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 module m multiplier is constructed using a binary modulo m SD adder tree. The implementation for the residue arithmetic circuits with VHDL description is proposed. The module m adders and multipliers have about 530 and 5000 gates, respectively, in cases of m=2¹⁶±1