Residue arithmetic circuits based on signed-digit number representation and the VHDL implementation

Residue arithmetic circuits based on radix-2 signed-digit(SD) number representation, using integers 2(P) and 2(P) +/- 1 as moduli of residue number system(RNS)! are presented. The modulo m addition, m = 2(P) or m 2(P) +/- 1, is performed by a carry-free SD adder and the modulo m multiplier is constructed using a binary module Tn SD adder tree. The implementation for the residue arithmetic circuits with VHDL description is proposed. The modulo m adders and multipliers have about 530 and 5000 gates, respectively, in cases of m = 2(16) +/- 1.