Residue arithmetic circuits using a signed-digit number representation

Abstract

A new concept on residue arithmetic using a radix-2 signed-digit (SD) number representation is presented, by which memoryless residue arithmetic circuits using SD adders can be implemented. For a given modulus m, 2/sup p/-1/spl les/m/spl les/2/sup p/+2/sup p-1/-1, in a residue number system (RNS), the modulo m addition is performed by using two p-digit SD adders. Thus, the module m addition time is independent of the word length of operands. When m=2/sup p/ or m=2/sup p//spl plusmn/1, especially, the module m addition is implemented by only using one SD adder. Moreover, a module m multiplier can be constructed using a binary modulo m SD adder tree, so that the modulo m multiplication can be performed in a time proportional to log/sub 2/p.