Improved Method of Determining the Alternative Set of Numbers in Residue Number System

Abstract

The article analyzes the most well-known practical methods of determining the alternative set (AS) of numbers in a residue numeral system (RNS). The AS determining is most frequently required to perform error verification, diagnosing and correction of data in RNS, that was introduced to a minimal information redundancy in the computational process dynamics. This suggests the occurrence of only a single error in a number. The main downside of the reviewed methods is a significant time needed to determine the AS. In order to reduce time for AS determining in RNS, one of the known methods has been improved in the article. The idea of method improvement supposes preliminary correspondence table compilation (first stage tables) for each correct number out of informational numeric range of a possible set of incorrect numbers, that are not included into the range. Based on the analysis of tables content, the second stage table is being compiled, which contains the correspondence of each incorrect number out of numeric range to a possible values of correct numbers. By applying introduced method, efficiency of data verification, diagnosing and correction is increased due to time reduction of the AS numbers determining in RNS.