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Документ The concept of performing the addition operation in the sistem of residual classes(Національний технічний університет "Харківський політехнічний інститут", 2022) Krasnobayev, Victor; Koshman, Sergey; Kovalchuk, DmytroThe subject of the article is the development of a method for implementing the arithmetic operation of adding the residuals of numbers, which are represented in the system of residual classes (RNS). This method is based on the use of positional binary adders. The purpose of the article is to improve the performance of computer systems (CS) and their components by introducing new ways of organizing calculations based on the use of RNS. Tasks: to analyze and identify the shortcomings of the existing number systems that are used in the construction of computer systems and components; explore possible ways to eliminate the identified deficiencies; explore the structure of binary positional adders, taking into account the scheme for adding two residues of numbers modulo RNS; to develop a method for constructing adders modulo RNS, which is based on the use of a set of binary single-digit positional adders. Research methods: methods of analysis and synthesis of computer systems, number theory, coding theory in RNS. The following results are obtained. The paper shows that one of the promising ways to improve the performance of the CS is the use of RNS. The mathematical basis of RNS is the Chinese remainder theorem, which states that an integer operation on one large modulus can be replaced by a set of operations on coprime small modules. This opens up broad prospects for optimizing calculations. On the one hand, it is possible to significantly simplify the performance of complex and cumbersome calculations, including on low-resource computing platforms. On the other hand, calculations for different modules can be performed in parallel, which increases the performance of the CS. Conclusions. The article considers the operation of adding two numbers. This operation is the basis for both traditional positional number systems and RNS, i.e. forms the computational basis of all existing CS components. A new method for calculating the sum of the residuals of numbers modulo an arbitrary is proposed, and examples are given that clearly demonstrate the effectiveness of the proposed method. This method can be used in various computer applications, including for improving computing performance, ensuring fault tolerance, etc.Документ Method for the control verification of digital information, represented in a residue number system(Національний технічний університет "Харківський політехнічний інститут", 2020) Krasnobayev, Victor; Yanko, Alina; Tur, SerhiiThe subject of the research in the article is the control methods for the data presented in the residue number system. The object of research is the process of monitoring data presented in the residue number system. The purpose of the work is to develop a method for increasing the reliability of control of data presented in the residue number system. The following tasksare solved in the article: research of data control methods presented in the residue number system; development of a method for increasing the reliability of data control; consideration of examples ofapplication of the developed method for a specific residue number system; demonstration of examples of calculation and comparative analysis of the reliability of data control presented in the residue number system. The following research methods are used: the basics of system analysis and the basics of machine arithmetic in the residue number system. The following results were obtained: A method for increasing the reliability of data control was developed; examples of application of the developed method for a specific residue number system are presented; examples of calculation and comparative analysis of the reliability of data control presented in the residue number system are given. Conclusions: This article presents the theoretical foundations of the process of increasing the reliability of control of data presented in the residue number system, based on the use of the procedure of zeroing numbers. A method for increasing the reliability of data control has been directly developed and presented. Examples of application of the developed method for a specific residue number system are given and examples of calculating the reliability of control of data presented in the residue number system are given. A method has been developed to increase the reliability of data control; it is a definite contribution to the theory of noise-resistant coding in a residue number system. Examples of calculation and comparative analysis of the reliability of data control confirm the practical significance of the results of this article.Документ Implementation of the arithmetic addition operation in the system of residual classes(Національний технічний університет "Харківський політехнічний інститут", 2020) Krasnobayev, V.; Koshman, S.; Kurchanov, V.The subject of the article is the development of a method for implementing the arithmetic operation of addition numbers that are represented in the system of residual classes (SRC). This method is based on the use of the principle of circular shift (PCS). The purpose of the article is to reduce the time it takes to implement the arithmetic operation of addition numbers that are represented in the SRC. Tasks: to analyze and identify the shortcomings of existing number systems that are used in the construction of computer systems and components, to explore possible ways to eliminate identified deficiencies, to evaluate the implementation time of the arithmetic addition operation based on the use of the developed method. Research methods: methods of analysis and synthesis of computer systems, number theory, coding theory in SRC. The following results are obtained. It is shown that the basic principle of the implementation of arithmetic operations in positional number systems is the use of binary adders. Moreover, the use of such number systems determines the presence of inter-bit connections, which in turn increases the time it takes to implement arithmetic operations, and also cause errors to occur. It is established that the use of a non-positional number system in residual classes allows us to eliminate these shortcomings, through the use of the basic properties of SRC. The peculiarity of the developed method is the result of the operation of adding numbers can be found by successive cyclic shifts of the bits of the contents of the data blocks by the corresponding SRC modules. The use of PCS allows eliminating the influence of inter-bit bonds between the residues of the processed numbers, which allows to reduce the implementation time of the operation of adding two numbers in the SRC. Conclusions. The results of the studies showed that the use of SRC allows to eliminate the existing shortcomings of positional number systems, and also improves the speed of implementation of arithmetic operations.