Intel ITANIUM ARCHITECTURE - SOFTWARE DEVELOPERS MANUAL VOLUME 1 REV 2.3 Manual page 1778

Figure 4-9.
Table 4-1
floating-point format. The table lists a progression of real number notations that leads
to the format that the processor uses. In this format, the binary real number is
normalized and the exponent is biased.
Table 4-1.
Ordinary Decimal
Scientific Decimal
Scientific Binary
Scientific Binary
(Biased Exponent)
Single Format (Normalized)
4.7.1.2 Normalized Numbers
In most cases, the processor represents real numbers in normalized form. This means
that except for zero, the significand is always made up of an integer of 1 and the
following fraction:
For values less than 1, leading zeros are eliminated. (For each leading zero eliminated,
the exponent is decremented by one.)
Representing numbers in normalized form maximizes the number of significant digits
that can be accommodated in a significand of a given width. To summarize, a
normalized real number consists of a normalized significand that represents a real
number between 1 and 2 and an exponent that specifies the number's binary point.
4.7.1.3 Biased Exponent
The processor represents exponents in a biased form. This means that a constant is
added to the actual exponent so that the biased exponent is always a positive number.
The value of the biasing constant depends on the number of bits available for
representing exponents in the floating-point format being used. The biasing constant is
chosen so that the smallest normalized number can be reciprocated without overflow.
4:476
Binary Floating-point Format
Sign
Exponent
Integer or J-Bit
shows how the real number 178.125 (in ordinary decimal format) is stored in
Real Number Notation
Notation
178.125
1 78125E
.
1 0110010001E
.
1 0110010001E

Sign
0
Significand
Fraction
Value
2
10
111
2
10000110
2
Biased Exponent
10000110
1.fff...ff
Volume 4: IA-32 SSE Instruction Reference
Significand
01100100010000000000000
1 (Implied)