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Draw the state diagram of an FSM which accepts a binary stream and outputs a 1 whenever it detects a pattern 1 1 1 1

Draw the state diagram of an FSM which accepts a binary stream and outputs a 1 whenever it detects a pattern 1111. Overlapping sequences are allowed. For example:
Input Stream: 111101111100101
Output: 000100001100000
a. Perform state encoding. Show the tabular representations of next state and output functions.
b. Derive minimized Boolean equations for next state and output functions.

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