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Automatic Control and Computer Sciences

, Volume 49, Issue 6, pp 354–365 | Cite as

Comparison of modular numbers based on the chinese remainder theorem with fractional values

  • N. I. Chervyakov
  • A. S. Molahosseini
  • P. A. Lyakhov
  • M. G. Babenko
  • I. N. Lavrinenko
  • A. V. Lavrinenko
Article

Abstract

New algorithms for determining the sign of a modular number and comparing numbers in a residue number system (RNS) have been developed using the Chinese remainder theorem with fractional values. These algorithms are based on calculations of approximate values of fractional values determined by moduli of the system. Instrumental implementations of the new algorithms are proposed and examples of their applications are given. Modeling these developments on Xilinx Kintex 7 FPGA showed that the proposed methods of decrease computational complexity of determining signs and comparing numbers in the RNS compared to that in well-known architectures based on the Chinese remainder theorem with generalized positional notation.

Keywords

residue number system Chinese remainder theorem modular arithmetic positional characteristic fractional values approximate method generalized positional notation 

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Copyright information

© Allerton Press, Inc. 2015

Authors and Affiliations

  • N. I. Chervyakov
    • 1
  • A. S. Molahosseini
    • 2
  • P. A. Lyakhov
    • 1
  • M. G. Babenko
    • 1
  • I. N. Lavrinenko
    • 1
  • A. V. Lavrinenko
    • 1
  1. 1.North Caucasus Federal UniversityStavropolRussia
  2. 2.Department of Computer EngineeringKerman Branch, Islamic Azad UniversityKermanIran

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