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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 diagnosing data errors of a computer system functioning in the system of residual classes(Національний технічний університет "Харківський політехнічний інститут", 2021) Koshman, Serhii; Krasnobayev, Victor; Nikolsky, SerhiiThe subject of the article is the development of a method for diagnosing data errors of a computer system functioning in the residue number system (RNS). This method is based on the tabular principle of data diagnostics operation implementation. The purpose of the article is to reduce the time of performing the operation of diagnosing the data of a computer system that functions in the RNS in the dynamics of the computational process. Tasks: to analyze the possible application of RNS as a number system in computer data processing systems; to investigate existing methods of data diagnostics and identify possible shortcomings in data diagnostics in the dynamics of the computational process with the introduction of minimal information redundancy; to develop a method for diagnosing the data presented in the RNS, which is based on the tabular principle of the implementation of the diagnostic operation. Research methods: methods of analysis and synthesis of computer systems, number theory, coding theory in RNS. The following results were obtained. The work shows that the data diagnostics is carried out after the control operation has been performed. To carry out the operation of diagnosing data in the RNS, when one-time errors occur, methods for determining an alternative set (AS) of numbers are used. In this case, the main disadvantage of the considered methods is the considerable time required to determine the AS. To reduce the time for determining the AC numbers in the work, the method for diagnosing data in the RNS has been improved. Improvement of the method involves the compilation of a table (the first stage) of correspondence to each correct number of a possible set of incorrect numbers when one-time errors occur in the data. Based on the analysis of the contents of the table of the first stage, a table (of the second stage) is drawn up of the correspondence of each incorrect number to the possible values of the correct numbers. Conclusions. The use of the improved method increases the efficiency of diagnostics of the data presented in the RNS by reducing the time for determining the AC numbers. This is achieved by quickly fetching pre-calculated AC table values.Документ The data diagnostic method of in the system of residue classes(Національний технічний університет "Харківський політехнічний інститут", 2021) Krasnobayev, Victor; Koshman, Sergey; Kovalchuk, DmytroThe subject of the article is the development of a method for diagnosing data that are presented in the system of residual classes (SRC). The purpose of the article is to develop a method for fast diagnostics of data in the SRC when entering the minimum information redundancy. Tasks: to analyze and identify possible shortcomings of existing methods for diagnosing data in the SRC, to explore possible ways to eliminate the identified shortcomings, to develop a method for prompt diagnosis of data in SRC. Research methods: methods of analysis and synthesis of computer systems, number theory, coding theory in SRC. The following results were obtained. It is shown that the main disadvantage of the existing methods is the significant time of data diagnostics when it is necessary to introduce significant information redundancy into the non-positional code structure (NCS). The method considered in the article makes it possible to increase the efficiency of the diagnostic procedure when introducing minimal information redundancy into the NCS. The data diagnostics time, in comparison with the known methods, is reduced primarily due to the elimination of the procedure for converting numbers from the NCS to the positional code, as well as the elimination of the positional operation of comparing numbers. Secondly, the data diagnostics time is reduced by reducing the number of SRC bases in which errors can occur. Third, the data diagnostics time is reduced due to the presentation of the set of values of the alternative set of numbers in a tabular form and the possibility of sampling them in one machine cycle. The amount of additionally introduced information redundancy is reduced due to the effective use of the internal information redundancy tha texists in the SRC. An example of using the proposed method for diagnosing data in SRC is given. Conclusions. Thus, the proposed method makes it possible to reduce the time for diagnosing data errors that are presented in the SRC, which increases the efficiency of diagnostics with the introduction of minimal information redundancy.