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Floating-point number representations: base choice versus exponent range.

Author: Paul Richman; STANFORD UNIV CALIF Dept. of COMPUTER SCIENCE.
Publisher: Ft. Belvoir Defense Technical Information Center 28 APR 1967.
Edition/Format:   Print book : English
Database:WorldCat
Summary:
A digital computer whose memory words are composed of r-state devices is considered. The choice of the base, beta, for the internal floating-point numbers on such a computer is discussed. Larger values of beta necessitate the use of more r-state devices for the mantissa, in order to preserve some 'minimum accuracy, ' leaving fewer r-state devices for the exponent of beta. As beta increases, the exponent range may  Read more...
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Document Type: Book
All Authors / Contributors: Paul Richman; STANFORD UNIV CALIF Dept. of COMPUTER SCIENCE.
OCLC Number: 227446902
Notes: Supported in part by NSF.
Description: 38 pages

Abstract:

A digital computer whose memory words are composed of r-state devices is considered. The choice of the base, beta, for the internal floating-point numbers on such a computer is discussed. Larger values of beta necessitate the use of more r-state devices for the mantissa, in order to preserve some 'minimum accuracy, ' leaving fewer r-state devices for the exponent of beta. As beta increases, the exponent range may increase for a short period, but it must ultimately decrease to zero. Of course, this behavior depends on what definition of accuracy is used. This behavior is analyzed for a recently proposed definition of accuracy which specifies when it is to be said that the set of q-digit base beta floating-point numbers is accurate to p-digits base t. The only case of practical importance today is t = 10 and r = 2; and in this case beta = 2 is always best. However, the analysis is done to cover all cases. (Author).

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