Assuming the generator polynomial x$^5+$ x$^3+$ x$^0,$ what is the CRC code for the following bit sequence:

$0110111001111011110111111010111?$

$1.$ Manually compute the solution for the question show your steps.

$2.$ Manually encode the message bits $10010011011$ with a Cyclic Redundancy Check $($CRC$)$ scheme using

polynomial x$^4+$ x $+1.$ Show your steps.

$3.$ If an error pattern of $100010000000000$ is introduced. Manually compute the bits received. Show your

steps. Will the error be detected?

$4.$ If an error pattern of $100110000000000$ is introduced. Manually compute the bits received. Show your

steps. Will the error be detected?