Shannon’s expansion theorem-based multiplexer synthesis using QCA

Quantum dot-cellular automata (QCA) achieved their fame in designing low-power nanodevices for logic computation. Shannon’s expansion theorem helps to achieve a design for digital logic circuits that has three or more levels of logic with minimum implementation cost – that is, a smaller number of logic gates. Moreover, Shannon’s expansion theorem reduces the number of fan-in of the given circuits and the required inputs to a gate input. Thus, the QCA-based realization of a logic circuit will have fewer majority gates due to the use of Shannon’s theorem, which will reduce the circuit complexity, the latency and the energy dissipation. In this paper, the QCA-based realization of a three-input exclusive OR (XOR) gate using a 2:1 multiplexer is performed. Shannon’s expansion theorem is used to achieve the minimum implementation cost for the proposed XOR gate. With respect to the individual input variable to this XOR gate, the implementation cost in terms of the required logic gates is estimated. The estimation reflects that the cost is the same no matter which input variable is used to expand. The design of such a circuit promises to yield considerable results within the QCA research community.