Using the CRC polynomial 1011 compute the CRC code word for

Using the CRC polynomial 1011, compute the CRC code word for the information word, 1011001. Provide the final information word in hex. Check the division performed at the receiver. Final CRC transmitted code in hex:

Solution

Information Word : 1011001

CRC Polynomial : 1011

Let us encode the Information Word with 3-bit CRC.

Information Word with 3 CRC bits padded on right : 1011001000

1011001 000 ß Input with CRC

1011                  ß Divisor

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0000001 000 ß Result is Bitwise XOR of the corresponding bits, rest are copied.

1 011 ß Right Shifting the divisor to corresponding first 1 of dividend.

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0000000 011 ß Remainder 3 bits. Divisor Algorithm stops here dividend is equal to 0.

Final Information word (in hex) : 2CB

Division performed at Receiver

1011001011

1011

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0000001011

1011

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0000000000

Remainder at receiver’s end is 0.