New Reverse Conversion for Four-Moduli Set and Five-Moduli Set

Abstract

Most reverse conversions in Residue Number Systems (RNS) are based on the Chinese Remainder Theorem (CRT) and the Mixed Radix Conversion (MRC). The complexity of the circuitry of the CRT is high due to the large modulo-M operation. The MRC has a simple circuitry but it's a sequential process in nature. The purpose of this research is to obtain an efficient reverse conversion method to reduce the computational overhead found in the conventional reverse conversion algorithms. In this paper, new algorithms for reverse conversion in RNS for four-moduli set and five-moduli set have been proposed and their correctness evaluated. Numerical evaluations to ascertain the correctness and simplicity of the algorithm have been presented. These algorithms have fewer multiplicative index operations than those in the conventional CRT and MRC. The large modulo-M operation has been eliminated which reduces the computational overhead.

An Efficient Parallel Reverse Conversion of Residue Code to Mixed-Radix Representation Based on the Chinese Remainder Theorem

“…Some reverse conversion methods use the special moduli sets with a limited number of moduli, such as [ 2 , 8 , 35 , 36 , 37 , 38 , 39 , 40 ]. Their main drawback consists in a small number of the selected moduli, typically from three to five.…”

Enhanced Local Binary Pattern Algorithm for Facial Recognition Using Chinese Remainder Theorem

“…Currently, available conversion algorithms are based on the Chinese Remainder Theorem or the Mixed Radix conversion techniques (Salifu, 2021). Chinese Remainder Theorem (CRT) is a proposition of number theory that expresses that if one knows the remainders of the Euclidean division of an integer n by several integers, then one can establish distinctively the remainder of the division of n by the product of these integers, under the condition that the divisors are pairwise coprime (Madandola&Gbolagade, 2019).According to (Salifu, 2021).…”

“…Currently, available conversion algorithms are based on the Chinese Remainder Theorem or the Mixed Radix conversion techniques (Salifu, 2021). Chinese Remainder Theorem (CRT) is a proposition of number theory that expresses that if one knows the remainders of the Euclidean division of an integer n by several integers, then one can establish distinctively the remainder of the division of n by the product of these integers, under the condition that the divisors are pairwise coprime (Madandola&Gbolagade, 2019).According to (Salifu, 2021). CRT can be expressed as: Given the moduli set {n1, n2, n3, ⋯, nm} with the dynamic range N = and the RNSrepresentation of an integer X be represented as Liangliang et al, (2021) presented An Enhanced Multiscale Block LBP (MB-LBP) Three-Dimensional (3D) Face Recognition Method to improve the accuracy and speed of 3D face identification.…”