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4-M2-soln - Midterm 2 Solutions ECE 25 Spring 2008 Tuesday...

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1) Sequential logic implementation (10 pts) Consider the following incompletely-specified Moore machine (“*” indicates don’t cares). S 1 + S 0 + S 1 S 0 I = 0 I = 1 F A A C 1 B C A 0 C B * 0 Suppose we use the following state encoding. State S 1 S 0 A 01 B 11 C 00 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 = ¯ S 1 S 0 S 1 + = ¯ S 0 S 0 + = ¯ I ¯ S 1 + IS 1 0 * 1 0 0 1 0 1 S 0 F S 1 1 0 * 0 0 * 0 * 1 1 * 0 0 * 1 * 00 01 11 10 S 1 S 0 S 0 + 00 01 11 10 S 1 S 0 S 1 + 00 01 00 01 I I 1
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2) Reverse engineer sequential circuit to finite state machine (10 pts) I F D-FF XOR XOR XOR S 1 S 1 + D-FF S 0 S 0 + a) Fill out the following functions (OK to use in functions). F = S 1 S 0 S 1 + = I S 0 S 0 + = ¯ I S 1 b) Assume initial state is 11 , fill in the following state table. If a state is not reacheable, indicate the appropriate don’t cares (use “*” to indicate don’t cares). S 1 + S 0 + S 1 S 0 I = 0 I = 1 F 00 01 10 0 01 11 00 1 10 00 11 1 11 10 01 0 c) With initial state = 11 , what states, if any, are not reacheable?
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