ON SOME NEW APPROACHES TO PERFORMING NON-MODULAR OPERATIONS IN THE RESIDUAL CLASS SYSTEM

The development of modern technologies, information and control systems requires the creation of new principles focused on the representation of numbers in the system of residual classes. At the same time, the implementation of new trends in the system of residual classes requires, along with the use of systems of mutually simple modules, the use of systems with all even modules. Moreover, the system of all even modules is built on the basis of a system of simple modules — the basis — by multiplying each module of the basis by an even number — the transition coefficient. This paper provides a brief overview of new approaches obtained over the past five years to the performance of some non-modular operations. The proposed approaches ensure the effective obtaining of the desired results, and it is advisable to consider them as one of the directions of research into ways to increase the efficiency of calculations in the system of residual classes.