The number rank of residue number system and its properties

Abstract

The residue number system is widely used in systems using addition and multiplication operations to increase their performance. However, operations such as converting numbers to and from the reside number system, the sign detection, and the numbers comparison are computationally complex in the residue number system and limit its practical application.The article presents the methods for calculating the number rank to the implementation of the reverse conversion operation of numbers from the residue number system to the positional number system. The possibility of representing the core function as an algebraic polynomial over ZP for efficient calculation of the number rank is investigated. The article develops methods for calculating the number rank by an approximate method. The accuracy of calculations for the approximate method was assessed.