Optimization of sum of product expressions in a novel quaternary algebra

In this work, several techniques for the optimization of expressions in a novel quaternary algebra are discussed thoroughly. This quaternary algebra, which can be used to implement any quaternary logic function, is closely related to Boolean algebra. A set of quaternary operators are defined and two ways to express any quaternary function mathematically are described. Finally, we have discussed several quaternary functions in which the rules of optimization are used to reduce the complexity of expressions. Since optimization can be done in both forms of SOP in this algebra, this new logic, with the rules of optimization, may be quite useful for efficient implementation of quaternary functions.