Generalized Signed-Digit Number Systems: A Unifying Framework for Redundant Number Representations
IEEE Transactions on Computers
CSC '90 Proceedings of the 1990 ACM annual conference on Cooperation
Exponentiation using canonical recoding
Theoretical Computer Science
Computer arithmetic: algorithms and hardware designs
Computer arithmetic: algorithms and hardware designs
Signed Digit Addition and Related Operations with Threshold Logic
IEEE Transactions on Computers
Optical Computing: An Introduction
Optical Computing: An Introduction
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Symbolic substitution, a parallel processing technique, has been proposed in computing literature to perform fast, carry-free addition of numbers. Several algorithms and corresponding symbolic substitution tables have been developed for addition of two numbers represented in binary, modified signed digit (MSD), and canonical modified signed digit (CMSD) number systems. In this paper, however, we present a new symbolic substitution based algorithm and corresponding substitution table for the addition of two numbers represented in canonical modified signed digit (CMSD) notation. In contrast with the existing algorithm in this regard, that derives the addition result in MSD system, our algorithm derives the result in CMSD notation and thus it could be employed to perform symbolic substitution based associative addition of a set of CMSD numbers.