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Basis Sets for Synthesis of Switching Functions
April 1992 (vol. 41 no. 4)
pp. 489-493

The synthesis of switching function f(x/sub 1/, x/sub 2/, . . ., x/sub n/) from a given family of functions g/sub i/(x/sub 1/, x/sub 2/, . . ., x/sub n/), 1>or=i>or=k, using a complete set of logic primitives is considered. Necessary and sufficient conditions for the synthesis of f from the g/sub i/'s are derived using the concept of a basis set. The independence between the basis property and the completeness of a set of logic primitives is shown, the conditions for extending a set (g/sub 1/, g/sub 2/, . . ., g/sub j/), j>n, to a basis set are found. Thus, the selection of a basis set and the logic primitives can be treated as separate problems. Finally, it is shown that there is a unique generalized Reed-Muller expansion for any f in terms of the basis functions (g/sub i/).

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Index Terms:
synthesis; switching function; completeness; basis set; logic primitives; Reed-Muller expansion; logic design; switching functions.
S. Kundu, "Basis Sets for Synthesis of Switching Functions," IEEE Transactions on Computers, vol. 41, no. 4, pp. 489-493, April 1992, doi:10.1109/12.135561
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