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Overview of IEEE Standard Single- and Double-Precision Formats
3-11Instruction SetSPRU733
Figure 3−1 shows the fields of a single-precision floating-point number repre-
sented within a 32-bit register.
Figure 3−1. Single-Precision Floating-Point Fields
31
e
23 22
0
30
s
f
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.
Normalized:
−1
s
× 2
(e−127)
× 1.f 0 < e < 255
Denormalized (Subnormal):
−1
s
× 2
−126
× 0.f e = 0; f nonzero
Table 3−4 shows the s,e, and f values for special single-precision floating-
point numbers.
Table 3−4. Special Single-Precision Values
Symbol Sign (s) Exponent (e) Fraction (f)
+0 0 0 0
−0 1 0 0
+Inf 0 255 0
−Inf 1 255 0
NaN x 255 nonzero
QNaN x 255 1xx..x
SNaN x 255 0xx..x and nonzero