7-3
FLOATING-POINT UNIT
7.2.1.Real Number System
As shown in Figure 7-1, the real-number system comprises the continuum of real numbers from
minus infinity (
??
) to plus infinity (+
?
).
Because the size and number of registers that any computer can have is limited, only a subset of
the real-number continuum can be used in real-number calculations. As shown at the bottom of
Figure 7-1, the subset of real numbers that a particular FPU supports represents an approxima-
tion of the real number system. The range and precision of this real-number subset is determined
by the format that the FPU uses to represent real numbers.
Figure 7-1. Binary Real Number System
Binary Real Number System
Subset of binary real-numbers that can be represented with
IEEE single-precision (32-bit) floating-point format
+10
10.0000000000000000000000
1.11111111111111111111111
Precision
24 Binary Digits
Numbers within this range
cannot be represented.
??
??
-100
-10-1
0
1
10
100
??
??
-100
-10-1
0
1
10
100
