The New proposed Non-Coprime moduli set using forward conversion in Residue Number System : Mathematical Proof

ANDRAWS, SWIDAN and MANSOUR, BADER (2017) The New proposed Non-Coprime moduli set using forward conversion in Residue Number System : Mathematical Proof. In: Sixth International Conference on Advances in Computing, Electronics and Communication - ACEC 2017, 09-10 December, 2017, Rome, Italy.

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Abstract

In this paper a mathematical proof of the new Binary-to-RNS Non-Coprime moduli set in RNS [1] of the form { 2n - 2, 2n, 2n + 2 } is presented. The modulies 2n - 2, 2n + 2 are known to be called conjugates of each other and has been discussed in previous literature [1 - 4]. Co-prime moduli sets are known to offer these benefits: 1) Large dynamic ranges. II) Fast RNS arithmetic. III) Simple and efficient RNS processing hardware. IV) Efficient weighted-to-RNS and RNS-to-Weighted converters. When comparing the Non-Coprime ones to them the DR (Dynamic Range) is the dominant. The dynamic range achieved by the set above is defined by the least common multiple ( LCM ) of the moduli and the non-coprime set was carefully chosen to do the mathematical calculations upon. This new non-coprime moduli set is unique and the only one of its shape.

Item Type: Conference or Workshop Item (Paper)
Uncontrolled Keywords: ALGORITHM, ARITHMETIC, DYNAMIC RANGE, FORWARD CONVERSION, RNS
Depositing User: Mr. John Steve
Date Deposited: 10 Mar 2019 09:30
Last Modified: 10 Mar 2019 09:30
URI: http://publications.theired.org/id/eprint/288

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