State A is the nowhere state, where we are looking for the first 1. On successive 1’s, we move to B and C; a 0 takes us to D and then a 1 produces the 1 output. Since overlapping is allowed, that 1 is the first 1 toward a new sequence, and we return to state B from D. We must also complete the failed paths. A 0 in any state other than C (where we are looking for a 0) returns us to state A. If, after getting two consecutive 1’s, we get a third, we need another state, E, which indicates that we have too many 1’s and are waiting for a 0 before we can go back to state A and start again. The complete state diagram for the overlapped solution is thus shown below.