This thesis deals with several aspects of the utilization of finite (Galois) fields in multiplevalued logic (MVL). Current-mode CMOS circuits are proposed that realize operations in Galois fields with four elements. A synthesis technique with such circuits and a transform method are presented; they are based on the Galois field polynomial representation. Methods for obtaining such representations are discussed in two steps, dealing with one-dimensional and multidimensional cases separately. A new method is developed for representation of single variable functions. It is limited to fields of small sizes (2 to 4), which is acceptable because only these fields are readily implementable with today's MVL technology. The method provides a natural way of dealing with incompletely specified functions and has better computational properties than other similar methods. A natural extension of the method to the multidimensional case is derived. The multidimensional representation algorithm has all the properties of the fast discrete transforms. Acknowledgements First and foremost, for his guidance, help and encouragement, I thank my advisor, Zvonko G. Vranesic. Not only did he introduce me to the multiple-valued logic and switching theory, but by serving as a positive example, he taught me how to perform research work. Essential is his material support, guidance through some of the very difficult moment during my studies, and an optimism that he tried to imbue on any occasion. Without him, nothing like this thesis could happen. I thank Prof. Molle, Prof. Rose and Prof. Zaky for their understanding while studying in Toronto. Many credits go to Professor Leo Budin in Zagreb who showed me the basics of the
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