Four$-$Bit Binary Code to Gray Code Converter

A Gray Code has the property that adjacent codewords differ in only one position. For example, a $4-$bit Gray Code counts in the following order:

$0000,0001,0011,0010,0110,0111,0101,0100,1100,1101,1111,1110,1010,1011,1001,1000.$

$($a$)$ Fill in the truth table for the $4-$input$/4-$output converter.

$\backslash$table$[[$Input $($Binary code$),$Output $($Gray number$)],[m,A,$B$,$C$,$D$,G_3,G_2,G_1,G_0$