Suppose you are designing a communication system that uses CRC for error detection. Consider the following scenarios:

Scenario $1$: You have a bit stream $1100110101$ and use the generator polynomial

$$

$3$

$+$

$$

$+$

$1$

x

$3$

$+$x$+1($binary $1011).$ After encoding and transmitting the bit stream, noise introduces a burst error of length $3$ at an arbitrary position. How can you detect this error using the CRC method?

Scenario $2$: Your system allows for the detection and correction of single$-$bit errors using a combination of CRC and Hamming codes. How would you integrate Hamming code with CRC to achieve both single$-$bit error correction and burst error detection? Provide the steps for encoding and decoding in this integrated system prepare a ppt on this question