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

1. Sep 26, 2012

enmar

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. Sep 27, 2012

LCKurtz

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
3. Sep 27, 2012

enmar

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

4. Sep 27, 2012

LCKurtz

Check that one.

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