The control of a train door should be implemented as follows:

In the start state, the train is in motion. Meanwhile, the door is closed and locked. The train stops when the brake $($B$)$ is applied. The door is still closed and locked. Now the train driver can release the door by sending a release $($F$).$ If the door is released but still closed, a green signal should light up on the door button $($GS$).$ Pressing the button $($K$)$ by a passenger then initiates the opening of the door. To open the door, a corresponding signal $($MS$1)$ must be applied to the motors until a switch $($T$1)$ indicates that the door is fully open. To simplify matters, you can assume that the train stops completely when the brake is applied. You can also assume that the door does not close again automatically and that the door is only released once per stop. If the door is released or open, the train driver can lock it again with the signal $($S$).$ This signal has a higher priority than all other signals. If the door is still closed, it can no longer be opened. Otherwise, it must be closed first. The door is closed in a similar way to opening by applying a signal $($MS$2)$ to the door motors until a switch $($T$2)$ indicates that the door is closed. For safety reasons, the door should emit a warning signal during closing $($WS$).$ If the door is still in the process of opening, the signal $($S$)$ is ignored. If the door is closed and locked, the train moves off again when the throttle lever $($G$)$ is operated. However, the throttle lever $($G$)$ is ignored if the door is released at the same time. At any time a signal $($ZS$)$ should be sent when the door is closed and locked. a$)$ Design a Moore automaton that implements the door control. The automaton uses the inputs B$,$ F$,$ K$,$ T$1,$ S$,$ T$2,$ G and the outputs GS$,$ MS$1,$ MS$2,$ WS$,$ ZS$.$ b$)$ Specify the state transition table and the output table for the automaton from the previous task. You do not have to code the states in binary. In the state transition table, use Don't Cares for transitions that are not used in a state transition.