$7\mathrm{.}28($Word Problem$)$ Two two$-$way streets meet at an intersection

controlled by a four$-$way traffic light. In the east and west direc$-$

tions, the lights cycle from green to yellow to red. The south$-$facing

lights do the same thing, except that they are red when the east$-$

west lights are green or yellow, and vice versa. However, the north$-$

facing lights are augmented with a green left$-$turn arrow. They

cycle red$-$green arrow$-$yellow arrow$-$green$-$yellow$-$red. Consider

the following additional problem specifications:

$($a$)$ When the green or yellow left$-$turn arrows are illuminated,

the lights in the other three directions are red.

$($b$)$ The timings for the north$-$facing lights are as follows: red,

$60$ seconds; green arrow, $20$ seconds; yellow arrow, $10$ sec $-$

onds; green, $45$ seconds; and yellow, $15$ seconds.

$($c$)$ The timings for the other lights can be derived from specifi$-$

cations $($a$)$ and $($b$).$ Assume you have as many programma$-$

ble timers as you need. These can be loaded with a time

constant $($in seconds$)$ and assert an output when they count

down to zero.