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: 1 1 1 1 0 1 1 1 1 1 0 0 1 0 1

Output: 0 0 0 1 0 0 0 0 1 1 0 0 0 0 0

• Perform state encoding. Show the tabular representations of next state and output functions.
• Derive minimized Boolean equations for next state and output functions.

please draw out state diagram and include Boolean equations. also provide explanation. I am unsure if the answers I came up with are correct. please help.