K-map for a 4-bit synchronous decade counter.

[muppen]

Homework Statement

I'm a bit at a loss here for a particular assignment we got for one of our labs. I've been using a certain method to derive the k-maps for some circuits, but for this particular one, it didn't really work out too well for some reason. We built and implemented a 4-bit synchronous decade counter. We were then told to make a state diagram, next-state table and a k-map for all the j-k inputs. I'm having a particular issue with the K4/J4 and the K2 maps.

Let me first give you a link to the actual circuit:

http://www.electronics-tutorials.ws/counter/cou14.gif

This is how far I've gotten, I've make a flip-flop transition table, next-state table and also been determining which cells to map with what from it.

http://imageshack.us/f/813/18768245.png/

Is there a flaw in my reasoning? For example, I first take Q1, and check the position 0000 against the next state. I then derive what to place in that position for J1 and K1, and I do the following for all the other positions and Q2-Q4. Am I using the wrong method, or have I mapped something wrong or written something wrong?

Here's how far I've gotten:
http://imageshack.dk//viewimage.php?file=/imagesfree/Fah58500.png

Homework Equations

J₁/K₁ should always be high, which is correct.
J₂/K₂ should be Q₁Q₄'. The J₂ is correct, but the K₂ is not.
J₃/K₃ should be Q₁Q₂, which is correct.
J₄/K₄ should be Q₁Q₂Q₃ + Q₁Q₄. I however, get some other results.

Where am I wrong in my reasoning? I know there's another way to solve the K-maps for this counter, by checking previous outputs when the current output toggles, but I've used this method before, and it has worked just fine. Am I marking the positions on the K-map wrong or am I using the wrong method, or does it not apply to these, or what?

I'm grateful for any help.

 

[muppen]

I noticed the link to the circuit might not work, so here's a working one: http://imageshack.dk//viewimage.php?file=/imagesfree/dr654051.png"

I had mapped 3 positions wrong in the K1 and K3 maps, but it didn't change the outcome at all. Here's the progress so far: http://imageshack.dk//viewimage.php?file=/imagesfree/xD854200.png"

 

[LCKurtz]

I looked at your work, and I agree with you for the values that you get for your J and K inputs on all four FF's. The ones you marked as possibly wrong are not wrong; they are correct.

What I don't understand is why in your circuit, you have the J and K inputs on each FF connected together. But on FF's 2 and 4 your expressions for J and K are not equal. I think all that is wrong is you haven't wired your circuit to agree with your logic.

 

[muppen]

It's because I just took a circuit from Internet, and implemented that, due to lack of time. It was only afterwards, while doing the report, that I realized it wasn't the same circuit as what circuit diagram showed. The expressions I got from my Karnaugh map were correct, it's just that there's more than one way to design a synchronous decade counter.

 

[LCKurtz]

It's because I just took a circuit from Internet, and implemented that, due to lack of time. It was only afterwards, while doing the report, that I realized it wasn't the same circuit as what circuit diagram showed. The expressions I got from my Karnaugh map were correct, it's just that there's more than one way to design a synchronous decade counter.

I gather that you realize that circuit you lifted from the internet isn't correct. It transitions from hex 6 to hex F : 0110 → 1111.