Interactive end-of-chapter exercises

Error Detection and Correction: Cyclic Redundancy Check

Consider the Cyclic Redundancy Check (CRC) algorithm discussed in Section 6.2.3 of the text. Suppose that the 4-bit generator (G) is 1001, that the data payload (D) is 10011010 and that r = 3.

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1. What are the CRC bits (R) associated with the data payload D, given that r = 3?


To compute the CRC, we begin by taking the value of D, 10011010, and multiplying it by 2^3, giving 10011010000. We then divide this number by the generator bits [G] = 1001, using modulo-2 arithmetic. The final remainder, R, after this division are then the CRC bits. Here is that calculation:

We've computed the remainder as R = 0011 and the quotient n = 10001011. You should verify that n*G XOR R is indeed equal to 10011010000. You can use this calculator to do the modulo-2 arithmetic if you don't want to do it by hand.

That's incorrect

That's correct

The answer was: 0011

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