Q$5(24\text{'})$

a$).$ If an $5-$bit $\frac{A}{D}$ converter with a $-5$ to $5$ V voltage range is used to sample an analog sensor$\text{'}$s voltage, what digital output code would correspond to the sensor value of $3$ V $?$

b$).$ Generate a plot similar to the Figure below for the $5-$bit converter used in Q$3($a$)$ if the input signal $($i$.$e$.,$ the sensor value$)$ is $2\mathrm{.}25$ V $.$

c$).$ As a mechatronic designer moves progressively from the above $5-$bit to $12-$bit A$/$D converter, what problem$($s$)$ might be incurred in the design of the data acquisition system?

d$).$ Why is a $12-$bit $\frac{A}{D}$ converter satisfactory for most laboratory measurements? $($Hint: the typical voltage range for most laboratory measurements is $\frac{+}{-}10V.)$