Question $1$: $(40$ points$)$ Please read the question before starting this problem and pick the important infor$-$

mation out.

$$ You are tasked to create a traffic controller Mealy state machines. There will be THREE

SEPARATE machines, and their descriptions will be listed below. Here is a diagram of

the system.

$$ Consider a system comprising three state machines: a Traffic Signal state machine, a

Pedestrian Walk Signal state machine, and a Timer state machine. Your task is to

construct a separate state diagram for each module.

When designing these specific FSMs$,$ you will only need to label the necessary signals

on your state diagram. For example, if the btn input for the Traffic Signal FSM is the only

one that matters in its initial state, only label all values of this input on transitions out of

the initial state.

$($a$)$ Signal Descriptions

i$.$ btn: A button the user presses to activate the Pedestrian Walk Signal.

ii$.$ down: A signal set by the timer indicating the timer has counted down.

iii. start $1$: A signal sent by the Traffic Signal FSM to tell the Timer FSM to start

counting.

iv$.$ start $2$: A signal sent by the Pedestrian Walk Signal FSM to tell the Timer FSM

to start counting.

v$.$ walk: A signal sent by the Traffic Signal FSM to the Pedestrian Walk Signal FSM

to make the Pedestrian Walk Signal display the walk sign.

vi$.$ done: A signal sent by the Pedestrian Walk Signal FSM stating that the FSM is

done.

vii. counting: An internal variable which counts. You will not need to worry about

designing where the signal comes from rather just focus on the fact that its there.

$($b$)$ Traffic Signal FSM:

This state machine should only need THREE states. Assume the light is initially

GREEN. When the btn is pressed $($i$.$e$.$ HIGH$),$ then the light should turn YELLOW,

and at the same time, start $1$ should transition to HIGH. When the down signal is

set to HIGH by the Timer FSM$,$ then the light should go RED. When the done signal

is set to HIGH by the Pedestrian Walk Signal, then the light should turn GREEN,

and walk should be LOW. Otherwise, walk should be HIGH, and the light should stay

RED.

$($c$)$ Pedestrian Walk Signal FSM:

This state machine should only need THREE states. Assume the Signal initially

displays a STOP symbol. If this module sees that walk is set to HIGH, then the

Pedestrian Walk Signal should display a walking symbol $($i$.$e$.$ a person$),$ and should

set start $2$ to HIGH. Once the Pedestrian Walk Signal sees down transitions to HIGH,

then the Pedestrian Walk Signal should start counting down and set the start $2$ to

HIGH; otherwise, the sign should keep showing a person. Once down has been set to

HIGH again, the Pedestrian Walk Signal should display a STOP symbol and set done

to HIGH.

$($d$)$ Timer FSM:

This state machine should only need TWO states. Assume the timer starts off waiting

for either start $1$ or start $2$ to go HIGH, set by the Traffic Signal or Pedestrian

Walk Signal. Once either start $1$ or start $2$ goes HIGH, then the timer should

count, and once the internal signal counting returns to LOW, the timer returns to its

idle$/$waiting state waiting for either start $1$ or start $2$ to go HIGH again. However,

before returning to its idle$/$waiting state, down should be HIGH. Otherwise, the timer

should keep counting if counting is not done $($i$.$e$.,$ HIGH$).$