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

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DRAFT IEEE Standard for Floating-Point Arithmetic – 2003 August 12 10:20 However, the decimal exponents do not satisfy the recommendation that “b (emax + emin +1) is the smallest integral power of b that is >= 4.” -JDD] 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. Page 20
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. Page 21
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DRAFT IEEE Standard for Binary Floating-Point Arithmetic - Sonic.net

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