$1.$ Write a sketch using Arduino IDE and include the full code as a text in your solution. $2.$ Design and simulate the hardware circuit using Proteus. Then, include the following images in your solution: a$.$ The design of your circuit before running your simulation. b$.$ All states of your simulation showing all possible cases.

Assume we want to design an embedded system using Arduino Uno board that will control a smart parking gate system. The parking gate consists of a metal stick attached to a servo motor, and an ultrasonic sensor to measure the distance of a car from that stick. The ultrasonic sensor$$s trigger pin and echo pin are connected to Arduino$$s $2$ and $3$ digital pins, respectively. On the other hand, the servo motor$$s orange cable is connected to Arduino$$s $6$ digital pin whereas the servo motor$$s red and brown cables are connected to $5$V and GND$,$ respectively. Initially, the servo motor is set to angle of $0$ degree and the ultrasonic sensor transmits a sonar wave and waits until receives the reflected sonar wave from the incoming car. Once, the ultrasonic sensor receives the reflected signal, the system will measure the distance in centimeter. If the measured distance is less than or equal $200$ cm$,$ the servo motor will be set to angle of $90$ degree which will make the stick in vertical position and thus opening the gate. The system will wait for $10$ seconds to let the car to enter the parking area and afterwards, the servo motor will be set to angel of $0$ degree again to make the stick in horizontal position and thus closing the gate. Finally, after closing the gate, the system will wait for $1$ second to repeat the process again.