On the design methodology of Boolean functions with quantum-dot cellular automata for reducing delay and number of wire crossings

摘要

Quantum-dot cellular automata (QCA) circuits are not based on transistors. Therefore, novel concepts and methodologies are required to be able to design Boolean functions in a systematic manner. Wire crossing is a problematic challenge in this technology, imposing considerable cost, complexity, and noise sensitivity. On the other hand, QCA circuits with multiple successive majority gates experience long delays. This paper deals with both problems. At first, some new diagrams are presented for the 13 standard functions, which are sufficient to represent all of the three-input Boolean functions. Some of the standard functions are designed with much fewer wire crossings in this paper compared with the previous designs. Then, with the aim of reducing delay, hierarchical multiplexers are merged together in order to generate wide Boolean functions with fewer layers of majority gates. Circuit compactness is based on some new merging rules.