Design a state machine for an automated room light switch. The room has one entrance, A, and one exit, B. Up to 3 people may be in the room at the same time. The light is initially OFF. The light should turn on when the first person enters the room and turn off when the last person exits the room. The sensor on door A produces a momentary 1 input when a person enters the room. The sensor on door B produces a momentary 1 input when a person exits the room. Assume that only one input changes at a given time instance (AB=11 is a don't care condition). Determine the symbolic Moore state transition diagram for the light control system. Assign a sequential binary state assignment for the number of states that you need. Create the encoded state transition table. Develop the reduced excitation and output equations for a state machine with D flip-flops.