User's Manual

1'1
L'
-1.67x10
308
OVERVIEW OF NUMERIC PROCESSING
NEGATIVE RANGE
(NORMALIZED)
• I
-5 -4 -3 -2 -1 :
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-4.19x10-
a07
I ,
POSITIVE RANGE
(NORMALIZED)
Figure 1-8. 80287 Number System
iii I
G30108
From a practical standpoint, the 80287's set of real numbers is sufficiently large and dense so as not
to limit the vast majority of microprocessor applications. Compared to most computers, including
mainframes, the
NPX provides a very good approximation of the real number system. It is important
to remember, however, that it is not an exact representation, and that arithmetic on real numbers is
inherently approximate.
Conversely, and equally important, the 80287
does perform exact arithmetic on integer operands. That
is, an operation
on two integers returns an exact integral result, provided that the true result is an
integer and
is in range. For example, 4 + 2 yields an exact integer. I + 3 does not, and 2
40
X 2
30
+ 1
does not, because the result requires greater than 64 bits of precision.
Data Types and Formats
The 80287 recognizes seven numeric data types, divided into three classes: binary integers, packed
decimal integers, and binary reals. A later section describes
how these formats are stored in memory
(the sign
is always located in the highest-addressed byte). Figure 1-9 summarizes the format of each
data type. In the figure, the most significant digits of all numbers (and fields within numbers) are the
leftmost digits. Table
1-5 provides the range and number of signficant (decimal) digits that each format
can accommodate.
1-15