A New Algorithm to Compare the Magnitude of Two RNS Numbers

TL;DR

This paper introduces a novel clustering-based algorithm for comparing the magnitude of two numbers in Residue Number Systems (RNS), avoiding conversion to binary and enhancing comparison efficiency.

Contribution

It proposes a new RNS comparison algorithm utilizing clustering, which improves comparison without binary conversion, a novel approach in RNS systems.

Findings

The algorithm accurately compares RNS numbers' magnitudes.

It operates efficiently without binary conversion.

The method is applicable to various RNS configurations.

Abstract

Comparison of two numbers in RNS systems is a challenging task. In this paper, a new algorithm to compare the magnitude of two RNS numbers, using a clustering method has been proposed. In the clustering process, each inputted number is assigned to a cluster. To compare the magnitude of two numbers, first the clusters of these numbers and their differences are obtained. Then by comparing these clusters, the relative magnitude of two numbers is determined. All of these processes are performed in RNS system without converting numbers to the binary system.