3 LX 4 z LX 2 6 z L X 8 | Select Equation mode. . º%: - º%: . º Enters the equation. / / Checksum and length. Cancels Equation mode. Now, solve the equation to find the root: Keys: Display: Description: I X 10 |H _ Initial guesses for the root. . º%: - º%: . º Selects Equation mode; displays the left end of the equation. X # %/ ) Solves for X; displays the result.
| / / Checksum and length. Cancels Equation mode. Now, solve the equation to find its positive and negative roots: Keys: 0 I X 10 Display: Description: _ Your initial guesses for the positive root. |H %: -%. Selects Equation mode; displays the equation. X # %/ ) Calculates the positive root using guesses 0 and 10. ) Final two estimates are the same. | 0 I X 10 ^ |H X | ) f(x) = 0. . _ Your initial guesses for the negative root. %: -%.
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: Display: Description: |H |"LX| ` | 1.5 | Selects Equation mode. 1%2/ ) Enter the equation. / / Checksum and length. Cancels Equation mode. Now, solve to find the root: Keys: 0 5 IX |H D–6 Display: Description: _ Your initial guesses for the root.
X # %/ ) | ) Shows root, to 11 decimal places. ) The previous estimate is slightly bigger. | . ) Finds a root with guesses 0 and 5. f(x) is relatively large. Note the difference between the last two estimates, as well as the relatively large value for f(x). The problem is that there is no value of x for which f(x) equals zero. However, at x = 1.99999999999, there is a neighboring value of x that yields ant opposite sign for f(x).
Now, solve to find the root. Keys: 2.3 2.7 IX Display: Description: ) _ Your initial guesses for the root. |H %ª1%: . 2. Selects Equation mode; displays the equation. X ! No root found for f(x). 8 8 8 ) f(x) is relatively large. When SOLVE Cannot Find a Root Sometimes SOLVE fails to find a root. The following conditions cause the message ! : The search terminates near a local minimum or maximum (see figure a, below).
f (x) f (x) x x b a f (x) x c Case Where No Root Is Found 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: |H 2 LX 6zLX 13 | Display: Description: Selects Equation mode. %: . º%- Enters the equation. / / Checksum and length.
Cancels Equation mode. Now, solve to find the root: Keys: Display: Description: 0IX 10 _ Your initial guesses for the root. |H %: . º%- Selects Equation mode; displays the equation. X ! Search fails with guesses 0 and 10 b| | ) ) ) Displays the final estimate of x. Previous estimate was not the same. Final value for f(x) is relatively large. Example: An Asymptote.
) | Previous estimate is the same. ) f (x) = 0 Watch what happens when you use negative values for guesses: Keys: Display: Description: 1 ^IX . ) 2 ^|H . #1%2 Selects Equation mode; displays the equation. %/ ) Solves for X; displays the result. X Your negative guesses for the root. Example: Find the root of the equation. [x ÷ (x + 0.3)] − 0.
Now attempt to find a negative root by entering guesses 0 and –10. Notice that the function is undefined for values of x between 0 and –0.3 since those values produce a positive denominator but a negative numerator, causing a negative square root. Keys: 0IX 10 ^ Display: Description: . _ |H !1%ª1%- ) 22 Selects Equation mode; displays the left end of the equation. X ! No root found for f(x). Clears error message; cancels Equation mode.
¶ ! Checksum and length: B956 75 You can subsequently delete line J0003 to save memory. Solve for X using initial guesses of 10–8 and –10–8. Keys: (In RPN mode) Display: a8^IX ^a8^ |WJ . . _ X %/ . ) 1 . ) Description: Enters guesses. . Selects program "J" as the function. Solves for X; displays the result.
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. (The calculator cannot represent infinity, anyway.
E 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, ³ 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.
f (x) x With this number of sample points, 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.
Keys: Display: Description: |H LXz LX|` | Select equation mode. %º % 1¾ Enter the equation. %º % 1.%2 End of the equation. / / Checksum and length. Cancels Equation mode. Set the display format to SCI 3, specify the lower and upper limits of integration as zero and 100499, than start the integration. Keys: Display: Description: { } 3 0 a 499 |H %º % 1.%2 Selects Equation mode; displays the equation.
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.
Note that the rapidity of variation in the function (or its low–order derivatives) must be determined with respect to the width of the interval of integration. With a given number of sample points, a function f(x) that has three 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.
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, 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.
[ ) . 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.
