# K-map for synchronous 4-bit decade counter

Discussion in 'Homework Help' started by muppen, May 8, 2011.

1. ### muppen Thread Starter New Member

May 8, 2011
3
0
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/Tns42285.png

2. Relevant 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.

2. ### Georacer Moderator

Nov 25, 2009
5,151
1,266
Your first link doesn't work, all it displays is the text /counter/cou14.gif.

Your state and transition tables look correct, nothing to comment there.

In the K1 map, you have forgotten a '1' but the outcome doesn't change.
In the K3 map, you have added two extra '0', but the outcome doesn't change.

Overall, your solution is correct. Did you try to simulate it or run it by hand?
I ran it by hand and the count is correct. Where did you find the supposed correct input functions from? Is it possible that they were referring to the full 4-bit counter up to 15?

Out of curiosity, can you elaborate more on the other way to build this circuit that you mentioned?

3. ### muppen Thread Starter New Member

May 8, 2011
3
0
My apologies, here's a working link to the circuit.

http://imageshack.dk//viewimage.php?file=/imagesfree/dr654051.png

It's a simple synchronous decade counter, which should count from 0000 to 1001 before recycling. The circuit there however, are not the expressions I get from my karnaugh map, so i'm not entirely sure where the fault lies. I fixed the wrong mappings that you mentioned on the K-maps, but like you said, it didn't change the outcome.

Here's my current progress: http://imageshack.dk//viewimage.php?file=/imagesfree/xD854200.png

4. ### muppen Thread Starter New Member

May 8, 2011
3
0
I've yet to build this circuit I got from the K-maps on my own, but I'll build it in multisim, to see if it actually works.

5. ### Georacer Moderator

Nov 25, 2009
5,151
1,266
As I told you before, I ran the circuit by hand, using the expressions you found in your Karnaugh maps. They work like a charm. Give them a try.

I also ran the ready circuit you posted by hand and it also works. It is an example to show that there isn't a single solution to a given problem. I 'd comment however, that I prefer your solution, as it needs less hardware to be built.

Try to ran your circuit by hand too to see for yourself that it is working. Don't always take ready solutions for granted.

Don't forget to answer my question about the other implementation way you used.

Oct 22, 2010
66
3
7. ### Georacer Moderator

Nov 25, 2009
5,151
1,266
It looks like MS Excel to me...