Sign detection in residue arithmetic units

Alia, Giuseppe; Martinelli, Enrico

doi:10.1016/s1383-7621(97)00085-4

Cited by 10 publications

(6 citation statements)

References 16 publications

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“…For all such applications, RNS provides outstanding performance with high computational speed, lesser area, and low power dissipation, which are the major objective of today's real-time processors. Additionally, the reverse conversion [15][16][17], division [18][19], scalar [20], magnitude comparison [21][22], overflow detection [23][24][25] and sign detection [26][27][28][29][30][31][32][33][34][35][36][37] are also the essential operation of RNS. These operations are not easy to perform in RNS.…”

Section: Introductionmentioning

confidence: 99%

“…Recently numerous efforts have been made in the area of sign detector, which presents different architectures of sign detector for different moduli sets. Some of them are designed for universal moduli set [26][27][28][29], 3-moduli set [30][31][32][33][34] and extended moduli set [35][36][37]. The 3-moduli set {2 n -1, 2 n , 2 n +1} is very popular as this results in less complex arithmetic circuits due to the availability of the number of modulo properties.…”

mentioning

confidence: 99%

“…These types of sign detectors were suitable only for small word-length and practically, it is not realizable for larger word-length as it requires huge memories. To overcome this problem, VLSI component based sign detector is proposed in [27] without using any look-uptable. However, the sign detector presented in [27] is very complex as it was implemented using modulo multipliers.…”

mentioning

confidence: 99%

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Design and analysis of RNS-based sign detector for moduli set {2^n, 2^n - 1, 2^n + 1}

Kumar

Mishra

2021

IJEECS

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Magnitude comparison, sign detection and overflow detection are essential operations of residue number system (RNS) that are used in digital signal processing (DSP) applications. Moreover, sign detection attracts significant attention in RNS as it can also be used in division and magnitude comparison operations. However, these operations are not easy to perform in RNS. So, there is a need arise to propose a computationally advanced RNS based sign detector. This paper presents an area and power-efficient sign detection circuit for modulo {2n - 1, 2n, 2n + 1} using mixed radix conversion technique. The proposed sign detector is constructed using a carry save adder (CSA), a modified parallel prefix adder and a carry-generation circuit. Based on the synthesized results using synopsys design compiler, the introduced design offers better results in terms of the area required and power consumption. Although, the speed will remain the same when compared to the recent sign detectors for the same moduli set.

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Section: Introductionmentioning

confidence: 99%

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confidence: 99%

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confidence: 99%

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Design and analysis of RNS-based sign detector for moduli set {2^n, 2^n - 1, 2^n + 1}

Kumar

Mishra

2021

IJEECS

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“…CRT II decreases the modulo multiplier size to less than

\sqrt{M}

. Read only memory (ROM)‐based architectures are proposed in [5, 6] but ROMs are not suitable for pipelining. A class of monotone functions are proposed in [7] that can be used for magnitude comparison in RNS.…”

Section: Introductionmentioning

confidence: 99%

Fast sign‐detection algorithm for residue number system moduli set {2 ⁿ − 1, 2 ⁿ , 2 ^{n
+1} − 1}

Niras¹,

Kong²

2016

IET Computers & Digital Techniques

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Sign detection is an essential part of many computer hardware designs, and is not a trivial task in residue number systems because it is a function of all the residues. This study proposes an algorithm for the residue number system with a three-moduli set {2 n − 1, 2 n , 2 n+1 − 1} using New Chinese Remainder Theorem II. The unit is built with one n-bit carry-save adder and a 2n-bit parallel prefix carry-generation unit. In the best case the Synoposys 90 nm synthesis result shows a 24% reduction in the area-delay product than existing algorithms for the same moduli set.

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“…In [Ali98], the sign detection method was based upon CRT and base-extension method wherein the sign of an integer X in the range 2 ,…”

Section: Rns Sign Detectionmentioning

confidence: 99%

New algorithms for hardware-efficient implementation of sign detection and magnitude comparison in residue number systems

Kumar¹

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Residue Number System (RNS), being a non-positional number system, is emerging as a promising data representation to substitute the accustomed two's complement number system for low-power and high-speed digital signal processing. Due to its carry free property at subword level, arithmetic operations such as addition, subtraction and multiplication can be performed at higher speed than any weighted number system. Nonetheless, the arithmetic operations such as sign detection, signed integer magnitude comparison are found to be more difficult to implement in RNS. This thesis aims to develop new algorithms for hardwareefficient implementation of these difficult operations in RNS. Specifically, the following new findings and results are reported in this thesis.

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Sign detection in residue arithmetic units

Cited by 10 publications

References 16 publications

Design and analysis of RNS-based sign detector for moduli set {2^n, 2^n - 1, 2^n + 1}

Design and analysis of RNS-based sign detector for moduli set {2^n, 2^n - 1, 2^n + 1}

Fast sign‐detection algorithm for residue number system moduli set {2 ⁿ − 1, 2 ⁿ , 2 ^{n
+1} − 1}

New algorithms for hardware-efficient implementation of sign detection and magnitude comparison in residue number systems

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Sign detection in residue arithmetic units

Cited by 10 publications

References 16 publications

Design and analysis of RNS-based sign detector for moduli set {2^n, 2^n - 1, 2^n + 1}

Design and analysis of RNS-based sign detector for moduli set {2^n, 2^n - 1, 2^n + 1}

Fast sign‐detection algorithm for residue number system moduli set {2 n − 1, 2 n , 2 n +1 − 1}

New algorithms for hardware-efficient implementation of sign detection and magnitude comparison in residue number systems

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Fast sign‐detection algorithm for residue number system moduli set {2 ⁿ − 1, 2 ⁿ , 2 ^{n
+1} − 1}