How Do You Design a JK Flip-Flop Synchronous Up/Down Counter?

[Mark200]

Exam question:

Use J-K flip-flops to design the logic for a synchronous up/down counter that counts "up" through the sequence 1 2 6 3 5 7 f the input switch UP is 1, and "down" through the sequence 7 2 1 5 3 6 if UP is 0. Verify that the counter is self-starting.


What I know so far:

Ok so in my book I've found a similar circuit, except it's to count through the sequence 1 2 3 4 and so on. And I'm not sure at all how I'd go about changing the circuit to work for the question above. The circuit I have is:

Any ideas?

 

[cepheid]

Hi Mark200, welcome to PF!

Hmmm...so it looks like you'll need three bits. And you want to go through the sequence:

001
010
110
011
101
111

It looks like the circuit you have makes great use of the fact that setting J = K = 1 toggles Q to change state, and setting J = Q = 0 keeps it the same. So I would expect that what would change would be which output of which AND gate goes where. That's all I've got though, short of actually trying to draw out different circuits.

 

[Mark200]

Ok I'm afraid I'm going to need to ask for more help on this question! I failed my exam and I have to do a repeat exam, and it's tomorrow hah. And this question came up on the original exam!

I've been trying to figure out how to do it. I found a way, but it involves having about three logic gates for every single input and it's extremely messy. There must be an easier way. I tried to scan my work so far in but my scanner isn't working! I've thought about changing where the outputs go but I don't think that'll work.

Any ideas?? As much help as possible would be great! Even if it doesn't come up on the exam tomorrow it'd just be a relief to finally know how to do this question

 

[LCKurtz]

Exam question:

Use J-K flip-flops to design the logic for a synchronous up/down counter that counts "up" through the sequence 1 2 6 3 5 7 f the input switch UP is 1, and "down" through the sequence 7 2 1 5 3 6 if UP is 0. Verify that the counter is self-starting.


What I know so far:

Ok so in my book I've found a similar circuit, except it's to count through the sequence 1 2 3 4 and so on. And I'm not sure at all how I'd go about changing the circuit to work for the question above. The circuit I have is:

Any ideas?

Ok I'm afraid I'm going to need to ask for more help on this question! I failed my exam and I have to do a repeat exam, and it's tomorrow hah. And this question came up on the original exam!

I've been trying to figure out how to do it. I found a way, but it involves having about three logic gates for every single input and it's extremely messy. There must be an easier way. I tried to scan my work so far in but my scanner isn't working! I've thought about changing where the outputs go but I don't think that'll work.

Any ideas?? As much help as possible would be great! Even if it doesn't come up on the exam tomorrow it'd just be a relief to finally know how to do this question

I'm sure it's a bit late for your exam. But instead of trying to find some ad-hoc jerry-rig that works, why don't you make a next state karnaugh map table with variables s, y0,y1,y2 from which you can solve for the J and K inputs? Takes a little time but also removes all the trial and error guesswork.