Problem $2$: Seven$-$segment displays are very common output display devices that are used in many common

application like clocks, radios, calculators, odometers, etc. It is one of the easiest way to implement a

numeric output for a digital circuit for a hexadecimal base. It takes a four$-$bit binary numeric input, and uses

a display made of seven long, thin LEDs arranged in a pattern of an eight to create to signals necessary to

drive the display. If we label the seven LEDs as $($a$,$ b$,$ c$,$ d$,$ e$,$ f$,$ g$),$ these seven outputs of the decoder select

the corresponding segments in the display, as it shown below: