$3-$ Write the truth table of the gray code with $4$ bits.

$4-$ Deduce the truth table of the gray code decoder $($Gray bits as inputs and ordinary binary codeas outputs$).$

$5-$ Deduce the logic functions: b$0($g$3,$ g$2,$g$1,$g$0),$ b$1($g$3,$ g$2,$g$1,$g$0),$ b$2($g$3,$ g$2,$g$1,$g$0),$ b$3($g$3,$ g$2,$g$1,$g$0).$

$6-$ Using K$-$map, simplify the function b$0,$b$1,$b$2,$ b$3.$