Residue-to-binary arithmetic converter for the moduli set (2/sup k/, 2/sup k/-1, 2/sup k-1/-1)

Hiasat, A.A.; Abdel-Aty-Zohdy, S.H.

doi:10.1109/82.661651

Cited by 95 publications

(30 citation statements)

References 20 publications

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“…For some special moduli sets, such as {2 n + 1, 2 n , 2 n − 1} and {2 n + 1, 2 n , 2 n − 1, 2 n+1 − 1}, dedicated efficient reverse converter designs are available [2,8,12,13]. While for other arbitrary moduli sets, a general CRT reverse converter design based on table look-up is used.…”

Section: Hardware Cost Estimationmentioning

confidence: 99%

Moduli Set Selection and Cost Estimation for RNS-Based FIR Filter and Filter Bank Design

Liu

Lai

2004

Des Autom Embed Syst

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Moduli selection is one of the most important issues in the implementation of systems that make use of residue number systems. In this paper, we describe a software tool that assists system designers in moduli selection for the design of RNS-based FIR filters and filter banks. According to some filter specification parameters, the software tool constructs valid moduli sets and calculates their estimated implementations cost in terms of delay, area and power consumption based on results obtained in logic synthesis. Moduli set that is most suitable for the user requirements is selected, together with the estimated cost, to be the output. Outputs of the software tool also indicate that certain level of trade-off among delay, area and power consumption exists for the RNS-based filter and filter bank implementation by using different moduli sets.

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Section: Hardware Cost Estimationmentioning

confidence: 99%

Moduli Set Selection and Cost Estimation for RNS-Based FIR Filter and Filter Bank Design

Liu

Lai

2004

Des Autom Embed Syst

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“…There are many different moduli set and among these three-moduli sets have received considerable attention. Such as {2 n -1, 2 n , 2 n +1} [9,10], {2 n , 2 n -1, 2 n-1 -1} [11,12], {2 n , 2 n -1, 2 n+1 -1} [13], {2 2n +1, 2 n +1, 2 n -1} [14] and {2 n , 2 2n -1, 2 2n +1} [15]. RNS application efficiency is highly depending on choosing proper residue to binary conversion algorithm based on selected moduli set [5].…”

Section: Introductionmentioning

confidence: 99%

A novel high speed residue to binary converter design based on the three-moduli set {2n, 2n+1+1, 2n+1−1}

Lotfinejad

Mosleh

Noori

2010

2010 East-West Design &Amp; Test Symposium (EWDTS)

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“…Moduli set choice is also an important issue since the complexity and the speed of the resulting conversion structure depend on the chosen moduli set. Several structures have been proposed to perform the reverse conversion for different moduli sets, e.g., {2 n , 2 n − 1, 2 n + 1} [2], {2 n , 2 n − 1, 2 n−1 − 1} [5], {2 n+1 + 1, 2 n+1 − 1, 2 n } [7], {2 n , 2 n+1 − 1, 2 n − 1} [6], [8], {2n + 2, 2n + 1, 2n} [4]. Efficient memoryless adder-based reverse converter have been proposed for the moduli set {2 n , 2 n − 1, 2 n + 1}.…”

Section: Introductionmentioning

confidence: 99%

“…Efficient memoryless adder-based reverse converter have been proposed for the moduli set {2 n , 2 n − 1, 2 n + 1}. This moduli set has the disadvantage [5] that multiplication by powers of 2 with respect to the (2 n + 1) modulus is not as simple as left circular rotation in a (2 n − 1) modulus. Due to this reason, the moduli set {2 n , 2 n − 1, 2 n−1 − 1} was proposed in [5].…”

Section: Introductionmentioning

confidence: 99%

Residue-to-binary converters for the moduli set {22n+1-1,22n,2n-1}

Gbolagade

Chaves²,

Sousa³

et al. 2009

2009 2nd International Conference on Adaptive Science &Amp; Technology (ICAST)

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In this paper, we propose two memoryless converters for the moduli set {2 2n+1 − 1, 2 2n , 2 n − 1}. First, we propose a novel reverse converter, which is purely adder based, using the traditional Chinese Remainder Theorem (CRT). Second, due to the fact that the proposed CRT based structure does not cover the entire dynamic range, a second converter, which covers the entire dynamic range based on Mixed Radix Conversion (MRC), is proposed. The CRT based converter outperforms the MRC based converter both in terms of area and delay. In comparison with related best known state of the art converters, they are all outperformed by the proposed CRT based scheme in terms of both area cost and conversion delay. The theoretical evaluation is supported by the experimental results, which are estimated on a Standard Cell 0.13-μm CMOS technology. These experimental results indicate that, on average, for the same dynamic range, the proposed CRT based converter achieves about 23% delay reduction with more than 3% area reduction, when compared to the existing state of the art MRC based converter. Additionally, the proposed CRT based converter is about 6% faster with about 4% area reduction when compared with the existing CRT based converter.Index Terms-Residue Number System, Reverse Converter, Chinese Remainder Theorem, Mixed Radix Conversion, Memoryless Converter. 26 978-1-4244-3523-4/09/$25.00 c 2009 IEEE

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Residue-to-binary arithmetic converter for the moduli set (2/sup k/, 2/sup k/-1, 2/sup k-1/-1)

Cited by 95 publications

References 20 publications

Moduli Set Selection and Cost Estimation for RNS-Based FIR Filter and Filter Bank Design

Moduli Set Selection and Cost Estimation for RNS-Based FIR Filter and Filter Bank Design

A novel high speed residue to binary converter design based on the three-moduli set {2<sup>n</sup>, 2<sup>n+1</sup>+1, 2<sup>n+1</sup>−1}

Residue-to-binary converters for the moduli set {2<sup>2n+1</sup>-1,2<sup>2n</sup>,2<sup>n</sup>-1}

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Residue-to-binary arithmetic converter for the moduli set (2/sup k/, 2/sup k/-1, 2/sup k-1/-1)

Cited by 95 publications

References 20 publications

Moduli Set Selection and Cost Estimation for RNS-Based FIR Filter and Filter Bank Design

Moduli Set Selection and Cost Estimation for RNS-Based FIR Filter and Filter Bank Design

A novel high speed residue to binary converter design based on the three-moduli set &#x007B;2<sup>n</sup>, 2<sup>n+1</sup>+1, 2<sup>n+1</sup>&#x2212;1&#x007D;

Residue-to-binary converters for the moduli set {2<sup>2n+1</sup>-1,2<sup>2n</sup>,2<sup>n</sup>-1}

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A novel high speed residue to binary converter design based on the three-moduli set {2<sup>n</sup>, 2<sup>n+1</sup>+1, 2<sup>n+1</sup>−1}