Compact Residue Arithmetic Multiplier Based on the Radix-4 Signed-Digit Multiple-Valued Arithmetic Circuits

Shugang WEI  Kensuke SHIMIZU  

Publication
IEICE TRANSACTIONS on Electronics   Vol.E82-C   No.9   pp.1647-1654
Publication Date: 1999/09/25
Online ISSN: 
DOI: 
Print ISSN: 0916-8516
Type of Manuscript: Special Section PAPER (Special Issue on Integrated Electronics and New System Paradigms)
Category: Non-Binary Architectures
Keyword: 
residue number system,  signed-digit (SD) number representation,  end-around SD adder,  binary adder tree,  multiple-valued circuits,  

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Summary: 
A compact residue arithmetic multiplier based on the radix-4 signed-digit arithmetic is 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, two radix-4 signed-digit (SD) number representations, {-2,-1,0,1,2} and {-3,-2,-1,0,1,2,3}, are introduced. The former is used for the input and output, and the later for the inner arithmetic circuit of the presented multiplier. Integers 4p and 4p 1 are used as moduli of residue number system (RNS), where p is a positive integer and both circuits for partial product generation and sum of the partial products can be efficiently constructed by using the multiple-valued current-mode circuits. The modulo m addition, m=4p or m=4p 1, can be performed by an SD adder or an end-around-carry SD adder with the multiple-valued circuits and the addition time is independent of the word length of operands. The modulo m multiplier can be compactly constructed using a binary tree of the multiple-valued modulo m SD adders, and consequently the modulo m multiplication is performed in O(log p) time. The number of MOS transistors required in the presented residue arithmetic multiplier is about 86p2 + 66p.