$2.$ Create a circuit for a $7-$segment display that can show decimal numbers from $1$ to $9.$ Use a decoder to

control each segment of the display. Based on the binary input, the output must correctly display the

corresponding decimal number. Provide the following:

a$.$ Construct a truth table for each segment $($a to g$)$ based on the binary input representing

decimal numbers from $1$ to $9.$

b$.$ Create K$-$maps for each segment $($a to g$)$ using the truth table.

c$.$ Simplify the Boolean expressions for each segment using the K$-$maps.

d$.$ Draw a detailed circuit diagram showing all the necessary logic gates $($AND$,$ OR$,$ NOT$)$ and the

decoder to control each segment of the $7-$segment display.