Efficient MRC-Based Residue to Binary Converters for the New Moduli Sets {22n, 2n -1, 2n+1 -1} and {22n, 2n -1, 2n-1 -1}

Amir Sabbagh MOLAHOSSEINI  Chitra DADKHAH  Keivan NAVI  Mohammad ESHGHI  

Publication
IEICE TRANSACTIONS on Information and Systems   Vol.E92-D   No.9   pp.1628-1638
Publication Date: 2009/09/01
Online ISSN: 1745-1361
DOI: 10.1587/transinf.E92.D.1628
Print ISSN: 0916-8532
Type of Manuscript: PAPER
Category: Computer Systems
Keyword: 
residue to binary converter,  mixed-radix conversion (MRC),  residue number system (RNS),  computer arithmetic,  

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Summary: 
In this paper, the new residue number system (RNS) moduli sets {22n, 2n -1, 2n+1 -1} and {22n, 2n -1, 2n-1 -1} are introduced. These moduli sets have 4n-bit dynamic range and well-formed moduli which can result in high-performance residue to binary converters as well as efficient RNS arithmetic unit. Next, efficient residue to binary converters for the proposed moduli sets based on mixed-radix conversion (MRC) algorithm are presented. The converters are ROM-free and they are realized using carry-save adders and modulo adders. Comparison with the other residue to binary converters for 4n-bit dynamic range moduli sets shown that the presented designs based on new moduli sets {22n, 2n -1, 2n+1 -1} and {22n, 2n -1, 2n-1 -1} are improved the conversion delay and result in hardware savings. Also, the proposed moduli sets can lead to efficient binary to residue converters, and they can speed-up internal RNS arithmetic processing, compared with the other 4n-bit dynamic range moduli sets.