Maximally redundant high-radix Signed-Digit Residue Number System

Carry propagation is a main problem in Residue Number System (RNS) arithmetic. This overhead can be eliminated by using redundant number representation which results in Redundant Residue Number System (RRNS). The RRNS which uses Signed-Digit (SD) encoding (SD-RNS) has been shown as an efficient number system. However, SD-RNS cannot provide flexible trade-off between area and speed. To solve this problem, we first propose a novel RRNS in this paper, which uses high-radix signed-digit (HRSD) encoding which is called HRSD-RNS. Then, we propose an efficient adder for HRSD-RNS. The results indicate that the HRSD-RNS modulo 2n-1 and modulo 2n+1 adders outperform power and power-delay-product (PDP) of the existing RRNS adders. Moreover, we demonstrate how the proposed representation can be utilized to derive a unified design for the moduli set {2n-1, 2n, 2n+1}, which opens the possibility to design reliable RRNS processors with low hardware redundancy. In addition, the proposed structure can be employed in conjunction with any fast state of the art HRSD adder without requiring any extra hardware for modular addition.