Residue arithmetic with a signed-digit number system

A new concept in residue arithmetic based on a radix-2 signed-digit (SD) number system is presented, by which memoryless residue arithmetic circuits using SD adders can be implemented. Conventional residue arithmetic circuits have been designed using binary number arithmetic system, but carry propagation arises which limits the speed of arithmetic operations in residue modules. In this paper, a p-digit radix-2 SD number system is introduced to simplify the residue operation. For a given modulus m, 2p-1