You have been asked by the Take$-$U$-2-$the$-$Top $($TU$2$TT$)$ elevator company to design the controller for a small freight elevator $($no passengers$)$ that will be used for transporting boxes between floors in a threestory warehouse. Each floor has $3$ push buttons. One calls the elevator. The other two select a floor to send the elevator to$.$ There is a sensor on each floor that detects when the car arrives at that floor. $($So there are a total of $4$ signals generated on each floor.$)$ There is a motor which winds and unwinds a cable that lifts the elevator. The motor controller has two logic$-$compatible inputs, UP and DOWN, which cause the motor to turn on and the elevator car to move in the direction indicated when one of them is asserted. De$-$asserting both UP and DOWN turns off the motor and stops the elevator.

Inputs to the elevator controller

$S_1,$ Sensor; asserted when elevator is centered at the $1$st floor

$C_1,$ Button on $1$st floor to call elevator

$P_{12}$ Button on $1$st floor to send elevator to $2$nd floor

$P_{13},$ Button on $1$st floor to send elevator to $3$rd floor

$S_2,$ Sensor; asserted when elevator is centered at the $2$nd floor

$C_2,$ Button on $2$nd floor to call elevator

$P_{21},$ Button on $2$nd floor to send elevator to $1$st floor

$P_{23}$ Button on $2$nd floor to send elevator to $3$rd floor

$S_3,$ Sensor; asserted when elevator is centered at the $3$rd floor

$C_3,$ Button on $3$rd floor to call elevator

$P_{31},$ Button on $3$rd floor to send elevator to $1$st floor

$P_{32},$ Button on $3$rd floor to send elevator to $2$nd floor

Outputs from the elevator controller

$U,$ Moves the elevator up when asserted

$D,$ Moves the elevator down when asserted

Notes

You don't need to worry about the details of braking and accelerating. Pretend that the elevator can start and stop moving instantly.

This elevator has no doors. You may ignore the safety ramifications.

It may be possible, and might simplify your design, if you combine some of the input signals before they become inputs to the state machine.

When your state machine is first powered up$,$ you don't know the exact location of the elevator. Assume that it is somewhere between floor $1$ and floor $3,$ but it could be above or below floor $2.$

Create a fully labeled state diagram for your design. $($You don't need to implement it$,$ e$.$g$.$ by deriving next$-$state and output logic equations.$)$ This is a trial$-$and$-$error process. Once you are happy with your design, please re$-$draw the state diagram nicely and turn that in$.$