Features of machine arithmetics of high-performance modular computing structures

Authors

  • Alexander F. Chernyavsky A. N. Sevchenko Institute of Applied Physical Problems, Belarusian State University, 7 Akademika Kurchatava Street, Minsk 220045, Belarus
  • Elena I. Kozlova A. N. Sevchenko Institute of Applied Physical Problems, Belarusian State University, 7 Akademika Kurchatava Street, Minsk 220045, Belarus
  • Andrey A. Kolyada A. N. Sevchenko Institute of Applied Physical Problems, Belarusian State University, 7 Akademika Kurchatava Street, Minsk 220045, Belarus

Keywords:

modular arithmetics, minimally redundant modular code, integral characteristics of minimally redundant modular code
Supporting Agencies
This work was supported by the state programme of scientific research «Digital and space technologies, security of society and the state» (subprogramme «Digital technologies and space informatics», assignment 5.1.6.3).

Abstract

The procedures for generating a modular code for various variants of modular number systems are herein considered. The features of machine arithmetic of the basic integral characteristics of the modular code are noted. Proof of the theorem on minimally redundant modular coding is proposed as an effective way to reduce the time of computing the integral characteristics of a modular code. It is shown that the introduction of minimal redundancy into a modular code greatly simplifies the calculation of interval-index characteristics and related forms of representing integers when implementing a number of non-modular operations. We noted a certain decrease in the efficiency of minimally redundant modular number systems if the number of integral characteristics of the modular code, the sign of the number or digits of the polyadic code increases in the used applications. This circumstance does not reduce the expediency of using minimally redundant modular number systems in a wide range of applications of minimally redundant modular arithmetics, including digital signal processing, information security, information technology, etc.

Author Biographies

  • Alexander F. Chernyavsky, A. N. Sevchenko Institute of Applied Physical Problems, Belarusian State University, 7 Akademika Kurchatava Street, Minsk 220045, Belarus

    doctor of science (engineering), academician of the National Academy of Sciences of Belarus, full professor; head of the laboratory of specialised computer systems

  • Elena I. Kozlova, A. N. Sevchenko Institute of Applied Physical Problems, Belarusian State University, 7 Akademika Kurchatava Street, Minsk 220045, Belarus

    PhD (physics and mathematics), docent; researcher at the laboratory of specialised computer systems

  • Andrey A. Kolyada, A. N. Sevchenko Institute of Applied Physical Problems, Belarusian State University, 7 Akademika Kurchatava Street, Minsk 220045, Belarus

    doctor of science (physics and mathematics); chief researcher at the laboratory of specialised computer systems

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Published

2023-08-18

Issue

No. 2 (2023): Journal of the Belarusian State University. Mathematics and Informatics

Section

Theoretical Foundations of Computer Science

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How to Cite

[1]
Chernyavsky, A.F. et al. 2023. Features of machine arithmetics of high-performance modular computing structures. Journal of the Belarusian State University. Mathematics and Informatics. 2 (Aug. 2023), 94–101. DOI:https://doi.org/10.33581/2520-6508-2023-2-94-101.