$(5$ pts$)$ Draw the state diagram of an FSM which accepts a binary stream and outputs a $\text{'}1\text{'}$ whenever it detects a pattern $"1111".$ Overlapping sequences are allowed. For example:

$\backslash$table$[[$Input Stream:,$1,1,1,1,0,1,1,1,1,1,0,0,1,0,1],[$Output:$,0,0,0,1,0,0,0,0,1,1,0,0,0,0,0]]$

$(5$ pts$)$ Perform state encoding. Show the tabular representations of next state and output functions.

$(5$ pts$)$ Derive minimized Boolean equations for next state and output functions.