Residue arithmetic circuits based on the signed-digit multiple-valued arithmetic circuits

Multiple-valued residue arithmetic circuits using integers 4^p and 4^p±1 as moduli of residue number system (RNS) are presented. Conventional residue arithmetic circuits have been designed using binary number arithmetic system, but the carry propagation arises which limits the speed of arithmetic operations in residue modules. In this paper, a radix-4 signed-digit (SD) number system is introduced, and the compact SD adder based on the multiple-valued current-mode circuits is applied for the implementation of high-speed and compact residue arithmetic circuits. The modulo m addition, m=4^p or m=4^p±1, can be performed by an SD adder or an end-around-carry SD adder with the multiple-valued circuits and the addition time was independent of the word length of operands. Modulo m multiplier can be compactly constructed using a binary modulo m SD adder tree based on the multiple-valued addition circuits, and the modulo m multiplication can be performed in a time proportional to log₂p