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Determine the Main Cycle of a Counter (JK flip-flops)

  1. Sep 26, 2012 #1
    1. The problem statement, all variables and given/known data
    For the counter shown below, determine the main cycle, and for each of the unused states, show what happens if it starts up there.

    http://i45.tinypic.com/33l1lhc.jpg

    2. Relevant equations
    N/A

    3. The attempt at a solution
    I thought I knew how to do this, but after some deliberation I've determined that I probably don't. It seems to me that, if I started at 000...I would get the sequence 000->010->100->101->010...which would then repeat through three states. I don't know why, but something tells me this isn't right. Can anyone explain to me how to do problems like these? And this is a synchronous counter, right?
     
  2. jcsd
  3. Sep 27, 2012 #2

    LCKurtz

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    Yes, it is a synchronous counter. I would solve it by setting up a little table like this$$
    \begin{array}{|c|c|c|c|c|c|}
    \hline
    Q_1Q_2Q_3& J_1=\bar Q_2& K_1= 1& J_2=\bar Q_3& K_2=Q_3& J_3=Q_1& K_3=Q_1\\
    \hline
    000&1&1&1&0&0&0 \\
    \hline
    110&&&&&& \\
    \hline
    &&&&&& \\
    \hline
    &&&&&& \\
    \hline
    \end{array}$$On the left in the first row you have the current state ##Q_1Q_2Q_3## which you use to fill out the J's and K's in the first row. That allows you to figure out ##Q_1Q_2Q_3## for the next row etc. Notice that we have a disagreement for the next state of 000 already.
     
    Last edited: Sep 27, 2012
  4. Sep 27, 2012 #3
    Well damn, that was a lot easier than I thought it was. So for the sequence, I get:

    000->110->011->001->101->000

    And when I start on the following out-of-sequence numbers, the following results:

    010->010->loop
    100->001->seq.
    111->000->seq.

    Thanks Kurtz
     
  5. Sep 27, 2012 #4

    LCKurtz

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    Check that one.
     
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