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In this paper, the new residue number system (RNS) moduli sets {2^{2n}, 2^{n} -1, 2^{n+1} -1} and {2^{2n}, 2^{n} -1, 2^{n-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 4*n*-bit dynamic range moduli sets shown that the presented designs based on new moduli sets {2^{2n}, 2^{n} -1, 2^{n+1} -1} and {2^{2n}, 2^{n} -1, 2^{n-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 4*n*-bit dynamic range moduli sets.

- Publication
- IEICE TRANSACTIONS on Information Vol.E92-D No.9 pp.1628-1638

- Publication Date
- 2009/09/01

- Publicized

- Online ISSN
- 1745-1361

- DOI
- 10.1587/transinf.E92.D.1628

- Type of Manuscript
- PAPER

- Category
- Computer Systems

The copyright of the original papers published on this site belongs to IEICE. Unauthorized use of the original or translated papers is prohibited. See IEICE Provisions on Copyright for details.

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Amir Sabbagh MOLAHOSSEINI, Chitra DADKHAH, Keivan NAVI, Mohammad ESHGHI, "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}" in IEICE TRANSACTIONS on Information,
vol. E92-D, no. 9, pp. 1628-1638, September 2009, doi: 10.1587/transinf.E92.D.1628.

Abstract: In this paper, the new residue number system (RNS) moduli sets {2^{2n}, 2^{n} -1, 2^{n+1} -1} and {2^{2n}, 2^{n} -1, 2^{n-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 4*n*-bit dynamic range moduli sets shown that the presented designs based on new moduli sets {2^{2n}, 2^{n} -1, 2^{n+1} -1} and {2^{2n}, 2^{n} -1, 2^{n-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 4*n*-bit dynamic range moduli sets.

URL: https://global.ieice.org/en_transactions/information/10.1587/transinf.E92.D.1628/_p

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@ARTICLE{e92-d_9_1628,

author={Amir Sabbagh MOLAHOSSEINI, Chitra DADKHAH, Keivan NAVI, Mohammad ESHGHI, },

journal={IEICE TRANSACTIONS on Information},

title={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}},

year={2009},

volume={E92-D},

number={9},

pages={1628-1638},

abstract={In this paper, the new residue number system (RNS) moduli sets {2^{2n}, 2^{n} -1, 2^{n+1} -1} and {2^{2n}, 2^{n} -1, 2^{n-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 4*n*-bit dynamic range moduli sets shown that the presented designs based on new moduli sets {2^{2n}, 2^{n} -1, 2^{n+1} -1} and {2^{2n}, 2^{n} -1, 2^{n-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 4*n*-bit dynamic range moduli sets.},

keywords={},

doi={10.1587/transinf.E92.D.1628},

ISSN={1745-1361},

month={September},}

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TY - JOUR

TI - 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}

T2 - IEICE TRANSACTIONS on Information

SP - 1628

EP - 1638

AU - Amir Sabbagh MOLAHOSSEINI

AU - Chitra DADKHAH

AU - Keivan NAVI

AU - Mohammad ESHGHI

PY - 2009

DO - 10.1587/transinf.E92.D.1628

JO - IEICE TRANSACTIONS on Information

SN - 1745-1361

VL - E92-D

IS - 9

JA - IEICE TRANSACTIONS on Information

Y1 - September 2009

AB - In this paper, the new residue number system (RNS) moduli sets {2^{2n}, 2^{n} -1, 2^{n+1} -1} and {2^{2n}, 2^{n} -1, 2^{n-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 4*n*-bit dynamic range moduli sets shown that the presented designs based on new moduli sets {2^{2n}, 2^{n} -1, 2^{n+1} -1} and {2^{2n}, 2^{n} -1, 2^{n-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 4*n*-bit dynamic range moduli sets.

ER -