FDNQA_manuscript

In this work, a novel quaternary algebra has been proposed that can be used to implement any quaternary logic function. Unlike other variants of quaternary algebra, this algebra is closely related to Boolean algebra and can be used to convert any binary function into quaternary without any significant modification. For this purpose, we have defined a set of quaternary operators and developed two ways to express any quaternary function mathematically. Finally, we have presented the design of several combinational logic circuits and compared these designs with several other variants of quaternary logic. Since a quaternary digit can contain as much information as a pair of binary digits, this new logic may be quite useful in the fields of communication and computing.