P$3(15$ points$)$ You are provided with the following state table for an FSM:

a$)(5$ points$)$ Perform a one$-$hot encoding state assignment for the FSM

b$)(5$ points$)$ Use Karnaugh maps $($K$-$maps$)$ to derive the logical expressions for the next state variables and output.

c$)(5$ points$)$ Draw the state diagram corresponding to the given state table.