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hw1soln

# hw1soln - ECE 152A Fall 2006 University of California Santa...

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ECE 152A – Fall 2006 10/10/2006 Homework #1 - Solution Page 1 of 33 University of California, Santa Barbara Department of Electrical and Computer Engineering ECE 152A – Digital Design Principles Homework #1 Solution Problem #1: Demonstrate by means of truth tables the validity of the following identities: 1. DeMorgan’s theorem for three variables: (xyz)’ = x’ + y’ + z’ x y z xyz (xyz)’ x’ y’ z’ x’ + y’ + z’ 0 0 0 0 1 1 1 1 1 0 0 1 0 1 1 1 0 1 0 1 0 0 1 1 0 1 1 0 1 1 0 1 1 0 0 1 1 0 0 0 1 0 1 1 1 1 0 1 0 1 0 1 0 1 1 1 0 0 1 0 0 1 1 1 1 1 1 0 0 0 0 0 2. The second distributive law: x + yz = (x + y)(x + z) x y z yz x + yz (x + y) (x + z) (x + y)(x + z) 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 0 0 0 1 0 0 0 1 1 1 1 1 1 1 1 0 0 0 1 1 1 1 1 0 1 0 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1

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