РЕАЛІЗАЦІЯ ДЕЯКИХ ПРОБЛЕМНИХ ОПЕРАЦІЙ У СИСТЕМАХ ЗАЛИШКОВИХ КЛАСІВ
Journal Title: Математичне моделювання - Year 2018, Vol 1, Issue 1
Abstract
IMPLEMENTATION OF SOME PROBLEMATIC OPERATIONS IN SYSTEMS OF RESIDUAL CLASSES Polissky Yu.D. Abstract Computing structures are constantly being demanded to improve performance. The use of the residual class system when performing arithmetic operations of addition, subtraction and multiplication makes it possible to improve the performance of such systems through natural parallelization of data processing. The merits of this representation of numbers also include the low-quality residuals, high accuracy and reliability, the ability of the system to self-correction. The aim of the research is to analyze analytically the system of residual classes with pairwise mutually simple modules and the residual class system with all even modules for implementing the basic problem operations of determining the number of a given half of the range and comparing numbers. It is shown that in the first case the representation of numbers in a polyadic code with the same set of modules as in the remainders of these modules is the only one. This makes it possible to realize the operation of determining the membership of a number in the given half of the range and, on its basis, the operation of comparing numbers. Algorithms for performing these operations are given. It is also shown that in the second case, the representation of numbers in a polyadic code with the same set of modules as in the remainders of these modules is not the only one, and therefore the search for a solution to the basic problem operations discussed above requires further research. The algorithm for comparing numbers in a system of residual classes with all even modules by an algorithm not based on the determination of the number of first or second half of the range is given, and the realization of the comparison of numbers by this algorithm is considered. References [1] Polissky Yu.D. Algorithm of the tabular implementation of modular exponentiation / / Yu.D. Polissky // Problems of mathematical modeling: the material of sciences.-method. conf., 25-27 May. 2016 р. – Dnipropetrovsk. – 2016. – P. 96–100. [2] Irhin V.P. Table realization of modular arithmetic operations / V.P. Irhin // 50 years of modular arithmetic: works of the anniversary Intern. scientific and technical. Conf. (23.11.-25.11.-2005). – Moscow: MIET. – P. 268–273. [3] Methods and algorithms for rounding, scaling and dividing numbers in modular arithmetic / N.I.Cherviakov [and others] // 50 years of modular arithmetic: works of the anniversary Intern. scientific and technical. Conf. (23.11.-25.11.-2005). – Moscow: MIET. – P. 268–273. [4] Chervyakov N.I. Methods and principles of constructing modular neurocomputers. N.I Chervyakov //50 years of modular arithmetic: works of the anniversary Intern. scientific and technical. Conf. (23.11.-25.11.-2005). – Moscow: MIET. – P. 232–242. [5] The Knut D. The art of programming / D. Knut. – Moscow: Dialectic-Williams, 2013. – 832 p. [6] Akushsky I.Ya., Yuditsky D.I. Machine arithmetic in the residual classes. [Text] / I.Ya. Akushsky., D.I. Yuditsky. – Moscow: Soviet Radio, 1968. – 440 p. [7] Polissky Yu.D. Determination of the membership of the number represented by the system of residual classes in the given half of the range / Yu.D. Polissky // Problems of mathematical modeling: the material of sciences.-method. conf., 24–26 May. 2017 р. – Dnipropetrovsk. – 2017. – P. 112–114. [8] Polissky Yu.D. On some approaches to the implementation of problematic operations in the system of residual classes. [Text] / Yu.D.Polissky // Electronic Modeling. – 2017.– P. 39.– No. 4. – P. 105–114.
Authors and Affiliations
Ю. Д. Поліський
Keywords
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- EP ID EP294855
- DOI 10.31319/2519-8106.1(38)2018.128944
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