Title | A method of majority logic reduction for quantum cellular automata |
Publication Type | Journal Article |
Year of Publication | 2004 |
Authors | Zhang, R., K. Walus, W. Wang, and G. A. Jullien |
Journal | Nanotechnology, IEEE Transactions on |
Volume | 3 |
Pagination | 443 - 450 |
Date Published | dec. |
ISSN | 1536-125X |
Keywords | adders, 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. |
URL | http://dx.doi.org/10.1109/TNANO.2004.834177 |
DOI | 10.1109/TNANO.2004.834177 |