Facile Algebraic Representation of a Novel Quaternary Logic

TL;DR

This paper introduces a new algebraic framework for quaternary logic that enables systematic implementation and simplification of complex logic functions, facilitating the design of advanced multi-valued logic circuits.

Contribution

It presents the first complete algebraic representation of a novel quaternary logic, bridging binary and quaternary systems for improved circuit design and analysis.

Findings

Successful design and comparison of logic circuits in binary and quaternary domains.

The algebraic framework simplifies manipulation and integration of quaternary logic functions.

Enhanced potential for complex logic circuit development using the proposed algebra.

Abstract

In this work, a novel quaternary algebra has been proposed that can be used to implement an arbitrary quaternary logic function in more than one systematic ways. The proposed logic has evolved from and is closely related to the Boolean algebra for binary domain; yet it does not lack the benefits of a higher-radix system. It offers seamless integration of the binary logic functions and expressions through a set of transforms and allows any binary logic simplification technique to be applied in quaternary domain. Since physical realization of the operators defined in this logic has recently been reported, it has become very important to have a well-defined algebra that will facilitate the algebraic manipulation of the novel quaternary logic and aid in designing various complex logic circuits. Therefore, based on our earlier works, here we describe the complete algebraic representation of this logic for the first time. The efficacy of the logic has been shown by designing and comparing several common logic circuits with existing designs in both binary and quaternary domain.