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63
62
s
Figure 6.2 Format of Double-Precision Floating-Point Number
The exponent is expressed in biased form, as follows:
e = E + bias
The range of unbiased exponent E is E
distinguished as follows. E
denormalized number, and E
Table 6.1 shows bias, E
Table 6.1
Floating-Point Number Formats and Parameters
Parameter
Total bit width
Sign bit
Exponent field
Fraction field
Precision
Bias
E
max
E
min
Floating-point number value v is determined as follows:
+ 1 and f ≠ 0, v is a non-number (NaN) irrespective of sign s
If E = E
max
If E = E
+ 1 and f = 0, v = (–1)
max
≤ E ≤ E
If E
min
max
– 1 and f ≠ 0, v = (–1)
If E = E
min
If E = E
– 1 and f = 0, v = (–1)
min
Table 6.2 shows the ranges of the various numbers in hexadecimal notation.
Rev. 2.0, 03/99, page 118 of 396
52 51
e
– 1 to E
min
– 1 indicates zero (both positive and negative sign) and a
min
+ 1 indicates positive or negative infinity or a non-number (NaN).
max
, and E
values.
min
max
Single-Precision
32 bits
1 bit
8 bits
23 bits
24 bits
+127
+127
–126
s
(infinity) [positive or negative infinity]
s
E
, v = (–1)
2
(1.f) [normalized number]
s
Emin
2
s
0 [positive or negative zero]
+ 1. The two values E
max
Double-Precision
64 bits
1 bit
11 bits
52 bits
53 bits
+1023
+1023
–1022
(0.f) [denormalized number]
f
– 1 and E
min
0
+ 1 are
max
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