Overview of IEEE Standard Single- and Double-Precision Formats
Instruction Set3-12 SPRU733
Table 35 shows hexadecimal and decimal values for some single-precision
floating-point numbers.
Figure 32 shows the fields of a double-precision floating-point number repre-
sented within a pair of 32-bit registers.
Table 35. Hexadecimal and Decimal Representation for Selected Single-Precision Values
Symbol Hex Value Decimal Value
NaN_out 7FFFFFFF QNaN
0 00000000 0.0
0 80000000 0.0
1 3F800000 1.0
2 40000000 2.0
LFPN 7F7FFFFF 3.40282347e+38
SFPN 00800000 1.17549435e38
LDFPN 007FFFFF 1.17549421e38
SDFPN 00000001 1.40129846e45
Figure 32. Double-Precision Floating-Point Fields
31
e
20 19 0 31 0
30
s
Odd register Even register
ff
Legend: s sign bit (0 = positive, 1 = negative)
e 11-bit exponent ( 0 < e < 2047)
f 52-bit fraction
0 < f < 1*21 + 1*22 + ... + 1*252 or
0 < f < ((252)1)/(252)
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.