The object of this thesis is to present certain matrix techniques which may be employed in the analysis and synthesis or binary combinational logic circuits. These techniques are readily implemented on the digital computer. In developing these methods care has been taken to avoid heuristic algorithms so that each technique has a firm mathematical foundation. The first chapter of the thesis considers a Boolean matrix approach to logic analysis and synthesis. These matrices allow the rigorous and formalised representation of logic circuits. An important property of these matrices is that they embody multiple-output circuit representation and that, together with certain matrix operations, they may be used in the synthesis of multiple output circuits on an iterative basis. The second chapter of the thesis describes a matrix transformation technique which has properties directly applicable to logic synthesis. This technique may be employed not only in the field of conventional logic design but also in the design of circuits using threshold gates. Certain transform-domain operations are used to synthesise logic circuits directly from the transformed truth-table representation of Boolean functions. These operations may also be used in the classification of Boolean functions. They may also be employed in the synthesis of multiple-output circuits and pattern recognition. The third section of the thesis concerns itself with other research work initiated by the topics discussed in chapters one and two. Of special interest is the description of a universal threshold logic gate and its role in logic synthesis.
|Date of Award||1973|