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Overview of IEEE Standard Single- and Double-Precision Formats
Figure 4–1. Single-Precision Floating-Point Fields
Table 4–5. Special Single-Precision Values
4-8
Figure 4–1 shows the fields of a single-precision floating-point number repre-
sented within a 32-bit register.
31
30
e
s
Legend: s
sign bit (0 positive, 1 negative)
e
8-bit exponent ( 0 < e < 255)
f
23-bit fraction
0 < f < 1*2 –1 + 1*2 –2 + ... + 1*2 –23 or
0 < f < ((2 23 )–1)/(2 23 )
The floating-point fields represent floating-point numbers within two ranges:
normalized (e is between 0 and 255) and denormalized (e is 0). The following
formulas define how to translate the s, e, and f fields into a single-precision
floating-point number.
Normal
s
(e–127)
–1
* 2
* 1.f
Denormalized (Subnormal)
s
–126
–1
* 2
* 0.f
e = 0; f nonzero
Table 4–5 shows the s,e, and f values for special single-precision floating-
point numbers.
Symbol
+0
–0
+Inf
–Inf
NaN
QNaN
SNaN
23 22
0 < e < 255
Sign (s)
Exponent (e)
0
0
1
0
0
255
1
255
x
255
x
255
x
255
f
Fraction (f)
0
0
0
0
nonzero
1xx..x
0xx..x and nonzero
0
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