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A method of realizing arbitrary combinational switching functions with multiplexers is derived. These circuits are divided in two classes where the first allows only uncomplemented variables as control inputs and the second has unrestricted inputs. The selected inputs to each multiplexer in the first class of circuits (tree circuits) are shown to be residue functions of the output function. Using this fact, it is demonstrated that many functional properties simplify realization procedures.
Implicitly exhaustive search, logic design automation, minimization algorithm, modular logic arrays, multiplexer, multiplexer universal logic module (MULM), numerical technique, Shannon's expansion, universal logic module (ULM).

T. Tabloski and F. Mowle, "A Numerical Expansion Technique and Its Application to Minimal Multiplexer Logic Circuits," in IEEE Transactions on Computers, vol. 25, no. , pp. 684-702, 1976.
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