Lect3 - 2

# Lect3 - 2 - EE 316 Digital Logic Design Lecture 3 Nur A...

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EE 316 - Digital Logic Design Lecture 3 Nur A. Touba University of Texas at Austin

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MULTIPLYING OUT EXPRESSIONS Product-of-Sums to Sum-of-Products Multiply out using two distributive laws X(Y+Z) = XY + XZ (X+Y)(X+Z) = X + YZ Additional useful theorem (X + Y)(X’ + Z) = XZ + X’Y
EXAMPLE (Q + AB’)(C’D + Q’)

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STRATEGY First Use (X + Y)(X’ + Z) = XZ + X’Y Then Use (X+Y)(X+Z) = X + YZ Last Use X(Y+Z) = XY + XZ Example: (A+B+C’)(A+B+D)(A+B+E)(A+D’+E)(A’+C)
FACTORING EXPRESSIONS Converting to Product-of-Sums Can use same Theorems in reverse Example: AC + A’BD’ + A’BE + A’C’DE

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EXCLUSIVE-OR Exclusive-OR Operation 0 0 = 0 0 1 = 1 1 0 = 1 1 1 = 0 X Y = X’Y + XY’
EXCLUSIVE-OR THEOREMS X 0 = X X 1 = X’ X X = 0 X X’ = 1 X Y = Y X (Cummutative Law) (X Y) Z = X (Y Z) = X Y Z (Associative Law) X(Y Z) = XY XZ (Distributive Law) (X Y)’ = X Y’ = X’ Y = XY + X’Y’ Can Prove by Substituting in X Y = X’Y+XY’

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## This note was uploaded on 11/30/2010 for the course EE 316 taught by Professor Brown during the Fall '08 term at University of Texas.

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Lect3 - 2 - EE 316 Digital Logic Design Lecture 3 Nur A...

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