Five-valued circuit quantitative theory and design of five-valued twisted-ring counter

This paper presents a six-valued algebra in order to form the theory of three essential elements for five-valued circuits, which is a mathematical tool for quantitative investigation on five-valued circuits. Based on the theory, the component level circuit structures are deduced firstly from five-valued circuit function by means of 5 expanded form. Secondly, two circuit structures of dynamic and static positive-edge-triggered five-valued D flip-flops are deduced from the same flip-flops characteristic equation. Finally, all five-valued counters are partitioned into five types, and then a five-valued resetting twisted-ring counter with simple circuit structure is designed. The above theory and circuits have been verified by computer simulations