An arithmetic free parallel mixed-radix conversion algorithm

Miller, David F.; McCormick, William S.

doi:10.1109/82.659469

Cited by 15 publications

(5 citation statements)

References 10 publications

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“…The paper [ 17 ] presents the parallel reverse conversion method, which uses the lookup table technique and requires no arithmetic or logical units. As reported, this algorithm is better than the ones presented in [ 15 , 16 ].…”

Section: Discussionmentioning

confidence: 99%

“…There are two canonical techniques of reverse conversion: the canonical method based on the Chinese Remainder Theorem (CRT) and the residue code conversion to a weighted representation in the Mixed-Radix System (MRS) [ 1 , 2 , 5 , 8 , 14 , 15 , 16 , 17 , 18 ]. In general, all other conversion methods represent different variants of these two methods.…”

Section: Reverse Conversion Of the Residue Code To Conventional Repre...mentioning

confidence: 99%

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An Efficient Parallel Reverse Conversion of Residue Code to Mixed-Radix Representation Based on the Chinese Remainder Theorem

Selianinau

Povstenko

2022

Entropy

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In this paper, we deal with the critical problems in residue arithmetic. The reverse conversion from a Residue Number System (RNS) to positional notation is a main non-modular operation, and it constitutes a basis of other non-modular procedures used to implement various computational algorithms. We present a novel approach to the parallel reverse conversion from the residue code into a weighted number representation in the Mixed-Radix System (MRS). In our proposed method, the calculation of mixed-radix digits reduces to a parallel summation of the small word-length residues in the independent modular channels corresponding to the primary RNS moduli. The computational complexity of the developed method concerning both required modular addition operations and one-input lookup tables is estimated as Ok2/2, where k equals the number of used moduli. The time complexity is Olog2k modular clock cycles. In pipeline mode, the throughput rate of the proposed algorithm is one reverse conversion in one modular clock cycle.

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Section: Discussionmentioning

confidence: 99%

Section: Reverse Conversion Of the Residue Code To Conventional Repre...mentioning

confidence: 99%

An Efficient Parallel Reverse Conversion of Residue Code to Mixed-Radix Representation Based on the Chinese Remainder Theorem

Selianinau

Povstenko

2022

Entropy

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“…Thus, the moduli set {2 n −1, 2 n , 2 n +1}, which is the most popular length three moduli set, has been enhanced to {2 n+1 + 1, 2 n+1 − 1, 2 n } [7] and {2 n+1 − 1, 2 n , 2 n − 1} [8], to mention just a few. Generally speaking, RNS-tobinary conversion is either based on the Chinese Remainder Theorem (CRT) [1,2,6] or the Mixed Radix Conversion (MRC) [9].…”

Section: Introductionmentioning

confidence: 99%

New Adder-Based RNS-to-Binary Converters for the Moduli Set

Gbolagade

2011

ISRN Signal Processing

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We investigate Residue Number System (RNS) to binary conversion, which is an important issue concerning the utilization of RNS numbers in Digital Signal Processing (DSP) applications. We propose two new reverse converters for the moduli set . First, we simplify the Chinese Remainder Theorem (CRT) to obtain a reverse converter that uses mod- operations instead of mod- operations required by other state-of-the-art equivalent converters. Next, we further reduce the hardware complexity by making the resulting reverse converter architecture adder based. Two hybrid Cost-Efficient (CE) and Speed-Efficient (SE) reverse converters are proposed. These two hybrid converters are obtained by combining the best state-of-the-art converter with the newly introduced area-delay efficient scheme. The proposed hybrid CE converter outperforms the best state-of-the-art CE converter in terms of delay with similar area cost. Additionally, the proposed hybrid SE converter requires less area cost with smaller delay when compared to the best state-of-the-art equivalent SE converter.

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“…Mixed radix converters proposed so far are based on a look up tables [12]. In this section we propose a new approach whereby all look up tables in previous implementations are replaced by arithmetic units.…”

Section: Memoryless Mrcmentioning

confidence: 99%

“…These stored values are accessed in a serial fashion [12]. The main drawback of this method is that it is hardware intensive and as bits per modulus increases the hardware grows exponentially.…”

Section: Introductionmentioning

confidence: 99%

New area efficient residue-to-weighted number system converters

Mathew

Radhakrishnan²,

Srikanthan³

ICECS'99. Proceedings of ICECS '99. 6th IEEE International Conference on Electronics, Circuits and Systems (Cat. No.99EX357)

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Residue number system is popular in high performance arithmetic applications like digital signal processing because of its carry free nature, modularity and error correcting properties. But these opportunities are eclipsed by the high area and time requirements for reverse conversion. In this regard, we present two new techniques for residue-toweighted number system conversion. The first one is based on the popular Chinese Remainder Theorem. Here by evaluating the quotient the number is decoded. The second one deals with residue-to-mixed radix conversions. The arithmetic based technique replaces the conventional hardware intensive look up tables by simple adders. An OHR based high speed MRC is also presented. The mixed radix converters described are memoryless and are hardware efficient compared to conventional techniques.

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An arithmetic free parallel mixed-radix conversion algorithm

Cited by 15 publications

References 10 publications

An Efficient Parallel Reverse Conversion of Residue Code to Mixed-Radix Representation Based on the Chinese Remainder Theorem

An Efficient Parallel Reverse Conversion of Residue Code to Mixed-Radix Representation Based on the Chinese Remainder Theorem

New Adder-Based RNS-to-Binary Converters for the Moduli Set

New area efficient residue-to-weighted number system converters

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