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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 fanins (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 (Kmaps) ■ Canonical representation of functions ■ Kmap 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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 Winter '08
 WU
 Boolean Algebra, Logic gate, Boolean function, minterms

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