Binary counter

A counter stores a binary representation of a state, usually advancing by one increment or decrement modulo $2^n$ when it has $n$ bits.

A digital counter cycling through six stored values. With ordinary binary representation, the valid three-bit states are $000,001,010,011,100,101$. The unused encodings require either an initialization assumption or specified recovery transitions.

A cascade in which an output transition of one flip-flop clocks the next. With positive-edge-triggered toggle stages and uncomplemented $Q$ connections, it decrements modulo $2^n$: a zero bit rises to one and propagates a borrow, while a one bit falls to zero and stops propagation. Ripple propagation takes time, so intermediate transient states are not the settled counter state.