Design of some quaternary combinational logic blocks using a new logic system

A new scheme for quaternary logic is proposed. The logic system is based on the extension of Boolean algebra, instead of conventional Fuzzy logic or Galois Field theory. This logic mainly focuses on the capability of handling coupled-binary input, where binary operands are coupled in pairs to form multivalued entities. Several operators are defined and a fully operational algebra is developed. To make it compatible with other quaternary logic systems, a method for expressing arbitrary functions in sum-of-product forms is also developed. Finally, using these operators and functions, combinational blocks like adder, multiplexer, demultiplexer, decoder and encoder are designed and their generalized equations are presented.