A new Josephson δ-gate ternary-valued logic

A new Josephson circuit of multi-valued logic gate (Josephson ternary δ-gate) is proposed. The simulation result of the Josephson δ-gate circuit demonstrated the feasibility and the reliability operations, where very low power consumption, and ultra high speed switching operation have been achieved. Mathematical properties of δ-gate are introduced. The δ-gate forms a complete set (completeness) with the ternary constant set {-1, 0. 1}. Based on δ-gate, it is possible to analyze, synthesize and realize an arbitrary ternary logic function of n-input variables. An application, a ternary logic half-adder is presented, its simulation results shows reliable operation and excellent performance. Finally, the δ-gate can transfer signals from gate to gate without loss of amplitude, the δ-gate is a multiplexor and it is very effective for a MV-FPGA (multi-valued field-programmable gate arrays) building blocks.