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.
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