ECE314sp07_HW3_solution - 1 ECE/CS 314 Spring 2007 Homework...

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Unformatted text preview: 1 ECE/CS 314 Spring 2007 Homework 3 Due Tuesday, March 6, 2007 before 10:00pm EST Homework Submission Policies 1. Show your work where appropriate. 2. Homework Assignments are done individually without calculators . 3. Homework must be typed and submitted in plain text or PDF format. No scanned PDF (or scanned ANYTHING) allowed. 4. All homework should be submitted through CMS. Under no circumstances should a submission be made by sending the completed assignments to a course staff by email, unless explicitly requested. (Make sure you are signed up for the class on CMS BEFORE the submission deadline.) 5. In general, late submissions will not be graded. However, if CMS is down prior to a deadline, please contact the course staff BEFORE the deadline and make a submission when the system is back up (it will not be penalized). 6. Questions may be directed to the ECE/CS 314 consultants. 2 Problem 1. (10 points) Consider the following Boolean expression F = XYZ + WXZ + WYZ + XYZ + WXZ (a) 3 pts. Construct the truth table for F W X Y Z F 0 0 0 0 1 0 0 0 1 0 0 0 1 0 1 0 0 1 1 0 0 1 0 0 1 0 1 0 1 0 0 1 1 0 1 0 1 1 1 0 1 0 0 0 1 1 0 0 1 1 1 0 1 0 1 1 0 1 1 0 1 1 0 0 0 1 1 0 1 1 1 1 1 0 0 1 1 1 1 0 (b) 3 pts. Draw the Karnaugh map, circle the prime implicants, and derive the minimized sum of product form for F. 1 1 0 1 0 0 1 1 0 0 0 0 1 1 0 1 F = WZ + XZ + WYZ W X Y Z 3 (c) 4 pts. Show that the first expression for F is equivalent to the minimized sum of product form for F using Boolean algebra. For each step of the derivation, mention which law of Boolean algebra you applied. F = XYZ + WXZ + WYZ + XYZ + WXZ WXZ + WXZ + XYZ + XYZ + WYZ Commutativity: A+B = B+A WZ (X+ X) + XZ(Y + Y) + WYZ Distributivity: AB+AC = A(B+C) WZ (1) + XZ(1) + WYZ Complements: A + A = 1 WZ + XZ + WYZ Identity: A1 = A 4 Problem 2. (10 points) (a) Draw the Karnaugh map, circle the prime implicants, and derive the minimized sum of product form for G=F (where F is the function from Problem 1). 0 0 1 0 1 1 0 0 1 1 1 1 0 0 1 0 G = YZ + WZ + WXZ (b) Show that F=G using Boolean algebra. For each step of the derivation, mention which law of Boolean algebra you applied. W X Y Z 5 F = G (YZ + WZ + WXZ) (YZ) (WZ) (WXZ) DeMorgans Law: (A+B) = AB (Y + Z) (W + Z) (W+X+Z) DeMorgans Law: AB = (A+B) Y(W+Z)(W+X+Z) + Z(W+Z)(W+X+Z) Distributivity: AB+AC = A(B+C) (W+Z)Y(W+X+Z) + (W+Z)Z (W+X+Z) Commutativity: AB=BA WY(W+X+Z) + ZY(W+X+Z) + WZ(W+X+Z) + ZZ (W+X+Z) Distributivity: AB+AC = A(B+C) WYW + WYX + WYZ + ZYW+ ZYX + ZYZ + WZW + WZX+...
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ECE314sp07_HW3_solution - 1 ECE/CS 314 Spring 2007 Homework...

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