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Digital Electronics: State machine

  1. Nov 25, 2009 #1
    1. The problem statement, all variables and given/known data

    (a) How many states does this system have?
    (b) How many rows will there be in a state transition table?
    (c) Provide the state transition table.
    (d) Draw a state diagram of the system.
    (e) Describe what the circuit does in words.


    2. Relevant equations

    3. The attempt at a solution

    a) I think there are two flip flops (or are they switches?), so that means that there are four states: 00, 01, 10, and 11.

    b) I think the state transition table will have 8 rows. These numbers will be at the beginning of each row:

  2. jcsd
  3. Nov 25, 2009 #2


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    Staff: Mentor

    Good. Correct so far. Now make label those three columns as A, B and Y (the inputs to the logic), and make 2 more columns for the "Next X, Next Y" outputs of the FFs. Use the logic terms shown for the J&K inputs for the 2 FFs to calculate what the Next X and Next Y outputs will be for each row. That is your transition table. Then use that to answer the rest of the questions.

    Show us what you end up with!
  4. Nov 26, 2009 #3
    A B Y Next X Next Y
    0 0 0
    0 0 1
    0 1 0
    0 1 1
    1 0 0
    1 0 1
    1 1 0
    1 1 1

    I'm a little bit confused as to what to do after this. I see the equation AB'Y + A'BY' going into J and K. So that means that J and K will always be the same. Is that right?
  5. Nov 26, 2009 #4


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    Staff: Mentor

    Yes, from the diagram, it does appear that J and K for each FF are the same. What does a JK FF do when both inputs are the same?
  6. Nov 26, 2009 #5
    When both J and K are 0, then there is no change in outputs.
    When they are both 1, then the outputs are toggled.

    A B Y Next X Next Y
    0 0 0

    I still get stuck at this part. I can tell that next Y is going to be 0, but I can't say what next X is, because the table doesn't tell me what X currently is.

    Another question. Is the circuit a Mealy machine, since the output is going back into the input?
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