Improving the efficiency of using multivalued logic tools: application of algebraic rings

The scheme considered below is intended to demonstrate the following fundamental circumstance, which is expressed by formula (26). It is possible to represent the element of the ring in the “hybrid” number system, formula (20). The digits of this number, if the operations proceed within the corresponding ring, can be handled independently.

This approach can be applied to various rings, but for the primary proof of its effectiveness in terms of implementation in the form of electronic circuits, it is permissible to restrict ourselves to the simplest example, which corresponds to the case of…