Generalised fault-tolerant stored-unibit-transfer residue number system multiplier for moduli set {2n−1, 2n, 2n+1}

Abstract

Residue number system (RNS) which utilises redundant encoding for the residues is called redundant residue number system (RRNS). It can accelerate multiplication which is a high-latency operation. Using stored-unibit-transfer (SUT) redundant encoding in RRNS called SUT-RNS has been shown as an efficient number system for arithmetic operation. Radix-2h SUT-RNS multiplication has been proposed in previous studies for modulo 2n−1, but it has not been generalised for each moduli lengths (n) and radix (r=2h). Also, SUT-RNS multiplication for modulo 2n+1 has not been discussed. In this study the authors remove these weaknesses by proposing general radix-2h SUT-RNS multiplication for the moduli set {2n−1, 2n, 2n+1}. Moreover, the authors demonstrate that our approach enables a unified design for the moduli set multipliers, which results in designing fault-tolerant SUT-RNS multipliers with low hardware redundancy. Results indicate that the proposed general SUT-RNS multiplier for the moduli set {2n−1, 2n, 2n+1} is a fast fault-tolerant multiplier which outperforms area, power and energy/operation of existing RRNS multiplier.