On building general modular adders from standard binary arithmetic components

We introduce an excess-δ residue representation 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 new representation leads to simple modular arithmetic with arbitrary residues, 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 2ⁿ ± 1 and 2ⁿ - 2^k ± 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.