Consider the $(2,1,3)$ convolutional encoder of Fig. below.

g$1=1011,$g$2=1111,$ ouptut is v$1=$u$+$b$1+$b$2$

$,$v$2=$u$+$b$0+$b$1+$b$2$

$($a$)$ Draw the state diagram, code tree $($t $=3)$ and Trellis diagram.

$($b$)$ Determine the codeword for the input u $=1011.$