DRAFT IEEE Standard for Binary Floating-Point Arithmetic - Sonic.net

DRAFT IEEE Standard for Floating-Point Arithmetic – 2003 August 12 10:20
3.2. Basic Binary Format Encodings
Each representable nonzero numerical value has just one encoding in a basic
binary format. To make the encoding unique, in terms of the parameters in section
3.1, the value of the significand m is maximized by decreasing the exponent value
until either the exponent is emin or m >= 2 p−1 . After this normalization process
is done, if the exponent is emin and m < 2 p−1 , the value is subnormal. Subnormal
numbers (and zero) are encoded with a reserved biased exponent value.
Numbers in the binary formats are encoded in the following three fields as shown
in Fig. 1-2:
1. 1-bit sign S
2. w-bit biased exponent E = e + bias
3. t = p−1 -bit trailing significand T = d 1 d 2 ... d p–1 ; the leading bit of
the logical significand, d 0 , is implicitly encoded in the exponent E.
Figure 1-2 Basic Binary Floating-Point Format §UF
width 1 bit w bits t = p–1 bits
field sign S biased
exponent E
trailing significand T
most/least
significant
bit
most.......least
E 0....................... E w-1
most...........................least
d 1.......................................................... d p-1
The values of w, bias, and t for the basic binary formats are listed in Table 1b.
The range of the representation's biased exponent E shall include:
• Every integer between the 1 and 2 w − 2, inclusive, to encode normal values
• The reserved value 0 to encode ± 0 and subnormal numbers
Copyright © 2003 by the Institute of Electrical and Electronics Engineers, Inc. This document is an unapproved
draft of a proposed IEEE-SA Standard - USE AT YOUR OWN RISK. See statement on page 1.
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