Making a counter using JK Flip-Flops

Thread Starter


Joined Nov 20, 2016
I have to make a circuit that counts in binary 1,2,3,5,7,0, using JK flip-flops and I'm having a little trouble building the overall truth table and karnaugh maps, could anyone lend me a hand with this?


Joined Mar 31, 2012
Yes, we can help you work through the spots that you are having problems with, but we won't just do your work for you. YOU need to show YOUR best attempt to at least get started on YOUR homework problem. That will let us see where you are going astray so that we can help you get back on track.


Joined Nov 13, 2010
There is a simple procedure for designing J-K state machines, not sure what it might be called but it could be 'transition mapping', where the state transitions for each flip-flop are arranged in a Karnaugh Map structure and the minimization will give the logic for driving the J-K inputs of the flip-flop.

Next-state transitions of a state variable are identified as 0,1,α,β according to the following guide:


These next-state transitions for each state variable (plus any "don't care" conditions) are plotted on a Karnaugh Map which shows all possible states (therefore it gets difficult beyond four state variables). There will be an identical K-map for each J & K input of a flip-flop (i.e., the Q output of the flip-flop is the state variable). For minimization of the J input, the 'α' transitions are mandatory and the 'β' & '1' transitions are optional; for minimization of the K input, the 'β' transitions are mandatory and the 'α' & '0' transitions are optional. That's all there is.

Now this can't show how to solve your particular problem, but can demonstrate the whole procedure for a similar problem: three J-K flip-flops counting the sequence 0,1,2,3,6,5,7,0..... After getting the J-K logic for each flip-flop, I created the circuit in Logisim (free software) to verify proper operation.