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May 7, 2008 - University of North Texas, Denton, Texas [email protected]. Brenda Luderman. ACES CAD. Lewisville, Texas brenda.luderman@gmail.

Exact Combinational Logic Synthesis and Non-Standard Circuit Design Paul Tarau

Brenda Luderman

Dept. of Computer Science and Engineering University of North Texas, Denton, Texas [email protected]

ACES CAD Lewisville, Texas [email protected]

ABSTRACT Using a new exact synthesizer that automatically induces minimal universal boolean function libraries, we introduce two indicators for comparing their expressiveness: the first based on how many gates are used to synthesize all binary operators, the second based on how many N -variable truth table values are covered by combining up to M gates from the library. By applying the indicators to an exhaustive enumeration of minimal universal libraries, two dual asymmetrical operations, Logic Implication “⇒” and Half XOR “, ∗, +, ⊕. Note that > is the symmetric of ^ ntail nand

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head + ,0 ,=> >,ntail =>,ntail