homework 1

homework 1 - ECE 152A Summer 2009 6/24/2009 University of...

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ECE 152A – Summer 2009 6/24/2009 Homework #1 Page 1 of 6 University of California, Santa Barbara Department of Electrical and Computer Engineering ECE 152A – Digital Design Principles Homework #1 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’ 2. The second distributive law: x + yz = (x + y)(x + z) 3. The consensus theorem: xy + x’z + yz = xy + x’z Problem #2: Simplify the following Boolean expressions to a minimum number of literals: 1. x’y’ + xy + x’y 2. (x + y) (x + y’) 3. x’y + xy’ + xy + x’y’ 4. x’ + xy + xz’ + xy’z’ 5. xy’ + y’z’ + x’z’ Problem #3: Simplify the following Boolean expressions to a minimum number of literals: 1. ABC + A’B + ABC’ 2. x’yz + xz 3. (x + y)’ (x’ + y’) 4. xy + x(wz + wz’) 5. (BC’ + A’D)(AB’ + CD’)
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ECE 152A – Summer 2009 6/24/2009 Homework #1 Page 2 of 6 Problem #4: Reduce the following Boolean expressions to the indicated number of literals: 1. A’C’ + ABC + AC’ to three literals 2. (x’y’ + z)’ + z + xy + wz to three literals 3. A’B(D’ + C’D) + B(A + A’CD) to one literal 4. (A’ + C)(A’ + C’)(A + B + C’D) to four (or fewer?) literals
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This note was uploaded on 12/18/2009 for the course ECE 152a taught by Professor Johnson during the Spring '07 term at UCSB.

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homework 1 - ECE 152A Summer 2009 6/24/2009 University of...

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