Synchronous 110 detector ($z_k=a_{k-2}{a}_{k-1}(1-a_k)$)

A synchronous sequential circuit emitting a one-cycle pulse at the first low sample after at least two consecutive high samples. Three D flip-flops can implement $q_1^{+}=a$, $q_2^{+}=q_1\wedge a$, and $z^{+}=q_2\wedge \neg a$, with all updates using the old state. Initializing all state bits to zero excludes a false startup history. The stored output changes only at clock edges. After a detecting low sample, $q_2$ becomes zero, so the next output is zero regardless of the next input. A longer high run still ends with the same three-sample pattern.