Hi im solving the example that our teacher gave us i started to solve it and these are the steps im gonna use:
1)Draw state table
2)Draw karnaugh from state table
3)Design circuit with equations from karnaugh
here is my solution: http://imgur.com/a/3gvsB

the problem is i dont know that if im doing it on the right way or not. So far i draw karnaugh map for the msb which is D1 as you can see from the image is my solution correct so far ?

notice that i used x=0 tab for up counter (0-1-2-3-4-5-6-7-0...) and x=1 tab for down counter (7-6-5-4-3-2-1-0-7...)

i circled all the groups in karnaugh for eliminating static-1 hazard but the question doesnt say anything about find hazards etc. so i think i can rule that step out.

So did i missed anything or should i keep continue like this and find D2 D3 eq. as well then draw the circuit ?

 

It looks okay for the 6 minterms you wrote.

You should clarify with your instructor if you're supposed to try to avoid glitches because you're designing a synchronous counter where that won't be a problem.

Some general comments on your truth table.

1. It's more common for Q3 to be more significant than Q1.
2. It's more common for the LSB to be Q0.
3. It will be clearer if you combined all of the data into a single table with 16 rows of data.
4. If you draw your Kmaps with MSB first it will be more natural to read.
5. It would be easier on you and anyone reading your truth table if you included the D excitation data.
6. It would be easier for you to transfer the data to a Kmap if you drew your truth table in "gray code" format (a single bit changing between subsequent rows).

For example, here's the first 4 entries and the Kmap for Dc (D1 from your drawing) for your problem:


Translation to your variables:
D = X
C = Q1
B = Q2
A = Q3
Dc = D1
Db = D2
Da = D3

It's more convenient for members if you post data (e.g. pictures) on this site. It avoids requiring members to go to another site, which might not be trusted, and avoids broken links if someone visits this thread in the future when your picture is gone.

 

It looks okay for the 6 minterms you wrote.

You should clarify with your instructor if you're supposed to try to avoid glitches because you're designing a synchronous counter where that won't be a problem.

Some general comments on your truth table.

1. It's more common for Q3 to be more significant than Q1.
2. It's more common for the LSB to be Q0.
3. It will be clearer if you combined all of the data into a single table with 16 rows of data.
4. If you draw your Kmaps with MSB first it will be more natural to read.
5. It would be easier on you and anyone reading your truth table if you included the D excitation data.
6. It would be easier for you to transfer the data to a Kmap if you drew your truth table in "gray code" format (a single bit changing between subsequent rows).

For example, here's the first 4 entries and the Kmap for Dc (D1 from your drawing) for your problem:
View attachment 118945 View attachment 118946

Translation to your variables:
D = X
C = Q1
B = Q2
C = Q3
Dc = D1
Db = D2
Da = D3

It's more convenient for members if you post data (e.g. pictures) on this site. It avoids requiring members to go to another site, which might not be trusted, and avoids broken links if someone visits this thread in the future when your picture is gone.

The next part of the question asks me to design the same table that you showed on your reply which is the easy part. Thanks for your tips and view on my answer.