Problem: The initial dictionary is shown below:

Encode "hillbillie$\_$bill$\_"$ using LZW method.

Show the construction of the table step$-$by step: show addition to the dictionary every time you send a code:

the entry index, the code saved$/$sent and the dictionary entry context as shown below"

Examples for steps $1$ and $2$ are provided below.

Step $1$: $"$h$"$ : send $1,$ add hi$(6)$:

Step $2$: $"$i$"$ : send $2,$ add $"$il$"(7)$:

Continue: