$1.$ With a $12$ bit Analog$-$to$-$digital Converter $($ADC$),$ solve for the following: a$.$ How many discrete analog values can be represented? b$.$ What is the smallest voltage step size this ADC can read $($in mV w$/$ a $5$V reference$)?$ c$.$ You read an analog voltage of $3\mathrm{.}11$ volts, what would be the output value from this ADC? $($Assume a reference value of $5$V$).$