$1.$ The brakes of your car operate when you press the brake pedal. The anti$-$lock brakes kick in when additional conditions arise. In this problem, you are to develop the Boolean expression that cover these conditions. Specifically, the expression will be true if the anti$-$lock brakes should be applied. You will then draw the circuit. The conditions are as follows, all of which have to be true, along with the expected values of the variables that the circuit will use.

$$ The brake pedal must be pressed, brake pedal pressed means P $=1$

$$ The tire sensors must indicate that the road is slick, tire sensors are a two$-$bit value s$1$s$0,$ which is $00$ for dry conditions, $01$ for wet, $10$ for icy, $11$ for snow, slick is defined as $01,10$ or $11$

$$ The temperature sensor must indicate that the temperature is below $40$ degrees, the temperature sensor is a two$-$bit value t$1$t$0$ which is $00$ for temperature below $32,01$

for temperature between $32$ but under $40,10$ for temperature between $40$ and $70,$ and $11$ for temperature above $70$

$$ The car$$s speed must be more than $7$ mph$,$ speed is indicated by a $7-$bit value from the odometer o$6$o$5$o$4$o$3$o$2$o$1$o$0,$ where $0000000$ means $0$ mph

a$.$ Derive the Boolean expression that will output a $1$ if the anti$-$lock brakes should activate. Simplify your expression.

Draw the circuit for the simplified expression from part a