Digital Design $(10\%)$

A modern dishwasher is equipped with three sensors to automatically select the most efficient cleaning cycle. The sensors monitor the following conditions:

Soil Level Sensor $($S$)$: Detects the amount of food residue on the dishes. $(S=1$ for high soil, $S=0$ for low soil$).$

Load Size Sensor $($L$)$: Measures the size of the the water is hard or big load, $L=0$ for small load$).$

Water Hardness Sensor $(H)$ : Id

The dishwasher must

$0$ Eco Cycle: For low soil levels and the following three cycles:

Normal Cycle: For high soil levels XOR big loads, regardless of water hardness.

Heavy Duty Cycle: For high soill levels AND loads, provided the water is soft.

loads, or if the water is hard and Eco cycle is not selected.

$C_1=1$ : Activates the Eco Cycle.

$C_2=1$ : Activates the Normal Cycle.

$C3=1$: Activates the Heavy Duty Cycle.

$($a$)$ List the $3$ inputs:

$($b$)$ List the $3$ outputs:

$($c$)$ On the page to the right, design a truth table for the system, listing all possible combinations of the inputs and their corresponding outputs.

$($d$)$ Populate the $k-$maps below, and write the simplified logic statements for each $k-$map.