Fact about Johnson counter

The Johnson counter is made of a simple shift register with an inverted feedback. That is if the complement output of a ring counter is fed back to the input instead of the true output, a Johnson counter results. Figure shows the 4-bit Johnson counter with 2*4=8 states.

Johnson counter have 2n states where "n" is the number of flip-flops. But normal binary counters have (2 power n) states for the same number of flops. Here the interesting news about the Johnson counter is unused states. The formula used to find out the unused states is (2 power n) - (2n). Here, in this case, the number of unused states are (2 power 4) - (2*4) = 8 states.