skip to main content
10.1145/1457838.1457864acmconferencesArticle/Chapter ViewAbstractPublication PagesafipsConference Proceedingsconference-collections
research-article
Free access

The residue number system

Published: 03 March 1959 Publication History

Abstract

In this paper we develop and investigate the properrties of a novel system, called the residue code or residue number system. The residue number system is of particular interest because the arithmetic operations of addition and multiplication may be executed in the same time as required for an addition operation. The main difficulty of the residue code relative to arithmetic operations is the determination of the relative magnitude of two numbers expressed in the residue code. The residue code is probably of little utility for general-purpose computation, but the code has many characteristics which recommend its use for special-purpose computations.

References

[1]
fr1 G. H. Hardy and E. M. Wright, "An Introduction to the Theory of Numbers," Oxford University Press, London, Eng.; 1956.
[2]
fr2 L. E. Dickson, "Modern Elementary Theory of Numbers," University of Chicago Press, Chicago, Ill., p. 16; 1939.
[3]
fr3 H. L. Garner, "Error Checking and the Structure of Binary Addition," Ph.D. dissertation, University of Michigan, Ann Arbor, pp. 105-140; 1958.
[4]
fr4 M. Valach, "Vznik kodu a ciselne soustavy zbytkovych trid," Stroje Na Zpracovani Informaci, Sbornik III; 1955.
[5]
fr5 A. Svoboda and M. Valach, "Operatorove obvody," Stroje Na Zpracovani Informaci, Sbornik III; 1955.
[6]
fr6 A. Svoboda, "Rational numerical system of residual classes," Stroje Na Zpracovani Informaci, Sbornik V; 1957.

Cited By

View all
  • (2025)Development and Realization of an FIR Filter Utilizing an Innovative RNS Form with a Dual Modular SetBroadband Communications, Networks, and Systems10.1007/978-3-031-81168-5_28(302-309)Online publication date: 7-Feb-2025
  • (2025)Enhancing Finite Impulse Response (FIR) Filtering with Distributive Arithmetic (DA) and Residue Number System (RNS) OptimizationBroadband Communications, Networks, and Systems10.1007/978-3-031-81168-5_25(272-281)Online publication date: 7-Feb-2025
  • (2024)TPU as Cryptographic AcceleratorProceedings of the International Workshop on Hardware and Architectural Support for Security and Privacy 202410.1145/3696843.3696844(37-44)Online publication date: 2-Nov-2024
  • Show More Cited By

Recommendations

Comments

Information & Contributors

Information

Published In

cover image ACM Conferences
IRE-AIEE-ACM '59 (Western): Papers presented at the the March 3-5, 1959, western joint computer conference
March 1959
391 pages
ISBN:9781450378659
DOI:10.1145/1457838
  • Conference Chair:
  • R. R. Johnson
Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

Sponsors

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 03 March 1959

Permissions

Request permissions for this article.

Check for updates

Qualifiers

  • Research-article

Contributors

Other Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

  • Downloads (Last 12 months)884
  • Downloads (Last 6 weeks)87
Reflects downloads up to 16 Feb 2025

Other Metrics

Citations

Cited By

View all
  • (2025)Development and Realization of an FIR Filter Utilizing an Innovative RNS Form with a Dual Modular SetBroadband Communications, Networks, and Systems10.1007/978-3-031-81168-5_28(302-309)Online publication date: 7-Feb-2025
  • (2025)Enhancing Finite Impulse Response (FIR) Filtering with Distributive Arithmetic (DA) and Residue Number System (RNS) OptimizationBroadband Communications, Networks, and Systems10.1007/978-3-031-81168-5_25(272-281)Online publication date: 7-Feb-2025
  • (2024)TPU as Cryptographic AcceleratorProceedings of the International Workshop on Hardware and Architectural Support for Security and Privacy 202410.1145/3696843.3696844(37-44)Online publication date: 2-Nov-2024
  • (2024)Photonics Multiply-Accumulation Computations System Based on Residue ArithmeticACS Photonics10.1021/acsphotonics.3c0170411:4(1540-1547)Online publication date: 6-Apr-2024
  • (2024)An Approximate Algorithm for Determining the Sign Function of a Number Using Neural Network MethodsAISMA-2023: International Workshop on Advanced Information Security Management and Applications10.1007/978-3-031-77229-0_25(247-255)Online publication date: 17-Nov-2024
  • (2024)Modification and Adaptation of Methods and Algorithms of the Active Security Concept for Fog SystemsAISMA-2024: International Workshop on Advanced Information Security Management and Applications10.1007/978-3-031-72171-7_28(277-285)Online publication date: 16-Oct-2024
  • (2024)Method for Detecting and Correcting Errors in Arithmetic Operations Based on Rank of a NumberCurrent Problems of Applied Mathematics and Computer Systems10.1007/978-3-031-64010-0_11(105-114)Online publication date: 2-Sep-2024
  • (2023)Fast Operation of Determining the Sign of a Number in RNS Using the Akushsky Core FunctionComputation10.3390/computation1107012411:7(124)Online publication date: 28-Jun-2023
  • (2023)Algorithm for Determining the Optimal Weights for the Akushsky Core Function with an Approximate RankApplied Sciences10.3390/app13181049513:18(10495)Online publication date: 20-Sep-2023
  • (2023)A Generalized Residue Number System Design Approach for Ultralow-Power Arithmetic Circuits Based on Deterministic Bit-StreamsIEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems10.1109/TCAD.2023.325060342:11(3787-3800)Online publication date: Nov-2023
  • Show More Cited By

View Options

View options

PDF

View or Download as a PDF file.

PDF

eReader

View online with eReader.

eReader

Login options

Figures

Tables

Media

Share

Share

Share this Publication link

Share on social media