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Title Binomial Number System
Authors Borysenko, Oleksii Andriiovych  
Matsenko, S.
Bobrovs, V.
Keywords binomial number systems (BNS)
generalized positional number systems (GPNS)
binomial code
constant-weight (CW) binomial code
Type Article
Date of Issue 2021
URI https://essuir.sumdu.edu.ua/handle/123456789/86352
Publisher MDPI
License Creative Commons Attribution 4.0 International License
Citation Borysenko, O.; Matsenko, S.; Bobrovs, V. Binomial Number System. Appl. Sci. 2021, 11, 11110. https://doi.org/10.3390/app112311110
Abstract 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.
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