$3-$ Write the truth table of the gray code with $4$ bits$\mathrm{.}4-$ Deduce the truth table of the gray code decoder $($Gray bits as inputs and ordinary binary codeas outputs$)\mathrm{.}5-$ 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$0).$