Overflow Detection in Residue Number System, Moduli Set {2n-1,2n,2n+1}
Residue Number System (RNS) is a non-weighted number system for integer number arithmetic, which is based on the residues of a number to a certain set of numbers called module set. The main characteristics and advantage of residue number system is reducing carry propagation in calculations. The elim...
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| Format: | Article |
| Language: | English |
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Science and Research Branch,Islamic Azad University
2016-02-01
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| Series: | Journal of Advances in Computer Engineering and Technology |
| Subjects: | |
| Online Access: | http://jacet.srbiau.ac.ir/article_8295_36ba3bb20badbcfa6d06f7b3d7c2788d.pdf |
| _version_ | 1819123404133892096 |
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| author | Babak Tavakoli Mehdi Hosseinzadeh Somayeh Jassbi |
| author_facet | Babak Tavakoli Mehdi Hosseinzadeh Somayeh Jassbi |
| author_sort | Babak Tavakoli |
| collection | DOAJ |
| description | Residue Number System (RNS) is a non-weighted number system for integer number arithmetic, which is based on the residues of a number to a certain set of numbers called module set. The main characteristics and advantage of residue number system is reducing carry propagation in calculations. The elimination of carry propagation leads to the possibility of maximizing parallel processing and reducing the delay. Residue number system is mostly fitted for calculations involving addition and multiplication. But some calculations and operations such as division, comparison between numbers, sign determination and overflow detection is complicated. In this paper a method for overflow detection is proposed for the special moduli set {2n-1,2n,2n+1} . This moduli set is favorable because of the ease of calculations in forward and reverse conversions. The proposed method is based on grouping the dynamic range into groups by using the New Chinese Theorem and exploiting the properties of residue differences. Each operand of addition is mapped into a group, then the sum of these groups is compared with the indicator and the overflow is detected. The proposed method can detect overflow with less delay comparing to previous methods. |
| first_indexed | 2024-12-22T07:07:48Z |
| format | Article |
| id | doaj.art-7e4c99bb0d664b679be59440b75b192c |
| institution | Directory Open Access Journal |
| issn | 2423-4192 2423-4206 |
| language | English |
| last_indexed | 2024-12-22T07:07:48Z |
| publishDate | 2016-02-01 |
| publisher | Science and Research Branch,Islamic Azad University |
| record_format | Article |
| series | Journal of Advances in Computer Engineering and Technology |
| spelling | doaj.art-7e4c99bb0d664b679be59440b75b192c2022-12-21T18:34:37ZengScience and Research Branch,Islamic Azad UniversityJournal of Advances in Computer Engineering and Technology2423-41922423-42062016-02-01219168295Overflow Detection in Residue Number System, Moduli Set {2n-1,2n,2n+1}Babak Tavakoli0Mehdi Hosseinzadeh1Somayeh Jassbi2Islamic Azad University, Science and Research BranchIslamic Azad University, Science and Research BranchIslamic Azad University, Science and Research BranchResidue Number System (RNS) is a non-weighted number system for integer number arithmetic, which is based on the residues of a number to a certain set of numbers called module set. The main characteristics and advantage of residue number system is reducing carry propagation in calculations. The elimination of carry propagation leads to the possibility of maximizing parallel processing and reducing the delay. Residue number system is mostly fitted for calculations involving addition and multiplication. But some calculations and operations such as division, comparison between numbers, sign determination and overflow detection is complicated. In this paper a method for overflow detection is proposed for the special moduli set {2n-1,2n,2n+1} . This moduli set is favorable because of the ease of calculations in forward and reverse conversions. The proposed method is based on grouping the dynamic range into groups by using the New Chinese Theorem and exploiting the properties of residue differences. Each operand of addition is mapped into a group, then the sum of these groups is compared with the indicator and the overflow is detected. The proposed method can detect overflow with less delay comparing to previous methods.http://jacet.srbiau.ac.ir/article_8295_36ba3bb20badbcfa6d06f7b3d7c2788d.pdfComputer ArithmeticOverflow DetectionResidue Number System |
| spellingShingle | Babak Tavakoli Mehdi Hosseinzadeh Somayeh Jassbi Overflow Detection in Residue Number System, Moduli Set {2n-1,2n,2n+1} Journal of Advances in Computer Engineering and Technology Computer Arithmetic Overflow Detection Residue Number System |
| title | Overflow Detection in Residue Number System, Moduli Set {2n-1,2n,2n+1} |
| title_full | Overflow Detection in Residue Number System, Moduli Set {2n-1,2n,2n+1} |
| title_fullStr | Overflow Detection in Residue Number System, Moduli Set {2n-1,2n,2n+1} |
| title_full_unstemmed | Overflow Detection in Residue Number System, Moduli Set {2n-1,2n,2n+1} |
| title_short | Overflow Detection in Residue Number System, Moduli Set {2n-1,2n,2n+1} |
| title_sort | overflow detection in residue number system moduli set 2n 1 2n 2n 1 |
| topic | Computer Arithmetic Overflow Detection Residue Number System |
| url | http://jacet.srbiau.ac.ir/article_8295_36ba3bb20badbcfa6d06f7b3d7c2788d.pdf |
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