ANALYSIS OF METHODS FOR THE IMPLEMENTATION OF ARITHMETIC OPERATIONS IN THE RESIDUAL CLASSES
Keywords:
residual classes, computer data processing facilities, computer systems, methods for implementing arithmetic operations, non-positional number system, positional number system
Abstract
The article discusses the features of the implementation of the arithmetic operations of nonpositional number systems in the residual classes. It is possible to increase the productivity of the computer system and the reliability of processing integer data based on the use of new machine arithmetic. In the positional numeral system, the execution of an arithmetic operation involves the sequential processing of the digits of operands according to the rules determined by the content of the operation, and cannot be completed until the values of all intermediate results are sequentially determined taking into account all the connections between the digits. Thus, positional numeral system, in which information is presented and processed in modern computers, have a significant drawback - the presence of inter-bit relations, which impose its imprint on the methods of implementing arithmetic operations, complicate the equipment and limit the speed. Therefore, it is natural to look for possibilities of using such arithmetic, in which there would be no queuing connections. In this regard, the system of calculus in the residual classes draws attention to itself. The implementation of arithmetic operations in the residual classes is performed independently and in parallel over the like digits (residues), and the structure of the operating unit of computer data processing facilities is represented as independent computational paths, each of which operates on its base mi of the residual classes. Adding, subtracting, and multiplying the residual classes is carried out using a very simple algorithm: these operations are modular and are implemented independently for each module of the residual classes within the boundary grid [0, M]. Methods of implementing modular arithmetic operations in the residual classes are considered and analyzed. There are three basic principles for the implementation of modular arithmetic operations in the residual classes, based on the following methods: an aggregation method (based on a low-level binary adder); tabular method; the method of a ring-shift, based on the use of ring shift registers.Downloads
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5. Koshman S. A. Method of bit-by-bit tabular realization of arithmetic operations in the system of residual classes / S. A. Koshman, V. I. Barsov, V. A. Krasnobayev, K. V. Yaskova, N. S. Derenko // Радіоелектронні і комп'ютерні системи. – 2009. – № 5 (39). – C. 44–48.
6. Gbolagade K. A. An O(n) Residue Number System to Mixed Radix Conversion technique / K. A. Gbolagade, S. D. Cotofana // IEEE International Symposium on Circuits and Systems (24–27 May, 2009). – New York : IEEE, 2009. – P. 521-524.
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8. Krasnobayev V. A method for operational diagnosis of data represented in a residue number system / V. Krasnobayev and S. Koshman // Cybernetics and Systems Analysis. – vol. 54, Issue 2. – 2018. – pp. 336-344.
9. Krasnobayev V. Algorithms of data processing in the residual classes system / V. Krasnobayev, A. Yanko and S. Koshman // 4th International Scientific-Practical Conference Problems of Infocommunications. Science and Technology (PIC S&T) . – Kharkiv. – 2017. – pp. 117-121.
Published
2019-02-05
How to Cite
Krasnobayev V. Analysis of methods for the implementation of arithmetic operations in the residual classes / V. Krasnobayev, A. Yanko, I. Fil // Control, Navigation and Communication Systems. Academic Journal. – Poltava: PNTU, 2019. – VOL. 1 (53). – PP. 120-124. – doi:https://doi.org/10.26906/SUNZ.2019.1.120.
Section
Information Technology
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
