Question

The message 11001001 is to be transmitted using the crc polynomial x3 +1 to protect it from errors. The message that should be transmitted is :

Answer 1

The polynomial x^3+1 corresponds to divisor is 1001.

11001001 000 <--- input right padded by 3 bits

1001 <--- divisor

01011001 000 <---- XOR of the above 2

1001 <--- divisor

00010001 000

1001

00000011 000

10 01

00000001 010

1 001

00000000 011 <------- remainder (3 bits)

See this for division process.

After dividing the given message 11001001 by 1001, we get the remainder as 011 which is the CRC. The transmitted data is, message + CRC which is 11001001 011.

Answer 2

Answer:

The message can be transmitted as 11001001011.

Explanation:

Given:

The polynomial $x^{3}+1$ .

To find:

The message 11001001 is to be transmitted utilizing the CRC.

Step 1

CRC polynomial:$x^{3}+1=1 \cdot x^{3}+0 \cdot x^{2}+0 \cdot x^{1}+1 \cdot x^{0}$

CRC generator: 1001

Since polynomial exists of order 3 append $30^{\prime}$ s at the end of the message.

Message: 11001001000

Step 2

11001001000

$\oplus 1001$

----------------------

          01011

         $\oplus 1001$

       --------------

           001000

             $\oplus 1001$

           --------------

             0001100

                 $\oplus 1001$

              ---------------

                    01010

                    $\oplus 1001$

                   -------------

                       $\mathbf{0 1 1}$

Transmitted Message: 11001001011

Therefore, the message can be transmitted as 11001001011.

SPJ3