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# HW4 - Ryan Zanski ECE 2504 Introduction to Computer...

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Ryan Zanski ECE 2504 Introduction to Computer Engineering, Summer I 2010 Homework 4 Due date: 3 Jun 10, 11:55pm Show all work. Use Logicworks to draw any circuit diagrams. 1. (6 pts) Simplify the following Boolean expressions. Provide the number of the Boolean identity used from Table 1-1 for each step. a. ABC’ + AC’ + AB’C’ AC'(B+1+B') 13 AC'(1) 7 AC' 4 b. x’ y’z + x’z + (z+y’)’y’ x'y'z+x'z+(z'y)y' 15 x'y'z+x'z+z'(yy') 12 x'y'z+x'z+z'(0) 8 x'y'z+x'z 2 x'(y'z+z) 13 x'(z) 5 x'z 2. (9 pts) Given the Boolean expression F = (x+y’+z’)•(x+z)•(x+y’+z) a. Derive a Boolean expression for the complement F’. F'=(x'yz)+(x'z')+(x'yz') b. Show that F + F’ = 1 using Boolean algebra. (x+y'+z')(x+z)(x+y'+z)+(x'yz)+(x'z')+(x'yz') = 1 X’((yz)+(z’)+(yz’))+(x+y’+z’)(x+z)(x+y’+z) 13 c. Show that F•F’ = 0 using Boolean algebra. (x+y’+z’)(x+z)(x+y’+z) (x’yz)+(x’z’)+(x’yz’) 3. (10 pts) Given the Boolean function F = xyz + xy z + x yz + x y z ′ ′ ′ ′ ′ 1

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a. List the truth table.
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