On Building General Modular Adders from Standard Binary Arithmetic Components

Abstract—We introduce an excess-δ representation of residues for residue number system (RNS) arithmetic, in which a flag bit selects one or the other subrange within the full range of n-bit values. We show that our special representation leads to simple modular arithmetic with arbitrary moduli, while using standard arithmetic components such as carry-save and carry-propagate adders that have been extensively optimized for area, power, and a host of other composite figures of merit. Further advantages of a unified treatment, as opposed to a multiplicity of specialized schemes previously proposed in connection with particular classes of moduli such as 2 � �1 and 2 � �2 � �1, include simplified design process, verification, testing, and fault tolerance. Both gate-level analyses and VLSI synthesis results point to advantages in latency, area, and/or power compared with other proposed designs in the literature. 1