Q$1.$

A seven segment display, as show in the figure, consist of seven LEDs $($eight if you count the decimal point$)$ that light up when connected. Design the simplest possible logic circuit for two of these segments $($select them randomly other than A$)$ that takes four inputs $(w,x,y,z)$ and displays its hexadecimal value. A table of the four bits input and the expected display output is shown below with segment A truth table as an example.

$\backslash$table$[[w,x,y,z,$Display,A$,,],[0,0,0,0,0,1,,],[0,0,0,1,1,0,,],[0,0,1,0,2,1,,],[0,0,1,1,3,1,,],[0,1,0,0,4,0,,],[0,1,0,1,5,1,,],[0,1,1,0,6,1,,],[0,1,1,1,7,1,,],[1,0,0,0,8,1,,],[1,0,0,1,9,1,,],[1,0,1,0,$A$,1,,],[1,0,1,1,$b$,0,,],[1,1,0,0,$C$,1,,],[1,1,0,1,$d$,0,,],[1,1,1,0,$E$,1,,],[1,1,1,1,$F$,1,,]]$