Binomial Number System
This paper presents and first scientifically substantiates the generalized theory of binomial number systems (BNS) and the method of their formation for reliable digital signal processing (DSP), transmission, and data storage. The method is obtained based on the general theory of positional number s...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-11-01
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| Series: | Applied Sciences |
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| Online Access: | https://www.mdpi.com/2076-3417/11/23/11110 |
| _version_ | 1797508144319954944 |
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| author | Oleksiy Borysenko Svitlana Matsenko Vjaceslavs Bobrovs |
| author_facet | Oleksiy Borysenko Svitlana Matsenko Vjaceslavs Bobrovs |
| author_sort | Oleksiy Borysenko |
| collection | DOAJ |
| description | This paper presents and first scientifically substantiates the generalized theory of binomial number systems (BNS) and the method of their formation for reliable digital signal processing (DSP), transmission, and data storage. The method is obtained based on the general theory of positional number systems (PNS) with conditions and number functions for converting BNS with a binary alphabet, also allowing to generate matrix BNS, linear-cyclic, and multivalued number systems. Generated by BNS, binomial numbers possess the error detection property. A characteristic property of binomial numbers is the ability, on their basis, to form various combinatorial configurations based on the binomial coefficients, e.g., compositions or constant-weight (CW) codes. The theory of positional binary BNS construction and generation of binary binomial numbers are proposed. The basic properties and possible areas of application of BNS researched, particularly for the formation and numbering of combinatorial objects, are indicated. The CW binomial code is designed based on binary binomial numbers with variable code lengths. BNS is efficiently used to develop error detection digital devices and has the property of compressing information. |
| first_indexed | 2024-03-10T04:58:08Z |
| format | Article |
| id | doaj.art-65b1f34940f942e5a26bc710403bc1c6 |
| institution | Directory Open Access Journal |
| issn | 2076-3417 |
| language | English |
| last_indexed | 2024-03-10T04:58:08Z |
| publishDate | 2021-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Applied Sciences |
| spelling | doaj.art-65b1f34940f942e5a26bc710403bc1c62023-11-23T02:02:39ZengMDPI AGApplied Sciences2076-34172021-11-0111231111010.3390/app112311110Binomial Number SystemOleksiy Borysenko0Svitlana Matsenko1Vjaceslavs Bobrovs2Department of Electronics and Computer Technology, Sumy State University, 40007 Sumy, UkraineCommunication Technologies Research Center, Riga Technical University, 1048 Riga, LatviaInstitute of Telecommunications, Riga Technical University, 1048 Riga, LatviaThis paper presents and first scientifically substantiates the generalized theory of binomial number systems (BNS) and the method of their formation for reliable digital signal processing (DSP), transmission, and data storage. The method is obtained based on the general theory of positional number systems (PNS) with conditions and number functions for converting BNS with a binary alphabet, also allowing to generate matrix BNS, linear-cyclic, and multivalued number systems. Generated by BNS, binomial numbers possess the error detection property. A characteristic property of binomial numbers is the ability, on their basis, to form various combinatorial configurations based on the binomial coefficients, e.g., compositions or constant-weight (CW) codes. The theory of positional binary BNS construction and generation of binary binomial numbers are proposed. The basic properties and possible areas of application of BNS researched, particularly for the formation and numbering of combinatorial objects, are indicated. The CW binomial code is designed based on binary binomial numbers with variable code lengths. BNS is efficiently used to develop error detection digital devices and has the property of compressing information.https://www.mdpi.com/2076-3417/11/23/11110binomial number systems (BNS)generalized positional number systems (GPNS)binomial codeconstant-weight (CW) binomial code |
| spellingShingle | Oleksiy Borysenko Svitlana Matsenko Vjaceslavs Bobrovs Binomial Number System Applied Sciences binomial number systems (BNS) generalized positional number systems (GPNS) binomial code constant-weight (CW) binomial code |
| title | Binomial Number System |
| title_full | Binomial Number System |
| title_fullStr | Binomial Number System |
| title_full_unstemmed | Binomial Number System |
| title_short | Binomial Number System |
| title_sort | binomial number system |
| topic | binomial number systems (BNS) generalized positional number systems (GPNS) binomial code constant-weight (CW) binomial code |
| url | https://www.mdpi.com/2076-3417/11/23/11110 |
| work_keys_str_mv | AT oleksiyborysenko binomialnumbersystem AT svitlanamatsenko binomialnumbersystem AT vjaceslavsbobrovs binomialnumbersystem |