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Basis sets for synthesis of switching functions

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1 Author(s)
Kundu, S. ; Digital Equipment Corp., Marlboro, MA, USA

The synthesis of switching function f(x1 , x2, . . ., xn) from a given family of functions gi(x1, x2, . . ., xn), 1⩽ik, using a complete set of logic primitives is considered. Necessary and sufficient conditions for the synthesis of f from the gi'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 {g1, g2 , . . ., gj}, 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 {gi}

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Computers, IEEE Transactions on  (Volume:41 ,  Issue: 4 )