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3-M2-soln - Solutions to Midterm 2 ECE 25 Fall 2008...

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Solutions to Midterm 2 1) Sequential logic implementation (10 pts) Consider the following incompletely-specified Mealy machine (“*” indicates don’t cares). 0/1 A B C 1/* 1/1 0/0 1/* 0/0 x 1 0 x x x x x x x 0 x x x x 1 00 01 11 10 00 01 11 10 I S2 S1 S0 F x 0 0 x 0 x x 0 x x 0 x x x x 1 00 01 11 10 00 01 11 10 I S2 S1 S0 S0+ x 0 1 x 1 x x 0 x x 0 x x x x 0 00 01 11 10 00 01 11 10 I S2 S1 S0 S1+ x 1 0 x 0 x x 1 x x 1 x x x x 0 00 01 11 10 00 01 11 10 I S2 S1 S0 S2+ Suppose we use the following state encoding. (Assume the name the input variable is I .) State S 2 S 1 S 0 A 100 B 010 C 001 Derive the minimum two-level logic for each of the following (you should minimize each logic function separately, no need to worry about sharing logic between logic functions). F = I + S 2 S 2 + = ¯ I ¯ S 0 + IS 0 = I ¯ S 0 either is OK S 1 + = ¯ IS 0 + IS 2 S 0 + = IS 1 1
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2) Datapath/registers (10 pts) Consider the following diagram. Q 3 + Q 2 + Q 1 + Q 0 + 0 1 MUX D-FF 0 1 MUX D-FF 0 1 MUX D-FF 0 1 MUX D-FF D-FF D-FF D-FF D-FF 1 0 1 MUX 0 1 MUX 0 1 MUX 0 1 MUX 0 X 3 X 2 X 1 X 0 Q 3 Q 2 Q 1 Q 0 P 3 P 2 P 1 P 0 P 3 + P 2 + P 1 + P 0 + S S S S
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