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Ch02-CombinationalLogic

# Ch02-CombinationalLogic - Clark Guest 2009 ECE 25 Logic and...

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Combinational Logic ECE 25: Lecture 2 ©Clark Guest 2009 ECE 25 Logic and Computer Design Topics Logic Gates and Operations Boolean Functions Boolean Identities Algebraic Reduction Minterms and Maxterms Sum of Products and Product of Sums 2 ©Clark Guest 2009 ECE 25 Logic and Computer Design Logic Gates and Operations A B A AND B 0 0 0 0 1 0 1 0 0 1 1 1 A B A NAND B 0 0 1 0 1 1 1 0 1 1 1 0 A B A OR B 0 0 0 0 1 1 1 0 1 1 1 1 A B A NOR B 0 0 1 0 1 0 1 0 0 1 1 0 A NOT A 0 1 1 0 A • B A ! B A + B A " B A A • B A ! B A + B A " B Truth- Tables Gates A’ ©Clark Guest 2009 ECE 25 Logic and Computer Design Extending AND & OR True only if all inputs are true True if one or more inputs are true AND OR

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©Clark Guest 2009 ECE 25 Logic and Computer Design Boolean Functions Boolean Binary F(A, B, C) = A • B + C A B C F A B C F 0 0 0 0 0 0 1 1 0 1 0 0 0 1 1 1 1 0 0 1 1 0 1 1 1 1 0 0 1 1 1 1 ©Clark Guest 2009 ECE 25 Logic and Computer Design Boolean Identities X + 0 = X X • 0 = 0 X + X’ = 1 X • 1 = X X + X = X X • X’ = 0 X + 1 = 1 X • X = X (X’)’ = X X+Y = Y+X X•Y=Y•X Commutative X+(Y+Z)=(X+Y)+Z X•(Y•Z)=(X•Y)•Z
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