Concurrent detection of additive overflow and arithmetic errors in residue codes

Abstract

The problems of detecting overflow and single or multiple residue digit errors in Redundant Residue Numeber Systems are considered through an unified approach. It is shown that a single intermodular procedure allows concurrent detection of additive overflow and single residue digit error, even in the case where the error affects a number in overflow. In addition, it is shown that codes of adequate redundancy may allow detection of additive overflow and single bit error, provided that the residue digits are appropriately encoded. The discussion concerns both separate residue codes (i. e., codes being referred to as RRNS, where one or more redundant residues are added) and Product Codes.