Draw the truth table for displaying octal numbers on a $7-$segment display, using the standard designations for a$,$ b$,$ c$,$ d$,$ e$,$ f$,$ and $g$ segments. It will have $3$ input columns $(A,B,$ and $C)$ and $7$ output columns for a through $g.$ Use it to write Boolean expressions for segments b and c$.$