CONSTRUCTION OF RESIDUE NUMBER SYSTEM USING DIAGONAL FUNCTION OF SPECIAL TYPE
Residue Number System (RNS) is a non-positional number system, which is a promising tool for increasing performance of digital devices. However, because of RNS is non-positional number system, magnitude comparison of numbers in RNS form is impossible, so division operation and operation of reverse c...
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| Format: | Article |
| Language: | Russian |
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North-Caucasus Federal University
2022-08-01
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| Series: | Современная наука и инновации |
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| Online Access: | https://msi.elpub.ru/jour/article/view/145 |
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| author | N. F. Semyonova N. I. Chervyakov P. A. Lyakhov M. V. Valueva G. V. Valuev |
| author_facet | N. F. Semyonova N. I. Chervyakov P. A. Lyakhov M. V. Valueva G. V. Valuev |
| author_sort | N. F. Semyonova |
| collection | DOAJ |
| description | Residue Number System (RNS) is a non-positional number system, which is a promising tool for increasing performance of digital devices. However, because of RNS is non-positional number system, magnitude comparison of numbers in RNS form is impossible, so division operation and operation of reverse conversion into positional form containing magnitude comparison operation that they are impossible too. One of the approaches to solve this problem is using Diagonal Function (DF). In this paper we propose the method of RNS construction with convenient form of DF, which leads to the calculations modulo2 ,21 or2 ~r1 and allows to design efficient hardware implementations. We constructed the hardware simulation of magnitude comparison and reverse conversion into positional form using RNS with different moduli sets construct by proposed method and using different approaches to perform magnitude comparison and reverse conversion: DF, Chinese Reminder Theorem (CRT) and CRT with fractional values (CRTf). The hardware simulation of magnitude comparison shows that, for three moduli, proposed method allows to reduce 5 98% 49 72% hardware resources by - in comparison with known methods. For four moduli, proposed method reduces delay by4-92% -21-95% and hardware costs to 2 times by comparison to known methods. Comparing of simulation results of proposed moduli sets and balanced moduli sets shows that using of proposed moduli sets allows to 2 times reduce circuit delay, although, in several cases it is required more hardware resources than balanced moduli sets. Residue Number System (RNS) is a promising tool for increasing performance of digital devices, which allows performing addition and multiplication operations fast and in parallel. However, RNS has disadvantages that some operations in RNS such as reverse conversion into positional form, magnitude comparison and division of numbers are problematic. One of the approaches to solve this problem is using Diagonal Function (DF). In this paper we propose the method of RNS construction with convenient form of DF, which leads to the calculations modulo 2n , 2 _1 or 2" + 1 and allows to design efficient hardware implementations. |
| format | Article |
| id | doaj-art-97c4dce2998c4cb19f58c096b6fe3f6d |
| institution | Kabale University |
| issn | 2307-910X |
| language | Russian |
| publishDate | 2022-08-01 |
| publisher | North-Caucasus Federal University |
| record_format | Article |
| series | Современная наука и инновации |
| spelling | doaj-art-97c4dce2998c4cb19f58c096b6fe3f6d2025-08-20T03:42:20ZrusNorth-Caucasus Federal UniversityСовременная наука и инновации2307-910X2022-08-01041021144CONSTRUCTION OF RESIDUE NUMBER SYSTEM USING DIAGONAL FUNCTION OF SPECIAL TYPEN. F. Semyonova0N. I. Chervyakov1P. A. Lyakhov2M. V. Valueva3G. V. Valuev4North-Caucasus Federal UniversityNorth-Caucasus Federal UniversityNorth-Caucasus Federal UniversityNorth-Caucasus Federal UniversityNorth-Caucasus Federal UniversityResidue Number System (RNS) is a non-positional number system, which is a promising tool for increasing performance of digital devices. However, because of RNS is non-positional number system, magnitude comparison of numbers in RNS form is impossible, so division operation and operation of reverse conversion into positional form containing magnitude comparison operation that they are impossible too. One of the approaches to solve this problem is using Diagonal Function (DF). In this paper we propose the method of RNS construction with convenient form of DF, which leads to the calculations modulo2 ,21 or2 ~r1 and allows to design efficient hardware implementations. We constructed the hardware simulation of magnitude comparison and reverse conversion into positional form using RNS with different moduli sets construct by proposed method and using different approaches to perform magnitude comparison and reverse conversion: DF, Chinese Reminder Theorem (CRT) and CRT with fractional values (CRTf). The hardware simulation of magnitude comparison shows that, for three moduli, proposed method allows to reduce 5 98% 49 72% hardware resources by - in comparison with known methods. For four moduli, proposed method reduces delay by4-92% -21-95% and hardware costs to 2 times by comparison to known methods. Comparing of simulation results of proposed moduli sets and balanced moduli sets shows that using of proposed moduli sets allows to 2 times reduce circuit delay, although, in several cases it is required more hardware resources than balanced moduli sets. Residue Number System (RNS) is a promising tool for increasing performance of digital devices, which allows performing addition and multiplication operations fast and in parallel. However, RNS has disadvantages that some operations in RNS such as reverse conversion into positional form, magnitude comparison and division of numbers are problematic. One of the approaches to solve this problem is using Diagonal Function (DF). In this paper we propose the method of RNS construction with convenient form of DF, which leads to the calculations modulo 2n , 2 _1 or 2" + 1 and allows to design efficient hardware implementations.https://msi.elpub.ru/jour/article/view/145residue number systemdiagonal functionchinese remainder theorem |
| spellingShingle | N. F. Semyonova N. I. Chervyakov P. A. Lyakhov M. V. Valueva G. V. Valuev CONSTRUCTION OF RESIDUE NUMBER SYSTEM USING DIAGONAL FUNCTION OF SPECIAL TYPE Современная наука и инновации residue number system diagonal function chinese remainder theorem |
| title | CONSTRUCTION OF RESIDUE NUMBER SYSTEM USING DIAGONAL FUNCTION OF SPECIAL TYPE |
| title_full | CONSTRUCTION OF RESIDUE NUMBER SYSTEM USING DIAGONAL FUNCTION OF SPECIAL TYPE |
| title_fullStr | CONSTRUCTION OF RESIDUE NUMBER SYSTEM USING DIAGONAL FUNCTION OF SPECIAL TYPE |
| title_full_unstemmed | CONSTRUCTION OF RESIDUE NUMBER SYSTEM USING DIAGONAL FUNCTION OF SPECIAL TYPE |
| title_short | CONSTRUCTION OF RESIDUE NUMBER SYSTEM USING DIAGONAL FUNCTION OF SPECIAL TYPE |
| title_sort | construction of residue number system using diagonal function of special type |
| topic | residue number system diagonal function chinese remainder theorem |
| url | https://msi.elpub.ru/jour/article/view/145 |
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