Q$4$: a$)$ A bit stream $10000101$ is transmitted using the standard CRC method described in the text. The generator polynomial is $x^3+1.$ Show the actual bit string transmitted.

Answer: actual bit string transmitted after applying the CRC method with the generator polynomial $x^3+1$ is: $10000101000$

b$)$ Suppose that the second bit from the left is inverted during transmission. Show that this error can be detected at the receiver's end.

Answer: If the second bit from the left is inverted during transmission, the received bit string becomes: $11000101000.$