Intel 64 and IA-32 Architectures Software Developers Manual Volume 1, Basic Architecture

4-8 Vol. 1
DATA TYPES
The exponent of each floating-point data type is encoded in biased format; see
Section 4.8.2.2, “Biased Exponent.” The biasing constant is 127 for the single-
precision format, 1023 for the double-precision format, and 16,383 for the double
extended-precision format.
Table 4-3. Floating-Point Number and NaN Encodings
Class Sign Biased Exponent Significand
Integer
1
Fraction
Positive +∞ 0 11..11 1 00..00
+Normals 0
.
.
0
11..10
.
.
00..01
1
.
.
1
11..11
.
.
00..00
+Denormals 0
.
.
0
00..00
.
.
00..00
0
.
.
0
11.11
.
.
00..01
+Zero 0 00..00 0 00..00
Negative −Zero 1 00..00 0 00..00
−Denormals 1
.
.
1
00..00
.
.
00..00
0
.
.
0
00..01
.
.
11..11
−Normals 1
.
.
1
00..01
.
.
11..10
1
.
.
1
00..00
.
.
11..11
−∞ 1 11..11 1 00..00
NaNs SNaN X 11..11 1 0X..XX
2
QNaN X 11..11 1 1X..XX
QNaN
Floating-Point
Indefinite
1 11..11 1 10..00
Single-Precision:
Double-Precision:
Double Extended-Precision:
← 8 Bits →
← 11 Bits →
←
15 Bits →
←
23 Bits →
← 52 Bits →
←
63 Bits →
NOTES:
1. Integer bit is implied and not stored for single-precision and double-precision formats.
2. The fraction for SNaN encodings must be non-zero with the most-significant bit 0.