Consider that you are to design a circuit that will operate the traffic lights at a four$-$way intersection consisting of two intersecting roads: road $1$ and road $2.$ Road $1$ has green, yellow, and red lights to indicate traffic instructions, and these will be called $G1,Y1,$ and $R1,$ respectively. Road $2$ also has lights, which will be called G$2,$ Y$2,$ and R$2.$ These lights will shine when they receive a logic $1.$ Recall that the typical procedure for traffic lights is as follows: consider that the circuit is currently operating such that G$1$ and R$2$ are on $($traffic for road $1$ is moving while traffic for road $2$ is stopped.$)$ To warn the road $1$ traffic that it will need to stop, G$1$ turns off and Y$1$ turns on$.$ Then, Y$1$ turns off and R$1$ turns on$.$ Note that R$1$ and R$2$ should be on at the same time for a short period to ensure that all traffic in the intersection leaves before road $2$ traffic is allowed to move. Then, R$2$ turns off and G$2$ turns on$,$ which is then followed by G$2$ turning off and Y$2$ turning on$,$ which is then followed by Y$2$ turning off and R$2$ turning on$.$ After $R1$ and $R2$ remain on for a few seconds $($again$,)$ the entire process should be repeated. The input to the circuit, A$,$ determines which set of lights should transition through their traffic pattern; if A $=0,$ then the sequence $G1Y1R1$ should occur, and if $A=1,$ then the sequence $G2Y2R2$ should occur. Note that, after the sequence begins, it will finish regardless of the value of A$.$ A is controlled by a timing circuit that does not need to be considered for the design.

Here are a few hints to help you with the design:

i$)$ This should be a Moore circuit. You could design it as a Mealy circuit, but it would just simplify down to a Moore circuit.

ii$)$ There should be five states.

iii$)$ Each of the lights is an output for the circuit, so there are six different outputs.

To help organize your work, write down definitions for each of the five states. That is$,$ explain which lights would be on for each state.

Based on the problem description, sketch a STG$.$ Because this is a Moore circuit with six outputs, six values should be listed inside each state. Please arrange the values as shown