A Johnson counter is often used in similar circumstances. To count eight states 0000 -> 0001 -> 0011 -> 0111 -> 1111 -> 1110 -> 1100 -> 1000 -> 0000 it wou

A Johnson counter is often used in similar circumstances. To count eight states 0000 -> 0001 -> 0011 -> 0111 -> 1111 -> 1110 -> 1100 -> 1000 -> 0000 it would have to be a four bit register ABCD where A = B, B = C, C = D, and D = NOT A It would be one more flip-flop but the counting logic would be free. A flip-flop has a NOT output. Decoding of the eight states are also simple: State 0000 is NOT A AND NOT D State 0001 is NOT C AND D and so on. Notice the NOTs are free.