METHOD FOR DETERMINING THE BIT GRID OVERFLOW OF A COMPUTER SYSTEM OPERATING IN THE SYSTEM OF RESIDUAL CLASSES

Abstract

Context. Consideration of a set of examples of practical application of the procedure for identifying overflow of the bit grid of a computer system operating in a non-positional number system in residual classes. The object of the study is the process of processing data represented in the residual class system.
 Objective. The goal of the work is to consider and analyze examples of the bit grid overflow definition of a computer system when implementing the operation of adding two numbers in a system of residual classes based on the application of a method for determining the bit grid overflow, based on the use of the concept of number rank.
 Method. The specificity of the functioning of a computer system in a system of residual classes requires the implementation of not only modular operations, but also requires the implementation of additional, so-called non-modular operations. Non-modular operations include the operation of determining the overflow of the bit grid of a computer system in the system of residual classes. In a non-positional number system in residual classes, implementing the process of detecting overflow of the bit grid of a computer system is a difficult task to implement. The method considered in the work for determining the overflow of the bit grid is based on the use of positional features of a non-positional code of numbers in the system of residual classes, namely the true and calculated ranks of a number. The process of determining the overflow of the result of the operation of adding two numbers in the system of residual classes has been studied, since this arithmetic operation is the main, basic operation performed by a computer system.
 Results. The developed methods are justified theoretically and studied when performing arithmetic modular operations of addition, subtraction and multiplication using tabular procedures.
 Conclusions. The main advantage of the presented method is that the process of determining the overflow of the bit grid can be carried out in the dynamics of the computing process of the computer system, i.e. without stopping the solution of the problem. This circumstance makes it possible to reduce the unproductive expenditure of the computer system in the system of residual classes. In addition, this method can be used to control the operation of adding two numbers in the residual class system. This increases the reliability of obtaining the true result of the operation of adding two numbers in the system of residual classes.