Because the calculation time depends on how soon a certain density of sample points is achieved in the region where the function is interesting, the 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.
F 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 b clears the message; pressing any other key clears the message and executes that key's function. ³ ! # A running program attempted to 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 Å or ¥. Data error: Attempted to calculate combinations or permutations with r >n, with non–integer r or n, or with n ≥1016. Attempted to use a trigonometric or hyperbolic function with an illegal argument: q with x an odd multiple of 90°. l or i with x < –1 or x > 1. : o with x ≤ –1; or x ≥ 1.
% ! ! Attempted to refer to a nonexistent program label (or line number) with V,V , X, 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 ( { Y { } ) indicates no program labels stored. ! SOLVE cannot find the root of the equation using the current initial guesses (see page D–8).
# 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.
G 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 { % } n. executed as Nonprogrammable functions have their names in key boxes. For example, b.
Name Keys and Description Page Displays previous entry in catalog; moves to previous equation in equation list; moves program pointer to previous step. 1–24 6–3 12–9 12–18 Displays next entry in catalog; moves to next equation in equation list; moves program pointer to next line (during program entry); executes the current program line (not during program entry).
Name Σ+ Keys and Description Accumulates (y, x) into Page ¼ 11–2 statistics registers. Σ– { Removes (y, x) from 11–2 statistics registers. Σx | {;º } 11–10 1 11–10 1 11–10 1 11–10 1 11–10 1 11–6 1 11–6 1 Returns the sum of x–values. Σx2 | {;º } Returns the sum of squares of x–values. Σxy | {;º¸ } Returns the sum of products of x–and y–values. Σy | {;¸ } Returns the sum of y–values. Σy2 | {;¸ } Returns the sum of squares of y–values.
Name ³ FN d variable Keys and Description | { ³ 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 of integration in the X–register. | ] Open parenthesis. ( Page ¼ 8–2 14–7 6–6 2 6–6 2 6–4 2 4–16 1 Starts a quantity associated with a function in an equation. | ` Close parenthesis. ) Ends a quantity associated with a function in an equation.
Name ASINH Keys and Description { { M Page ¼ 4–6 1 Hyperbolic arc sine. Returns sinh –1 x. ATAN { S Arc tangent. Returns tan –1 x. 4–4 1 ATANH { {S 4–6 1 1 Hyperbolic arc tangent. Returns tanh –1 x. b | {E } Returns the y–intercept of the regression line: y – m x . 11–10 {x Displays the base–conversion menu. 10–1 BIN { x { } 10–1 Selects Binary (base 2) mode.
Name Keys and Description Page {c Displays menu to clear numbers or parts of memory; clears indicated variable or program from a MEM catalog; clears displayed equation. 1–6 1–24 { c { } Clears all stored data, equations, and programs. 1–24 { c { } Clears all programs (calculator in Program mode). 12–20 { c { } Clears the displayed equation (calculator in Program mode). CLΣ { c {´} ¼ 12–6 11–11 Clears statistics registers. CLVARS { c {# } 3–4 Clears all variables to zero.
Name CMPLX × Keys and Description { G z Complex Page ¼ 9–2 multiplication. Returns (z1x + i z1y) × (z2x + i z2y). CMPLX ÷ { G q Complex 9–2 division. Returns (z1x + i z1y) ÷ (z2x + i z2y). CMPLX1/x { G Complex 9–2 reciprocal. Returns 1/(zx + i zy). CMPLXCOS { G R Complex cosine. Returns cos (zx + i zy). 9–2 CMPLXex {G 9–2 Complex natural exponential. (z + iz y ) . Returns e x CMPLXLN {G 9–2 Complex natural log. Returns log e (zx + i zy). CMPLXSIN { G O Complex sine.
Name Keys and Description { R Hyperbolic COSH Page ¼ 4–6 1 cosine. Returns cosh x. | Functions to use 40 physics constants. DEC { x { } 4–8 10–1 Selects Decimal mode. { } DEG 4–4 Selects Degrees angular mode. DEG { v Radians to degrees. Returns (360/2π) x. 4–13 Displays menu to set the display format. 1–19 DSE variable | m variable Decrement, Skip if Equal or less. For control number ccccccc.
Name Keys and Description Page Separates two numbers keyed in sequentially; completes equation entry; evaluates the displayed equation (and stores result if appropriate). 1–17 6–4 6–11 ENTER ¼ 2–5 Copies x into the Y–register, lifts y into the Z–register, lifts z into the T–register, and loses t. |H Activates or cancels (toggles) Equation–entry mode. ex Natural exponential. Returns e raised to the x power. EXP Natural exponential.
