Headlight Control

Your aid is needed in developing the next$-$generation automatic headlight control system for Fjord Motors. You must design an FSM that

monitors the current ambient light level, provided to your FSM as a $2-$bit unsigned number L$,$ and automatically turns the headlights

on$/$off through an output $H(H=1$ means the headlights are on$).$

Your design should turn the headlights on whenever the light level $L$ has been $1$ or less for two consecutive cycles, and should turn the

headlights off whenever the light level $L$ has been $2$ or more for two consecutive cycles $($remember that $L$ is a $2-$bit unsigned number,

hence ranges from $0$ to $3).$

a$.$ Complete the abstract state transition diagram below by adding transitions labeled as DARK and LIGHT from each state. These labels

correspond to $L2$ and respectively.

b$.$ Now choose a representation for the states. The "DAY" state should use $S_1{S}_0=00.$ If possible, choose bit patterns such that all

transitions change only one state bit rather than changing both state bits.

c$.$ Write a truth table for the output $H$ in terms of the current state $S_1{S}_0,$ and a next$-$state table for the next state bits $S_1^{+}$and $S_0^{+}$in

terms of the ambient light level $L=L_1{L}_0$ and the current state $S_1{S}_0.$

d$.$ Copy the truth table and next$-$state table from part $($c$)$ into separate K$-$maps $($one for $H$ and one for each next$-$state variable$).$

e$.$ Use the K$-$maps from part $($d$)$ to find expressions for each output and next$-$state variable with minimal area. $($Minimize each variable

independently$-$do not try to share gates for implementations.$)$ You must consider both minimal SOP and minimal POS solutions, but you

should only circle the better of the two choices $($SOP or POS$)$ on your K$-$maps and write the corresponding expressions when handing in

your homework.

f$.$ For the luxury model of Fjord's new vehicle, the driver has a control knob to adjust the automatic headlights' light$-$level threshold. This

knob produces an $8-$bit unsigned number T$.$ The light sensor L has also been upgraded to produce an $8-$bit unsigned value $($instead of a $2-$

bit value$).$ The values $L$ and $T$ are fed into an $8-$bit unsigned comparator that produces a signal $x$ whenever $x=1x=0LTL,$ and $x=0$ when $LT.$ Explain how $to$ integrate your $FSM$ design with the comparator for the luxury version $of$ the vehicle. Hint:

You should not need $to$ change your design's structure.$L.In$ other words, $x=1$

when $L,$ and $x=0$ when $LT.$ Explain how $to$ integrate your $FSM$ design with the comparator for the luxury version $of$ the vehicle. Hint:

You should not need $to$ change your design's structure.