Transformation in the system of residual number classes from one system of modules to another

Abstract

The purpose of the study. The purpose of the study is an analytical consideration of the system of residual classes for the implementation of the operation of converting numbers from one system of residual classes to another. Method. System analysis, number theory, and the Chinese remainder theorem are tools of the research methodology. The method uses the representation of the number both by its remainders and in the polyadic code. The methodology is based on determining the positional characteristics for this module on the basis of the received positional characteristics for the remaining modules of the original system, with the subsequent construction on their basis of the residuals for the modules of the sought system. The proposed method is algorithmically simple. The results. The theoretical substantiation of the considered approach to obtain an effective solution of the non-modular transformation operation in the system of residual classes for the transition from the representation of a number by one system of modules to its representation by another system of modules is performed. It is shown that the proposed method provides the desired result. On the basis of the proposed approach, an increase in the performance of the conversion operation is achieved. Scientific novelty. The theoretical justification of the presented approach to the solution of the non-modular transformation operation in the system of residual classes for the transition from the representation of a number in one system of modules to its representation in another system of modules is proposed. It seems appropriate to apply the proposed approach as a prospective direction of research of complex operations in the system of residual classes. Practical significance. It follows from the importance of theoretical conclusions and obtained research results.It is based on the fact that there is a reasonably simple and effective approach to solving the problem of performing a non-modular conversion operation in the system of residual classes for the transition from the representation of a number in one system of modules to its representation in another system of modules. The considered solutions have high speed and can be effective in the development of modular computing structures for promising information technologies.