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Number Conversions between RNS and Mixed-Radix Number System Based on Modulo (2p - 1) Signed-Digit Arithmetic

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1 Author(s)
Wei, S. ; Dept. of Comput. Scicence, Gunma Univ.

In this paper, new hardware algorithms converting the numbers of a residue number system (RNS) into and from the mixed-radix number system(MRNS) using a radix-two signed-digit (SD) arithmetic circuits are presented. In each residue digit of the RNS integers mi = (2 p i - 1) are used as the moduli and the modulo m i addition and multiplication can be performed by an end-around-carry SD adder and a binary modulo mi SD adder tree, respectively. Therefore, the modulo mi addition time is independent of the word length of operands, and the modulo mi multiplication can be performed in a time proportional to log2 pi. An efficient method for calculating a multiplicative inverse number of a modulus is also presented by using the SD arithmetic. By the use of the fast SD arithmetic circuits, number converters of RNS-to-MRNS and MRNS-to-RNS can be implemented with shorter delay time than that using a binary number system

Published in:

Integrated Circuits and Systems Design, 18th Symposium on

Date of Conference:

4-7 Sept. 2005