Digital Electronics: State machine

  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. berkeman

    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. 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. berkeman

    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. 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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