Johnson Counter

While Ring counter, we have connected Q of last to D of 1^st FF, but in Johnson Counter we connect Q bar of last to D of 1^st FF as shown below and we also don’t need to connect preset of 1^st FF. This is also called Twisted Ring counter:

And JK implementation is as follow:

And we have outputshas follow:

Clock                     Q₄ Q₃ Q₂ Q₁

Initially                  0000

1^st tick                   0001

2^nd                          0011

3^rd                           0111

4^th                           1111

5^th                           1110

6^th                           1100

7^th                           1000

8^th                           0000

We can also note that we use only 8 out of 16 possible states and in general we have used 2n states and hence we have 2ⁿ-2n unused states