Issue No. 04 - April (1983 vol. 32)

ISSN: 0018-9340

pp: 359-369

null Shauchi Ong , IBM T. J. Watson Research Center

ABSTRACT

This paper describes aspects of an arithmetic design system (ADS) to support the quantitative evaluation of alternate number systems with respect to a given application and realization technology. In computer arithmetic we are concerned with establishing a correspondence between abstract quantities (numbers) and some physical representation (symbols), and with simulating the operations on these symbols. The ADS is intended to help study the cost and performance of alternate simulations. A finite number system is a triple consisting of a symbol set (elements are called "digit-vectors"), an interpretation set, a mapping between these two sets, and a set of operators (digit-vector algorithms) defined on its symbol set. A set of these digit vector algorithms are proposed for conducting arithmetic design. A number system matrix defines the digit vector algorithm for numerous number systems and a method for computing time and space complexity of compositions of these algorithms is proposed. An example of how the system could be used to compare addition, with and without out-of-range detection, for three number systems is given.

INDEX TERMS

time-space complexity, Arithmetic design language, arithmetic design system, number system, out-of-range detection, quantitative comparison

CITATION

null Shauchi Ong, D.E. Atkins, "A Basis for the Quantitative Comparison of Computer Number Systems",

*IEEE Transactions on Computers*, vol. 32, no. , pp. 359-369, April 1983, doi:10.1109/TC.1983.1676237