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Quiz7Soln - 1 X 1 X 1 1 T B = S’A’ SB’ SC ABC’ or...

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Quiz #7 EE102 Fall 2006 November 8, 2006 Show all work to receive maximum credit. Make sure your final answer is clearly marked. Name: 1. Random Counters (100 points) A select input, S, is used to select between random count sequences as shown below. State 010 is not used in Loop 1 and State 100 is not used in Loop 2. (a) (50 pts) Fill out the state table and values for T-flop inputs S A B C A* B* C* T A T B T C 0 0 0 0 1 1 1 1 1 1 0 0 0 1 0 1 1 0 1 0 0 0 1 0 X X X X X X 0 0 1 1 0 0 0 0 1 1 0 1 0 0 0 0 1 1 0 1 0 1 0 1 1 0 0 0 0 1 0 1 1 0 1 0 1 0 1 1 0 1 1 1 1 1 0 0 0 1 1 0 0 0 1 1 1 1 1 1 1 0 0 1 0 1 0 0 1 1 1 0 1 0 0 1 1 0 0 1 1 0 1 1 0 0 0 0 1 1 1 1 0 0 X X X X X X 1 1 0 1 1 1 0 0 1 1 1 1 1 0 0 0 1 1 1 1 1 1 1 1 1 0 1 0 1 0 000 010 101 001 100 011 111 110 010 100 111 101 001 011 000 LOOP 1, S = 0 LOOP 2, S = 1 0 1
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(b) (30 pts) Determine the functions for the Flop inputs T A = B’C’ + SAC’
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Unformatted text preview: 1 X 1 X 1 1 T B = S’A’ + SB’ + SC + ABC’ or SC + A’B’ +A’C + ABC’ 1 1 1 X 1 X 1 1 1 1 1 1 T C = C’ + S’A + SA’ + S’B + SB’ = C’ + S ⊕ A + S ⊕ B or = (S+A+B+C’)(S’+A’+B’+C’) using the 0’s. 1 1 X 1 1 1 1 X 1 1 1 1 1 1 (c) (20 pts) From your answer in (b) determine what state would follow 010 in Loop 1 and 100 in Loop 2. Draw that connection on the state diagram. You can determine what state these will go to by either plugging in the value into the equation, or by looking to see if that value is circled on the K-Maps. For 0010 in Loop 1, noticed that it is circled for T B and T C , but not T A . Thus, 0010 will go to 0001, where only the last two bits toggle. Note that if the 2 nd equation is used for T B , the next state will become 0011. For 1100, the next state will either be 1011 or 1001, depending on your equation for T B . S A B C...
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