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Residue-To-Decimal Conversion with Overflow Detection for a Moduli Set of the Form

by Mohammed I. Daabo
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International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 185 - Number 11
Year of Publication: 2023
Authors: Mohammed I. Daabo
10.5120/ijca2023922782

Mohammed I. Daabo . Residue-To-Decimal Conversion with Overflow Detection for a Moduli Set of the Form. International Journal of Computer Applications. 185, 11 ( May 2023), 18-23. DOI=10.5120/ijca2023922782

@article{ 10.5120/ijca2023922782,
author = { Mohammed I. Daabo },
title = { Residue-To-Decimal Conversion with Overflow Detection for a Moduli Set of the Form },
journal = { International Journal of Computer Applications },
issue_date = { May 2023 },
volume = { 185 },
number = { 11 },
month = { May },
year = { 2023 },
issn = { 0975-8887 },
pages = { 18-23 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume185/number11/32744-2023922782/ },
doi = { 10.5120/ijca2023922782 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-07T01:25:50.314682+05:30
%A Mohammed I. Daabo
%T Residue-To-Decimal Conversion with Overflow Detection for a Moduli Set of the Form
%J International Journal of Computer Applications
%@ 0975-8887
%V 185
%N 11
%P 18-23
%D 2023
%I Foundation of Computer Science (FCS), NY, USA
Abstract

Reverse Conversion and Overflow Detection are some of the limiting factors that affect the full implementation of RNS-Based processors in general purpose computing. In this paper, a novel Reverse Converter with overflow detection scheme has been proposed. The Algorithm utilizes the Remainder Theorem and has the property that for any given moduli set { m_(1 ) 〖,m〗_(2 ) 〖,m〗_3 } , the residue number ( x_1 〖,x〗_2 〖,x〗_3 ) can be converted into their decimal equivalent X using m_1 α+x_1, |m_1 α+x_1 |_(m_2 )= x_2 and |m_1 α+x_1 |_(m_3 )= x_3 for α = 0, 1, 2, 3, …. The Algorithm detects overflow in RNS operations if m_1 α+x_1≥M. The Algorithm was fully implemented on both moduli sets with common factors and moduli sets with non-coprime factors. Theoretical analysis and simulated results showed that the architecture is built with lesser hardware and has low delay.

References
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Index Terms

Computer Science
Information Sciences

Keywords

Residue Number System Reverse Converter Remainder Theorem Overflow Detection MRC CRT.

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