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HW5_solution

HW5_solution - ECE 2504 Introduction to Computer...

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ECE 2504 Introduction to Computer Engineering, Fall 2008 Homework 5 Due date: 5 Oct 08, 11:59pm Show all work. Use LogicWorks to draw circuit diagrams. 1. (4 pts) Simplify the following Boolean function G together with the don’t care conditions d in product-of-sums form using a K-map. Draw the logic diagram. G(m,n,p,q)= mnpq’ + mnp’q + mn’p’q + mnp’q’ + mnpq + m’n’p’q d(m,n,p,q)= m’nq’ + mn’p’q’ + n’pq pq mn 00 01 11 10 00 0 1 X 0 01 X 0 0 X 11 1 1 1 1 10 X 1 X 0 G’ = m’n + n’q’ G = (m+n’)(n+q) m n q G OR m n G q 2. (3 pts) Repeat problem 1 using sum-of-products form. pq mn 00 01 11 10 00 0 1 X 0 01 X 0 0 X 11 1 1 1 1 10 X 1 X 0 G = mn + n’q m n q G OR m n q G

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3. (6 pts) A sequential circuit has two D flip flops A and B, two inputs x and y, and one output z. The flip flop input equations and the circuit output are as follows. D A = x’y + xA D B = xB +y’A’ z = (A+B)’ Draw the logic diagram. Complete the state table. D C Q A D C Q B x y z Present State Inputs Next State Output A B X Y A B Z 0 0 0 0 0 1 1 0 0 0 1 1 0 1 0 0
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