Encode the $6-$bit data message sequence $111110$ using the generator polynomial C$($x$)=$

x$3+$x$2+1$ and give the codeword in polynomial form.

$1)(6$ points$)$ Use polynomial long division $($or binary long division$)$ to show how the CRC

generation is calculated.

$(1$ point$)$ What is the transmitted codeword P$($X$)$ in polynomial form? $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

$(1$ point$)$ What is the transmitted codeword P$($X$)$ in binary? $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

Now assume that the channel introduces an error pattern $001110000($i$.$e$.,$ the bits in position $3,4$

and $5$ from left, will be received in error$).$ What is the received codeword P$($X$)?$

$(1$ point$)$ Received codeword P$($X$)$ in polynomial form: $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

$(1$ point$)$ Received codeword P$($X$)$ in binary: $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$