Hi everyone. I'm currently trying to design a 1,4,3,5,7,6,2,1.... synchronous counter that uses JK flip flops but struggling with my state tables.

i have my current but i'm not certain my next state is correct.
001
100
011
101
111
110
010
001
100

is this right?

and, i have no idea how to get my other table to start building my kmaps.

Can you help me?

 

I have always like to make my current state part of the table just go 0,1,2,3,... all the way to 7 for your three bits. That way you can go straight to the Kmap from there.

current state --> next state.
C2 C1 C0 --> N2 N1 N0
Fill in the table for ever option of the current state.

 

You may benefit from reading over the section of the AAC book on state machines, namely, Moore state machnies...

 

Draw a table with all possible states (eight for a 3-bit machine) going from 0 to 7.
To the right of each state, write down the next state, for example,

000 -> xxx
001 -> 100
010 -> 001
:
:
:

 

Thanks everyone. Also, thanks for the tutorial link. I looked around the site for help before asking you for help, and found the link then. It has been used on this site many times.

I have my state table, but what I still need is the output table. For the life of me I can't figure out how to make the jump from state to output. I need JC, KC, JB, KB, JA, KA which will then determine my Kmaps. That's where I am stuck.

in advance, thank you for your advice.

 

Treat each flip flop independently, so you have a table with eight rows. For each row, list what that FF output is currently and what you want that FF output to become next. Then determine, based on the transition table for a JK flip flop, what J and K have to be. Do that for each row. You know have two tables, one for J and one for K, that you can do a K-map for separately.

 

how do i know what i want it to become next? i really cannot grasp this concept, not sure why.

can you show me the first one?

if my starting bit was 000, and the next state is 001 because 1 is the first number on my list, what do the 6 variables (JC,KC,JB,KB,JA,KA) become based on your instruction?

Treat each flip flop independently, so you have a table with eight rows. For each row, list what that FF output is currently and what you want that FF output to become next. Then determine, based on the transition table for a JK flip flop, what J and K have to be. Do that for each row. You know have two tables, one for J and one for K, that you can do a K-map for separately.

 

Starting with 000, this is not a state in your sequence: 1,4,3,5,7,6,2,1
Hence the next state from 000 is "don't care". You mark this as xxx.

The next on the list is 001.
The state in the sequence after 001 is 100.
Hence you write down
001 -> 100

The next on the list is 010.
The state in the sequence after 010 is 001
Write down
010 -> 001

The next on the list is 011.
The state in the sequence after 011 is 101
Write down
011 -> 101

etc.

keep doing this for 4, 5, 6, 7

 

since i have a series that uses 7 numbers before it repeats, does this mean that 7 out of the 8 will have a "next" to write down? i will only have one row with don't cares?

 

Correct. If the number is not on your list, it will never appear. Hence we don't care what the outcome will be. It will never happen.

 

Okay, i get all that.

But, I have 6 slots to fill. How do I know where to put a 0, 1, or X?
image here: http://www.freeimagehosting.net/2wghg

 

Your table is incorrect.
Do it the way I showed you.

0 -> x
1 -> 4
2 -> 1
3 -> 5
4 -> 3
5 -> 7
6 -> 2
7 -> 6

 

So for Jc and Kc you must determine what inputs are needed on a J and K inputs of the flip flip to make a transition indicated in the table for Qc to Qc+1.

A JK flip flop transition table is needed.

 

Your table is incorrect.
Do it the way I showed you.

0 -> x
1 -> 4
2 -> 1
3 -> 5
4 -> 3
5 -> 7
6 -> 2
7 -> 6

wait - if i start out with current, that is the first glimpse of the problem. why isn't the next state the reflection of 1, which is my next state?

 

I don't understand your question.

You could do it this way:

1 -> 4
4 -> 3
3 -> 5
5 -> 7
7 -> 6
6 -> 2
2 -> 1
0 -> x

It doesn't really matter what order you do it as long as you get all eight of them and the next state is correct.
Doing it in order 0-7 makes sure you don't leave out any.

 

my series does not have a 0. why would we include 0?

 

Because it could simplify the expression. You will find out when we get to the Karnaugh map.