Exercise $3\mathrm{.}20$ You are designing an FSM to keep track of the mood of four students working in the digital design lab. Each student's mood is either HAPpY the circuit works$),$ SAD $($the circuit blew up$),$ BUSY $($working on the circuit$),$ CLUELESS $($confused about the circuit$),$ or ASLEEP $($face down on the circuit board$).$ How many states does the FSM have? What is the minimum number of bits necessary to represent these states?