Name FS? n Keys and Description | y { @ } n Page ¼ 13–11 If flag n (n = 0 through 11) is set, executes the next program line; if flag n is clear, skips the next program line. GAL | Converts liters to 4–13 1 gallons. GRAD { } 4–4 Sets Grads angular mode. GTO label { V label Sets the program pointer to the beginning of program label in program memory. { V label 13–4 13–17 Sets program pointer to line nnnn of program label. 12–19 {V Sets program pointer to PRGM TOP.
Name ( i) Keys and Description LI Indirect. Value of variable whose letter corresponds to the numeric value stored in variable i. IN | Converts centimeters to Page ¼ 6–4 13–21 2 4–13 1 6–15 2 4–2 1 4–16 1 inches. IDIV { F Produces the quotient of a division operation involving two integers. INT÷ { F Produces the quotient of a division operation involving two integers. INTG | K Obtains the greatest integer equal to or less than given number.
Name KG Keys and Description { } Converts pounds to Page ¼ 4–13 1 4–13 1 kilograms. L { Converts gallons to liters. LASTx { 2–7 Returns number stored in the LAST X register. LB | ~ 4–13 1 Converts kilograms to pounds. LBL label { label 12–3 Labels a program with a single letter for reference by the XEQ, GTO, or FN= operations. (Used only in programs.) LN Natural logarithm. Returns log e x. 4–1 1 LOG { Common logarithm. 4–1 1 Returns log10 x.
Name OCT Keys and Description { x { ! } Page ¼ 10–1 Selects Octal (base 8) mode. | Turns the calculator off. Pn,r { _ Permutations of n items 1–1 4–14 2 taken r at a time. Returns n!÷(n – r)!. {e Activates or cancels (toggles) Program–entry mode. PSE | f Pause. Halts program execution briefly to display x, variable, or equation, then resumes. (Used only in programs.
Name RCL variable Keys and Description L variable Page ¼ 3–5 Recall. Copies variable into the X–register. RCL+ variable L variable 3–5 Returns x + variable. RCL– variable L variable. Returns x – variable. 3–5 RCLx variable L z variable. 3–5 Returns x × variable. RCL÷ variable L q variable. 3–5 Returns x ÷ variable. RMDR | D Produces the remainder of a division operation involving two integers. 6–15 2 RND { J Round.
Name Rµ Keys and Description | Roll up. Moves t to the X–register, z to the T–register, y to the Z–register, and x to the Y–register in RPN mode. Page ¼ 2–3 C–6 Displays the X1~X4 menu to review the stack in ALG mode. | Displays the standard–deviation Menu. 11–4 SCI n { } n Selects Scientific display with n decimal places. (n = 0 through 11.) 1–19 SEED | i Restarts the 4–14 random–number sequence with the seed x . SF n { y { } n 13–11 Sets flag n (n = 0 through 11).
Name p Keys and Description g Inserts a blank space Page ¼ 13–14 2 character during equation entry. SQ ! Square of argument. 6–15 2 SQRT # Square root of x. 6–15 2 STO variable I variable 3–2 Store. Copies x into variable. STO + variable I variable 3–4 Stores variable + x into variable. STO – variable I variable Stores variable – x into variable. 3–4 STO × variable I z variable 3–4 Stores variable × x into variable.
Name TAN TANH Keys and Description Page ¼ U Tangent. Returns tan x. 4–3 1 { U Hyperbolic 4–6 1 tangent. Returns tanh x. VIEW variable | variable Displays the labeled contents of variable without recalling the value to the stack. 3–3 12–13 X Evaluates the displayed equation. 6–12 XEQ label X label Executes the program identified by label. 13–2 x2 ! Square of x. 4–2 1 x3 { $ Cube of x. 4–2 1 # Square root of x. 4–2 1 { @ Cube root of x. 4–2 1 The xth root of y.
Name Keys and Description Page ¼ 1 xw Returns weighted mean of x values: (Σyixi) ÷ Σyi. 11–4 | Displays the mean (arithmetic average) menu. 11–4 x<> variable | Z x exchange. 3–6 Exchanges x with a variable. x<>y [ x exchange y. 2–4 Moves x to the Y–register and y to the X–register. {n Displays the "x?y" comparison tests menu. 13–7 x≠y { n {≠} 13–7 If x≠y, executes next program line; if x=y, skips next program line.
