Method for Determining the Sign in the Residue Number System Based on the Chinese Theorem on Fractional Remainders

Abstract

Determining the sign of a number is one of the key problems solved in the residue number system. This operation is important because it serves as a basis for implementing more complex calculations, such as comparing numbers and division. Traditional approaches use specially selected sets of modules, which limits their application to certain cases. In this paper, a new algorithm for determining the sign of a number in the residue number system is proposed, based on the application of the Chinese theorem on fractional remainders. The developed method ensures the execution of the operation without the need to select special modules, which makes it more universal. The results of software modeling showed that the proposed algorithm has higher performance compared to the existing method using fast transformation in the generalized positional number system. This allows applying the proposed solution in various types of residue number system, including digital signal processing problems.