Scenario: Design a traffic light control system for a two$-$way intersection, where each direction has a red, yellow, and green light.

Inputs:

A: Sensor for Direction $1(1$ if a vehicle is present, $0$ otherwise$)$

B: Sensor for Direction $2(1$ if a vehicle is present, $0$ otherwise$)$

C: Emergency Vehicle Signal $(1$ if an emergency vehicle is approaching, $0$ otherwise$)$

Tasks:

i$.$ Design a truth table for the traffic light system, specifying the output signals for each light $($R$1,$ G$1,$ Y$1$ for Direction $1$ and R$2,$ G$2,$ Y$2$ for Direction $2).$

ii$.$ Derive the logic expressions for each output using AND, OR$,$ and NOT gates based on the truth table.

iii. Implement the logic expressions using basic gates and draw the circuit diagram.

iv$.$ Write the gate level HDL$.$