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. 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 $($ 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.