Name x≠0? Keys and Description | o {≠} Page ¼ 13–7 If x≠0, executes next program line; if x=0, skips the next program line. x≤0? | o {≤} 13–7 If x≤0, executes next program line; if x>0, skips next program line. x<0? | o {<} 13–7 If x<0, executes next program line; if x≥0, skips next program line. x>0? | o {>} 13–7 If x>0, executes next program line; if x≤0, skips next program line. x≥0? | o {≥} 13–7 If x≥0, executes next program line; if x<0, skips next program line.
Name yx Keys and Description Page ¼ Power. Returns y raised to the xth power. 4–2 1 Notes: 1. Function can be used in equations. 2. Function appears only in equations.
Index Special Characters , 6–5 ∫ FN. See integration % functions, 4–6 . See equation–entry cursor ~. See backspace key ". See integration z, 1–14 â, 1–23 π, 4–3, A–2 Algebraic mode, 1–10 ALL format.
asymptotes of functions, D–8 B viewing all digits, 3–3, 10–6 borrower (finance), 17–1 branching, 13–2, 13–16, 14–7 backspace key canceling VIEW, 3–3 clearing messages, 1–5, F–1 clearing X–register, 2–2, 2–6 deleting program lines, 12–18 equation entry, 1–5, 6–8 leaving menus, 1–5, 1–9 operation, 1–5 program entry, 12–6 starts editing, 6–8, 12–6, 12–18 balance (finance), 17–1 base affects display, 10–4 arithmetic, 10–2 converting, 10–1 default, B–3 programs, 12–22 setting, 10–1, 14–11 base mode default, B
program, 1–24, 12–20 using, 1–24 variable, 1–24, 3–3 chain calculations, 2–11 change–percentage functions, 4–6 changing sign of numbers, 1–14, 1–17, 9–3 checksums equations, 6–18, 12–6, 12–21 programs, 12–20 CLEAR menu, 1–6 clearing equations, 6–8 general information, 1–5 memory, 1–24, A–1 messages, 1–23 numbers, 1–14, 1–16 programs, 1–24, 12–20 statistics registers, 11–2, 11–11 variables, 1–24, 3–3, 3–4 X–register, 2–2, 2–6 conversion functions, 4–9 conversions angle format, 4–13 angle units, 4–13 coordin
adjusting contrast, 1–1 annunciators, 1–11 function names in, 4–17 X–register shown, 2–2 display format affects integration, 8–2, 8–5, 8–7 affects numbers, 1–19 affects rounding, 4–16 default, B–3 periods and commas in, 1–18, A–1 setting, 1–19, A–1 DISPLAY menu, 1–19 do if true, 13–6, 14–6 dot product, 15–1 DSE, 13–18 equality equations, 6–9, 6–10, 7–1 equation list adding to, 6–4 displaying, 6–6 editing, 6–8 EQN annunciator, 6–4 in Equation mode, 6–3 operation summary, 6–3 Equation mode backspacing, 1–5,
functions, 6–5, 6–15, G–1 in programs, 12–4, 12–6, 12–21, 13–10 integrating, 8–2 lengths, 6–18, 12–6, B–2 list of.
fractional–part function, 4–16 G Fraction–display mode V affects rounding, 5–7 affects VIEW, 12–13 setting, 1–23, 5–1, A–2 fractions accuracy indicator, 5–2, 5–3 and equations, 5–8 and programs, 5–8, 12–13, 13–9 base 10 only, 5–2 calculating with, 5–1 denominators, 1–22, 5–4, 5–5, 13–9, 13–14 displaying, 1–23, 5–1, 5–2, 5–4, A–2 flags, 5–6, 13–9 formats, 5–5 not statistics registers, 5–2 reducing, 5–2, 5–5 rounding, 5–7 round–off, 5–7 setting format, 5–5, 13–9, 13–14 showing integer digits, 5–4 typing,
imaginary part (complex numbers), 9–1, 9–2 inverse trigonometric functions, 4–4 indirect addressing, 13–20, 13–21, 13–22 ISG, 13–18 INPUT inverse-normal distribution, 16–11 K always prompts, 13–10 entering program data, 12–11 in integration programs, 14–8 in SOLVE programs, 14–2 responding to, 12–13 integer–part function, 4–16 keys integration LAST X register, 2–7, B–6 accuracy, 8–2, 8–5, 8–6, E–1 base mode, 12–22, 14–11 difficult functions, E–2, E–7 display format, 8–2, 8–6, 8–7 evaluating progr
order of calculation, 2–13 real–number, 4–1 stack operation, 2–4, 9–1 matrix inversion, 15–12 clearing, 1–5, 1–23 displaying, 12–14, 12–16 in equations, 12–14 responding to, 1–23, F–1 summary of, F–1 maximum of function, D–8 mean menu, 11–4 minimum of function, D–8 means (statistics) modes.
