On the Design of RNS Reverse Converters for the Four-Moduli Set +1, 2^-1, 2^, 2^+1}+1

In this brief, we propose a method to design efficient adder-based converters for the four-moduli set {2 n +1, 2 n -1, 2 n , 2 n+1 +1} with n odd, which provides a dynamic range of 4n+1 bits for the residue number system (RNS). This method hierarchically applies the mixed radix approach to balanced...

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Veröffentlicht in:IEEE transactions on very large scale integration (VLSI) systems 2013-10, Vol.21 (10), p.1945-1949
Hauptverfasser: Sousa, Leonel, Antao, Samuel, Chaves, Ricardo
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creator Sousa, Leonel
Antao, Samuel
Chaves, Ricardo
description In this brief, we propose a method to design efficient adder-based converters for the four-moduli set {2 n +1, 2 n -1, 2 n , 2 n+1 +1} with n odd, which provides a dynamic range of 4n+1 bits for the residue number system (RNS). This method hierarchically applies the mixed radix approach to balanced pairs of residues in two levels. With the proposed method, only simple binary and modulo 2 k -1 additions are required, fully avoiding the usage of modulo 2 k +1 arithmetic operations, which is a significant advantage over the currently available RNS reverse converters for this type of moduli set. Experimental results show that the delay of the proposed converters is significantly reduced when compared with the related state of the art; for example, for a 65-nm CMOS ASIC technology and a dynamic range of 21 bits, the conversion time and the circuit area are reduced by about 44% and 30%, respectively, while the conversion time is reduced by 34% for a dynamic range of 37 bits with the circuit area increasing only by 25%. Moreover, the proposed reverse converters outperform the related state of the art for any value of n by up to 70%, according to the figure-of-merit energy per conversion.
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subjects Adders
Application specific integrated circuits
Application-specific integrated circuit (ASIC)
Delay
digital hardware design
Dynamic range
Field programmable gate arrays
field-programmable gate array (FPGA)
Hardware
residue number system (RNS)
reverse conversion
Very large scale integration
title On the Design of RNS Reverse Converters for the Four-Moduli Set +1, 2^-1, 2^, 2^+1}+1
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