Computation of positional characteristics of numbers in RNS based on approximate method

Abstract

Residue number system (RNS) can be emphasized among contemporary nonpositional number systems. Its features and nonpositional structure of calculations made it an effective tool for solving a number of resource-consuming tasks, such as digital signal processing, cryptography and so on. An important RNS feature is the ability to parallelize operations, that makes it effective when implemented in FPGA. However, positional calculations in RNS are difficult. An important task is to choose an algorithm to compute positional characteristics of numbers in RNS that would work quickly and require little resources. This paper proposes a method of calculating the approximate positional characteristics in order to compare and restore the positional notation of the numbers in RNS. The proposed technique is analyzed in terms of the required accuracy and applicability and compared with the known counterparts