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UBC Theses and Dissertations

Switching circuits as information networks Matheson, William Stephen


A single-output combinational switching network has a number of input terminals, each carrying a signal variable which may take one of two values, and an output terminal, the signal variable of which has a value determined ideally by the input signals only. In this thesis, we make an arbitrary assignment of probabilities to each of the possible configurations of input signal values, (namely that each configuration is equally likely). This is an interpretation of switching variables as random variables with known statistics. We can therefore define and compute the joint source entropy of sets of variables, including the output variable. We use these information quantities, or entropies, to classify switching functions into Equivalence Classes under Permutation and Complementation of input variables, and Negation of the Function. The entropies can also be used to predict some of the useful properties of switching functions, in some cases more simply than conventional methods which employ Boolean Algebra. The model also suggests a switching circuit design philosophy based on the idea of using circuit elements, or gates, to pass information in the input signals which is relevant to the output, while blocking the irrelevant information. Several algorithms are described, and their performance on the design of circuits with small numbers of variables is encouraging. The design philosophy seems particularly able to handle topological constraints, of the type becoming significant in modern switching circuit design.

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