A method of majority logic reduction for quantum cellular automata

TitleA method of majority logic reduction for quantum cellular automata
Publication TypeJournal Article
Year of Publication2004
AuthorsZhang, R., K. Walus, W. Wang, and G. A. Jullien
JournalNanotechnology, IEEE Transactions on
Volume3
Pagination443 - 450
Date Publisheddec.
ISSN1536-125X
Keywordsadders, Boolean functions, Boolean primitive, cellular automata, logic design, majority expression, majority logic, majority logic reduction, nanoelectronics, QCA, QCA adder, quantum cellular automata, quantum gates, sum-of-products expression, three-variable Boolean function
Abstract

The basic Boolean primitive in quantum cellular automata (QCA) is the majority gate. In this paper, a method for reducing the number of majority gates required for computing three-variable Boolean functions is developed to facilitate the conversion of sum-of-products expression into QCA majority logic. Thirteen standard functions are introduced to represent all three-variable Boolean functions and the simplified majority expressions corresponding to these standard functions are presented. We describe a novel method for using these standard functions to convert the sum-of-products expression to majority logic. By applying this method, the hardware requirements for a QCA design can be reduced. As an example, a 1-bit QCA adder is constructed with only three majority gates and two inverters. The adder is designed and simulated using QCADesigner, a design and simulation tool for QCA. We will show that the proposed method is very efficient and fast in deriving the simplified majority expressions in QCA design.

URLhttp://dx.doi.org/10.1109/TNANO.2004.834177
DOI10.1109/TNANO.2004.834177

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