Design Problem $2$:

This is a problem that involves Gray Code, a binary numeral system where two successive values differ in only one bit. You are asked to design a combinational logic circuit that converts a $4-$bit Gray Code to a $4-$bit binary number. The provided table shows the Gray Code corresponding to decimal values $0-15.$ For example, the Gray Code for $7$ is given as $0100,$ and the corresponding binary value for $7$ is $0111.$ So the circuit should convert from the Gray Code $0100$ to the binary equivalent $0111.$

$\backslash$table$[[$Binary$,$Gray Code$],[0000,0000],[0001,0001],[0010,0011],[0011,0010],[0100,0110],[0101,0111],[0110,0101],[0111,0100],[1000,1100],[1001,1101],[1010,1111],[1011,1110],[1100,1010],[1101,1011],[1110,1001],[1111,1000]]$

$\backslash$table$[[$INPUTS $($GRAY CODE$)],[\backslash$table$[[$G$3,$G$2,$G$1,$G$0,$B$3,$B$2,$B$1,$B$0],[0,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,1],[0,0,0,0,0,0,1,0],[,,,,,,,],[,,,,,,,],[,,,,,,,],[,,,,,,,],[,,,,,,,],[,,,,,,,],[,,,,,,,],[,,,,,,,],[,,,,,,,],[,,,,,,,],[,,,,,,,]]]]$