This thesis is concerned with the developments firstly in combinational logic, where the problems involved in multi-threshold realisations are examined, and secondly in sequential logic, where the specific type of system known as serial input logic is considered. Chapter 1 is an introduction which discusses the areas covered by this thesis and indicates their relationship to one another within the general framework of logic design. Chapter 2 sets out to extend the number of functions that can be realised by a multi-threshold logic gate with near optimal weights and thresholds. Use is made of the already existing spectral translation method of obtaining a single threshold solution with additional exclusive-or gates, a multi-threshold solution being obtained by algebraic manipulation of the weights and threshold. The mathematical basis that enables this to be done is derived and examples given. Chapter 3 discusses the possible advantages of using a multi-threshold logic gate within a charge-coupled device over the alternative Boolean AND/OR and quaternary logic gates. The fundamental operations of a charge-coupled device are reviewed, and the tolerancing problems that result from the charge transfer inefficiency and voltage fluctuations are considered as limiting factors on the logical complexity of the gate. Chapter 4 is concerned with the subject of serial input logic. Initially it sets out to define serial input logic in terms of a general sequential system, and then goes on to show that with regard to state reduction using compatibles it is unique since it only requires the derivation of the implied maximal compatibles. Furthermore, a modular realisation is given, where the design procedure consists of the use of reverse response trees. Various labelling schemes are considered and finally one is considered that guarantees an optimal solution. Throughout the thesis emphasis is placed on finding general solutions whenever possible, so that not only do they apply to the situations described herein, but also may prove useful in as yet undeveloped areas of research.
|Date of Award||1982|