Overview of IEEE Standard Single- and Double-Precision Formats
Instruction Set
3-12
SPRU733
Table 3
−
5 shows hexadecimal and decimal values for some single-precision
floating-point numbers.
Figure 3
−
2 shows the fields of a double-precision floating-point number repre-
sented within a pair of 32-bit registers.
Table 3
−
5. Hexadecimal and Decimal Representation for Selected Single-Precision Values
Symbol
Hex Value
Decimal Value
NaN_out
7FFF FFFF
QNaN
0
0000 0000
0.0
−
0
8000 0000
−
0.0
1
3F80 0000
1.0
2
4000 0000
2.0
LFPN
7F7F FFFF
3.4038
SFPN
0080 0000
1.17549435e
−
38
LDFPN
007F FFFF
1.17549421e
−
38
SDFPN
0000 0001
1.40129846e
−
45
Figure 3
−
2. Double-Precision Floating-Point Fields
31
e
20 19
0 31
0
30
s
Odd register
Even register
f
f
Legend
: s
sign bit (0 = positive, 1 = negative)
e
11-bit exponent ( 0 < e < 2047)
f
52-bit fraction
0 < f < 1*2
−
1
+ 1*2
−
2
+ ... + 1*2
−
52
or
0 < f < ((2
52
)
−
1)/(2
52
)
The floating-point fields represent floating-point numbers within two ranges:
normalized (e is between 0 and 2047) and denormalized (e is 0). The following
formulas define how to translate the s, e, and f fields into a double-precision
floating-point number.