A sequential circuit has one input and one output. In the input sequence whenever a pattern 010 or 0001 is detected, the output becomes 1 when the last symbol of the pattern is received. Otherwise, the output equals to 0. What will be the minimum number of states of the equivalent state diagram of this synchronous sequential circuit?

To detect patterns 010 and 0001, we need states representing partial matches. State diagram needs: initial state (S0), after '0' (S1), after '01' (S2), after '010' (S3 - output 1), after '00' (S4), after '000' (S5), after '0001' (S6 - output 1). However, some states can be merged, and the minimal implementation requires 5 states to track all necessary prefix information without redundancy.