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week2a - Implementation of Boolean Functions ■ Boolean...

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Unformatted text preview: Implementation of Boolean Functions ■ Boolean Function: F = X + YZ Truth Table: X Y Z F 1 1 1 1 1 1 1 1 1 1 1 1 Circuit Diagram: Truth Table Boolean Function Implementation Implementation of Boolean Functions ■ Boolean Function: F = (X + Y)Z Truth Table: X Y Z F 1 1 1 1 1 1 1 1 1 1 1 1 Circuit Diagram: Logic Minimization: What & Why? 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 Logic Minimization ■ Consider two methods ■ Use of Boolean Algebra ■ Use of Karnaugh Maps (K-maps) ■ Canonical representation of functions ■ K-map method Basic Boolean Identities: X + 0 = X * 1 = X + 1 = X * 0 = X + X = X * X = X + X = X * X = X = 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) Boolean Manipulations ■ Boolean Function: F = XYZ + XY + XYZ Reduce function using identities & laws: Advanced Laws (Absorbtion)...
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week2a - Implementation of Boolean Functions ■ Boolean...

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