$3.(15$ points$)$ A snail has a Mealy machine FSM brain. The snail smiles whenever it slides over the pattern $1101$ or the pattern $1110.$ Your tasks are:

$1.(5$pt$)$ Sketch the state transition diagram for this happy snail using as few states as possible.

$2.(3$pt$)$ Choose state encodings and write a combined state transition and output table using your encodings.

$3.(4$pt$)$ Write the next state and output equations and $(3$pt$)$ sketch your FSM schematic.