Help with designing counters

[Hollgam]

One more problem that I can't figure out about counters. I hope you'll be able to help! Thanks in advance.

I need to design 2 counters:

- a 2-bit counter that counts 2, 1, 0, 2, 1, 0 … (If the counter happens to be in state 3 in the beginning, it must first go to zero: 3, 0, 2, 1, 0, 2, 1, 0 …)

- a 3-bit counter that counts 7, 5, 1, 0, 7, 5, 1, 0 … (If the counter happens to be in state 2, 3, 4 or 6 in the beginning, it must first go to zero, e.g.: 2, 0, 7, 5, 1, 0, 7, 5, 1, 0 …)

I would appreciate it really a lot if you could explain me how to solve this.

 

[eklikeroomys]

What are you allowed to use for designing the counters?

 

[Hollgam]

Thanks for your reply! We are studying just basics and we've covered D, J-K flips flops before counters and I think these and simple things like AND, NOR etc. are the only components that we are allowed to use.

 

[Kral]

The straighforward way to solve these problems is to constrocct a truth table showing the current state and desired next state of the counter. From the current state you develop the equation (in terms of the current state) for the input(s) to each stage required to produce the correct next state.

 

[Hollgam]

Thanks for your help!

 

[yadavvlsi]

I suggest you to read one of the following book( whichever is available):

1. Fundamentals of Digital circuit by Anand Kumar >>> prefer this one if possible
2. Modern Digital Electronics by R.P. Jain
3. Digital Electronic by R.K Gaur