  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.
