02_Boolean&TwoLevel - Representations of Boolean...

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20 Representations of Boolean Functions Readings: 2.5,2.5.2-2.10.3 Boolean Function: F = X + YZ Truth Table: X Y Z F 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1 Circuit Diagram: 21 Why Boolean Algebra/Logic Minimization? Logic Minimization: reduce complexity of the gate level implementation reduce number of literals (gate inputs) reduce number of gates reduce number of levels of gates fewer inputs implies faster gates in some technologies fan-ins (number of gate inputs) are limited in some technologies fewer levels of gates implies reduced signal propagation delays number of gates (or gate packages) influences manufacturing costs
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22 Basic Boolean Identities: X + 0 = X * 1 = X + 1 = X * 0 = X + X = X * X = X + X = X * X = X = 23 Basic Laws Commutative Law: X + Y = Y + X XY = YX Associative Law: X+(Y+Z) = (X+Y)+Z X(YZ)=(XY)Z Distributive Law: X(Y+Z) = XY + XZ X+YZ = (X+Y)(X+Z)
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