Question: A digital electronic system consists of four inputs $($A$,$ B$,$ C and D$)$ and a single output $($Q$).$ The system will produce a $"1"$ at the output only if the input is a power of $2.$

i$.$ Determine the truth table of the digital system and derive the corresponding Boolean equation $($sum of products$).$

ii$.$ Draw the corresponding K$-$map and write the Boolean equation under its simplest form $($use further simplifications if required$).$ Then, draw the corresponding logic circuit using $2-$input gates only.