internal representation, 1–19, 10–4 large and small, 1–14, 1–16 limitations, 1–14 mantissa, 1–15 negative, 1–14, 9–3, 10–4 order in calculations, 1–18 periods and commas in, 1–18, A–1 precision, 1–19, D–13 prime, 17–6 range of, 1–16, 10–5 real, 4–1, 8–1 recalling, 3–2 reusing, 2–6, 2–9 rounding, 4–16 showing all digits, 1–21 storing, 3–2 truncating, 10–4 typing, 1–14, 1–15, 10–1 P π, A–2 parentheses in arithmetic, 2–11 in equations, 6–5, 6–6, 6–14 pause.
checksums, 12–21 clearing, 12–5 duplicate, 12–5 entering, 12–3, 12–5 executing, 12–9 indirect addressing, 13–20, 13–21, 13–22 moving to, 12–10, 12–19 purpose, 12–3 typing name, 1–3 viewing, 12–20 program lines. See programs program names. See program labels program pointer, 12–5, 12–10, 12–17, 12–19, B–3 Program–entry mode, 1–5, 12–5 programs.
testing, 12–9 using integration, 14–9 using SOLVE, 14–6 variables in, 12–11, 14–1, 14–7 prompts affect stack, 6–13, 12–12 clearing, 1–5, 6–13, 12–13 equations, 6–12 INPUT, 12–11, 12–13, 14–2, 14–8 programmed equations, 13–10, 14–1, 14–8 responding to, 6–12, 12–13 showing hidden digits, 6–13 PSE pausing programs, 12–11, 12–17, 14–10 preventing program stops, 13–10 Q quadratic equations, 15–21 questions, A–1 quotient and remainder of division, 4–2 R g ending prompts, 6–10, 6–13, 7–2, 12–13 interrupting pro
SOLVE, D–13 statistics, 11–9 trig functions, 4–4 routines Sign value, 4–16 calling, 13–2 nesting, 13–3, 14–11 parts of programs, 13–1 RPN slope (curve–fit), 11–7, 16–1 compared to equations, 12–4 in programs, 12–4 origins, 2–1 running programs, 12–9 S Î equation checksums, 6–18, B–2 equation lengths, 6–18, B–2 fraction digits, 5–4 number digits, 1–21, 12–6 program checksums, 12–20, B–2 program lengths, 12–20, B–2 prompt digits, 6–13 variable digits, 3–3, 12–13 ®, 13–14 sample standard deviations, 11–6
effect of , 2–5 equation usage, 6–11 exchanging with variables, 3–6 exchanging X and Y, 2–4 filling with constant, 2–6 long calculations, 2–11 operation, 2–1, 2–4, 9–1 program calculations, 12–12 program input, 12–11 program output, 12–11 purpose, 2–1, 2–2 registers, 2–1 reviewing, 2–3, C–6 rolling, 2–3, C–6 separate from variables, 3–2 size limit, 2–4, 9–1 unaffected by VIEW, 12–14 stack lift.
time value of money, 17–1 transforming coordinates, 15–32 T–register, 2–4 trigonometric functions, 4–4, 9–3 troubleshooting, A–4, A–5 turning on and off, 1–1 TVM, 17–1 twos complement, 10–2, 10–4 two–variable statistics, 11–2 U uncertainty (integration), 8–2, 8–5, 8–6 underflow, D–14 units conversions, 4–13 V variable catalog, 1–24, 3–3 variables arithmetic inside, 3–4 catalog of, 1–24, 3–3 clearing, 1–24, 3–3, 3–4 clearing all, 1–6, 3–4 clearing while viewing, 12–13 default, B–3 exchanging with X, 3–6 in
clearing in programs, 12–6 displayed, 2–2 during programs pause, 12–17 exchanging with variables, 3–6 exchanging with Y, 2–4 not clearing, 2–5 part of stack, 2–1 testing, 13–7 unaffected by VIEW, 12–14 Index–15
