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The Application of the Rademacher?Walsh Transform to Boolean Function Classification and Threshold Logic Synthesis
January 1975 (vol. 24 no. 1)
pp. 48-62
C.R. Edwards, School of Electrical Engineering, University of Bath
Five operations are defined in the Rademacher-Walsh transform domain. It is shown that these operations allow Boolean functions to be classified in a very concise way. The result of applying this classification to Boolean functions of up to fourth order indicates that threshold functions play an important part in the composition of Boolean functions. A synthesis method is developed for the synthesis of any Boolean function using, as a basic element, an "optimized universal threshold logic gate." This gate overcomes the analog threshold tolerancing problems encountered in other threshold gate designs and is readily fabricated in an integrated circuit form. The use of this gate in logic design is expected to provide a considerable cost-saving over conventional methods.
Index Terms:
Boolean function classification, logic synthesis, Rademacher-Walsh transform, threshold logic.
Citation:
C.R. Edwards, "The Application of the Rademacher?Walsh Transform to Boolean Function Classification and Threshold Logic Synthesis," IEEE Transactions on Computers, vol. 24, no. 1, pp. 48-62, Jan. 1975, doi:10.1109/T-C.1975.224082
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