$($b$)$ An LED $(3$C$2$LED$1)$ is to be driven directly from a CMOS inverter output $(3$C$2-4007)$ to indicate if the gate is outputting a high or low. An excerpt of the datasheet of $3$C$2-3007$ is shown here:

$\backslash$begin$\{$tabular$\}\{$lccccc$\}$

$\backslash$hline Characteristic & $\backslash ($ V$\_\{\backslash$mathrm$\{$DD$\}\}\backslash )$ & Min. & Typ$.$ & Max. & Unit $\backslash \backslash$

$\backslash$hline$\backslash ($ I$\_\{\backslash$mathrm$\{$OL$\}\}\backslash )$ & $5$ V & & & $0\mathrm{.}5$ & mA $\backslash \backslash$

$\backslash ($ I$\_\{\backslash$mathrm$\{$OH$\}\}\backslash )$ & $5$ V & $-0\mathrm{.}5$ & & mA $\backslash \backslash$

$\backslash$hline$\backslash ($ V$\_\{\backslash$mathrm$\{$OL$\}\}\backslash )$ & $5$ V & & & $0\mathrm{.}05$ & V $\backslash \backslash$

$\backslash ($ V$\_\{\backslash$mathrm$\{$OH$\}\}\backslash )$ & $5$ V & $4\mathrm{.}95$ & & V $\backslash \backslash$

$\backslash ($ V$\_\{\backslash$mathrm$\{$iL$\}\}\backslash )$ & $5$ V & & $1$ & V $\backslash \backslash$

$\backslash ($ V$\_\{\backslash$mathrm$\{$iL$\}\}\backslash )$ & $5$ V & $4$ & & V $\backslash \backslash$

$\backslash$hline

$\backslash$end$\{$tabular$\}$

i$)$ Draw a possible schematic of the CMOS gate driving the LED clearly indicating if the CMOS gate is sourcing or sinking current and the value of any other components needed.

ii$)$ Calculate the maximum brightness of the LED for input voltages to the CMOS interter of $0$ V and $5$ V for your circuit if the circuit is powered by a $5$ V supply.