Method of Tabular Implementation of the Arithmetic Operation of Multiplying Two Numbers Represented in the System of Residual Classes

2022 IEEE 9th International Conference on Problems of Infocommunications, Science and Technology (PIC S&T) Pub Date : 2022-10-10 DOI:10.1109/PICST57299.2022.10238624

V. Krasnobayev, A. Yanko, D. Kovalchuk

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Abstract

The article discusses the method of tabular implementation of the arithmetic operation of multiplying two numbers represented in the system of residual classes (SRC). The existing methods of tabular implementation of the arithmetic operation of multiplying two numbers in the SRC allow you to implement this operation only in a positive numerical range. This circumstance significantly narrows the area of effective application of tabular arithmetic (TA) in the SRC. In order to further develop the scope of TA, the method of tabular implementation of the arithmetic operation of multiplication in the SRC has been improved in the article due to the additional possibility of simultaneously performing operations of both arithmetic and algebraic multiplication. For this, a mathematical model (MM) of the process of tabular implementation of the operation of modular multiplication in positive and negative numerical ranges is synthesized. The MM developed in the article is the basis for the method of tabular implementation of the arithmetic operation of multiplication. An example of the application of this method of multiplication of two numbers in the SRC in the negative numerical range is given. In the future, MM and an improved method for multiplying two numbers can be used as the basis for a generalized method for fast processing of arithmetic operations of modular addition, subtraction, and multiplication in the SRC.

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残差类系统中两数乘法运算的表格实现方法

本文讨论了残差类系统(SRC)中两数相乘算术运算的表格实现方法。SRC中两个数字相乘的算术运算的现有表格实现方法允许您仅在正数值范围内实现此操作。这种情况大大缩小了表格算法在SRC中的有效应用范围。为了进一步发展TA的范围，本文改进了SRC中乘法算术运算的表格实现方法，增加了同时执行算术和代数乘法运算的可能性。为此，综合了正、负数值范围内模乘法运算的表格化实现过程的数学模型。本文开发的数学模型是乘法算术运算的表格实现方法的基础。文中给出了该方法在负数值范围内的应用实例。在未来，MM和一种改进的两数相乘方法可以作为在SRC中快速处理模加法、减法和乘法运算的广义方法的基础。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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2022 IEEE 9th International Conference on Problems of Infocommunications, Science and Technology (PIC S&T)

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