Efficient Modular Binary Signed-Digit Multiplier for the moduli set {(2^n) -1, 2^n, (2^n) +1}

Efficient Modular Binary Signed-Digit Multiplier for the moduli set {(2^n) -1, 2^n, (2^n) +1}

Maryam Saremi, Somayeh Timarchi

Abstract

Arithmetic operations on Binary Signed-Digit (BSD) number system are performed in a constant time due to the carry free addition capability in redundant number system. Applying BSD number representation to Residue Number System (RNS) leads to a number system called BSD-RNS. There are three BSD-RNS encodings: 2’s complement, 1-out-of-3, and posibit-negabit. Up to now, BSD-RNS multipliers with 2’s complement and 1-out-of-3 encoding have been reported in the related literatures. In this work, we propose posibit-negabit BSDRNS multiplier for the moduli set {2^n-1, 2^n, 2^n+1}. Afterwards, we compare it to the existing BSD-RNS multipliers. Synthesis results show that the proposed architecture is more efficient than the two existing BSD-RNS multipliers from the viewpoint of delay, area, and power consumption.

Keywords

Digital Computer Arithmetic, Residue Number System (RNS), Binary Signed-Digit (BSD) Number Representation, Carry Free Addition, Modular Multiplier