CRTf-based reverse converter for RNS with low-cost modules { 2n, 2n- 1, 2n + 1- 1 }

In this paper, we propose a reverse converter from the balanced Residue Number System (RNS) with low-cost moduli set {2^n, 2^n−1, 2^(n + 1)−1} to the Binary Number System (BNS). The proposed method is based on the Chinese remainder theorem with fractions (CRTf) for the reverse conversion device. Con...

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প্রধান লেখক:	Bergerman, M. V., Бергерман, М. В., Lyakhov, P. A., Ляхов, П. А., Semyonova, N. F., Семенова, Н. Ф.
বিন্যাস:	Статья
ভাষা:	English
প্রকাশিত:	Springer Science and Business Media Deutschland GmbH 2022
বিষয়গুলি:	Chinese remainder theorem (CRT) Chinese remainder theorem with fractions (CRTf) Hardware design Residue number system (RNS) Reverse conversion RNS balance
অনলাইন ব্যবহার করুন:	https://dspace.ncfu.ru/handle/20.500.12258/19638
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id	ir-20.500.12258-19638
record_format	dspace
spelling	ir-20.500.12258-196382022-05-31T09:25:01Z CRTf-based reverse converter for RNS with low-cost modules { 2n, 2n- 1, 2n + 1- 1 } Bergerman, M. V. Бергерман, М. В. Lyakhov, P. A. Ляхов, П. А. Semyonova, N. F. Семенова, Н. Ф. Chinese remainder theorem (CRT) Chinese remainder theorem with fractions (CRTf) Hardware design Residue number system (RNS) Reverse conversion RNS balance In this paper, we propose a reverse converter from the balanced Residue Number System (RNS) with low-cost moduli set {2^n, 2^n−1, 2^(n + 1)−1} to the Binary Number System (BNS). The proposed method is based on the Chinese remainder theorem with fractions (CRTf) for the reverse conversion device. Constant coefficients are calculated in detail, where the bit width depends only on the value of n. Proposed a device architecture using parallel adders to speed up calculations. Hardware modeling of a reverse converter from balanced RNS with moduli set {2^n, 2^n−1, 2^(n + 1)−1} to the positional number system (PNS) was carried out using the field-programmable gate arrays (FPGA) in the VHDL. The results show that the proposed method achieves a faster performance by an average of 8.5% and lower hardware costs by an average of 10.5% compared to the state-of-the-art method. The proposed development can find wide applications in both digital signal and image processing based on RNS. 2022-05-31T09:24:10Z 2022-05-31T09:24:10Z 2022 Статья Bergerman, M., Lyakhov, P., Semyonova, N., Bogaevskiy, D., Kaplun, D. CRTf-based reverse converter for RNS with low-cost modules { 2n, 2n- 1, 2n + 1- 1 } // Lecture Notes in Networks and Systems. - 2022. - Том 424. - Стр.: 29 - 39. - DOI10.1007/978-3-030-97020-8_4 http://hdl.handle.net/20.500.12258/19638 en Lecture Notes in Networks and Systems application/pdf Springer Science and Business Media Deutschland GmbH
institution	СКФУ
collection	Репозиторий
language	English
topic	Chinese remainder theorem (CRT) Chinese remainder theorem with fractions (CRTf) Hardware design Residue number system (RNS) Reverse conversion RNS balance
spellingShingle	Chinese remainder theorem (CRT) Chinese remainder theorem with fractions (CRTf) Hardware design Residue number system (RNS) Reverse conversion RNS balance Bergerman, M. V. Бергерман, М. В. Lyakhov, P. A. Ляхов, П. А. Semyonova, N. F. Семенова, Н. Ф. CRTf-based reverse converter for RNS with low-cost modules { 2n, 2n- 1, 2n + 1- 1 }
description	In this paper, we propose a reverse converter from the balanced Residue Number System (RNS) with low-cost moduli set {2^n, 2^n−1, 2^(n + 1)−1} to the Binary Number System (BNS). The proposed method is based on the Chinese remainder theorem with fractions (CRTf) for the reverse conversion device. Constant coefficients are calculated in detail, where the bit width depends only on the value of n. Proposed a device architecture using parallel adders to speed up calculations. Hardware modeling of a reverse converter from balanced RNS with moduli set {2^n, 2^n−1, 2^(n + 1)−1} to the positional number system (PNS) was carried out using the field-programmable gate arrays (FPGA) in the VHDL. The results show that the proposed method achieves a faster performance by an average of 8.5% and lower hardware costs by an average of 10.5% compared to the state-of-the-art method. The proposed development can find wide applications in both digital signal and image processing based on RNS.
format	Статья
author	Bergerman, M. V. Бергерман, М. В. Lyakhov, P. A. Ляхов, П. А. Semyonova, N. F. Семенова, Н. Ф.
author_facet	Bergerman, M. V. Бергерман, М. В. Lyakhov, P. A. Ляхов, П. А. Semyonova, N. F. Семенова, Н. Ф.
author_sort	Bergerman, M. V.
title	CRTf-based reverse converter for RNS with low-cost modules { 2n, 2n- 1, 2n + 1- 1 }
title_short	CRTf-based reverse converter for RNS with low-cost modules { 2n, 2n- 1, 2n + 1- 1 }
title_full	CRTf-based reverse converter for RNS with low-cost modules { 2n, 2n- 1, 2n + 1- 1 }
title_fullStr	CRTf-based reverse converter for RNS with low-cost modules { 2n, 2n- 1, 2n + 1- 1 }
title_full_unstemmed	CRTf-based reverse converter for RNS with low-cost modules { 2n, 2n- 1, 2n + 1- 1 }
title_sort	crtf-based reverse converter for rns with low-cost modules { 2n, 2n- 1, 2n + 1- 1 }
publisher	Springer Science and Business Media Deutschland GmbH
publishDate	2022
url	https://dspace.ncfu.ru/handle/20.500.12258/19638
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CRTf-based reverse converter for RNS with low-cost modules { 2n, 2n- 1, 2n + 1- 1 }

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