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

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.