The state diagram shown is an FSM for detecting an overlapping three-bit sequence. Its input is In, output is Out, and initial state is S0. For input sequence 10101101001101, read from the left-most bit, the number of times Out is 1 is ________.
The output-one transition is S2 to S3 on input 1. Reaching S2 means the recent input suffix is 10, so that transition detects 101.
S3 retains the relevant suffix after detection, allowing overlapping matches rather than restarting without memory.
In 10101101001101, the substring 101 ends at bit positions 3, 5, 8 and 14, counting from one. Each produces one output pulse. Thus Out equals one **4 times**.
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