On the Design of Modulo Arithmetic Units Based on Cyclic Groups

Stephen S. Yau, Jackson Chung

Research output: Contribution to journalArticle

6 Scopus citations

Abstract

Many of the modulo arithmetics can be considered as cyclic groups. A generalized method for implementing the cyclic groups is established based on a decomposed mapping approach. In order to obtain efficient implementation of cyclic groups, certain mapping relations and a proper binary encoding method are investigated. Furthermore, a new class of code, called the circulative code, is developed, and two methods for generating such a code are presented. Various modulo arithmetic units can then be easily designed through a unique formula and can also be machine implemented. The modulo arithmetic units using this design approach are usually simpler than those conventional ones.

Original languageEnglish (US)
Pages (from-to)1057-1067
Number of pages11
JournalIEEE Transactions on Computers
VolumeC-25
Issue number11
DOIs
StatePublished - Nov 1976
Externally publishedYes

Keywords

  • Binary encoding
  • arithmetics
  • cyclic groups
  • design
  • modulo
  • modulo arithmetic units
  • residue number system

ASJC Scopus subject areas

  • Software
  • Theoretical Computer Science
  • Hardware and Architecture
  • Computational Theory and Mathematics

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