Addition and Subtraction in the Residue Number System

Improved residue expression and new arithmetic algorithms for addition and subtraction are proposed. In the proposed system positive and negative integers of any magnitude can be handled regardless of the particular choice of the set of relatively prime bases. And such problems as difficulties in overflow detection, handling of sign change in subtraction, or complementation of negative numbers do not exist in the proposed system as far as addition and subtraction are concerned. The difficult problem itself of magnitude comparison in the residue system, however, still remains to be attacked. The proposed system assumes existence of an I/O unit, independent of the residue mode computer, for the purpose of the necessary conversions before and after the computation. Basic properties of the proposed arithmetic algorithms are also derived.