Author :
Wang, Wei ; Swamy, M.N.S. ; Ahmad, M.O.
Author_Institution :
Dept. of Electr. & Comput. Eng., Univ. of Western Ontario, London, Ont., Canada
Abstract :
In this paper, we carry out a study on an important issue concerning the use of residue numbers in the design of digital systems, namely, the moduli selection. Based on a new formulation of the Chinese remainder theorem and the efficient residue-to-binary (R/B) converters designed therefrom, we propose a guideline for the selection of the low-cost moduli sets for different dynamic ranges. These sets consist of the low-cost moduli of the form 2n, ( 2n-1) or (2n + 1), which can offer simplified modulo adders and multipliers. It is shown that for medium dynamic ranges (less than 22 bits), the three-moduli set {2n,2n + 1,2n - 1} is the most efficient one in terms of the design of a complete RNS system. On the other hand, for large dynamic ranges (equal to or larger than 22 bits), the general-moduli set in the form (2n, 2n + 1,2n - 1,2n ±1,...,2n, ±1), with a length greater than three, is the most efficient one. These results provide the possibility of a wide range of applications of the residue number system in the design of DSP, telecommunication and cryptography systems.
Keywords :
CMOS digital integrated circuits; VLSI; adders; integrated circuit design; logic design; multiplying circuits; residue number systems; CMOSIS VLSI technology; Chinese remainder theorem; DSP; RNS; cryptography systems; digital system design; dynamic ranges; efficient VLSI implementation; general-moduli set; low-cost moduli sets; moduli selection; modulo adders; modulo multipliers; residue numbers; residue-to-binary converters; telecommunication; three-moduli set; Cathode ray tubes; Costs; Cryptography; Design engineering; Design methodology; Digital signal processing; Digital systems; Dynamic range; Guidelines; Very large scale integration;
