Development of a novel quaternary algebra with the design of some useful logic blocks

A completely new scheme for quaternary logic is proposed. Instead of conventional fuzzy logic or Galois Field theory, the logic system is based on the extension of Boolean algebra. The logic is capable of handling both quaternary and coupled-binary inputs, where binary operands are coupled in pairs to form quaternary entities. All necessary operators are defined and several theorems and properties are derived to develop a way of expressing arbitrary truth tables with sum-of-product functions. To demonstrate the functionality of this novel logic scheme, some useful logic blocks such as decoder, multiplexer, and half-adder are designed.