# cyclic redundancy check

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## cyclic redundancy check

[′sīk·lik ri′dən·dən·sē ‚chek] (computer science)

A block check character in which each bit is calculated by adding the first bit of a specified byte to the second bit of the next byte, and so forth, spiraling through the block.

## cyclic redundancy check

(algorithm)(CRC or "cyclic redundancy code") A number derived
from, and stored or transmitted with, a block of data in order
to detect corruption. By recalculating the CRC and comparing
it to the value originally transmitted, the receiver can
detect some types of transmission errors.

A CRC is more complicated than a checksum. It is calculated using division either using shifts and exclusive ORs or table lookup (modulo 256 or 65536).

The CRC is "redundant" in that it adds no information. A single corrupted bit in the data will result in a one bit change in the calculated CRC but multiple corrupted bits may cancel each other out.

CRCs treat blocks of input bits as coefficient-sets for polynomials. E.g., binary 10100000 implies the polynomial: 1*x^7 + 0*x^6 + 1*x^5 + 0*x^4 + 0*x^3 + 0*x^2 + 0*x^1 + 0*x^0. This is the "message polynomial". A second polynomial, with constant coefficients, is called the "generator polynomial". This is divided into the message polynomial, giving a quotient and remainder. The coefficients of the remainder form the bits of the final CRC. So, an order-33 generator polynomial is necessary to generate a 32-bit CRC. The exact bit-set used for the generator polynomial will naturally affect the CRC that is computed.

Most CRC implementations seem to operate 8 bits at a time by building a table of 256 entries, representing all 256 possible 8-bit byte combinations, and determining the effect that each byte will have. CRCs are then computed using an input byte to select a 16- or 32-bit value from the table. This value is then used to update the CRC.

Ethernet packets have a 32-bit CRC. Many disk formats include a CRC at some level.

A CRC is more complicated than a checksum. It is calculated using division either using shifts and exclusive ORs or table lookup (modulo 256 or 65536).

The CRC is "redundant" in that it adds no information. A single corrupted bit in the data will result in a one bit change in the calculated CRC but multiple corrupted bits may cancel each other out.

CRCs treat blocks of input bits as coefficient-sets for polynomials. E.g., binary 10100000 implies the polynomial: 1*x^7 + 0*x^6 + 1*x^5 + 0*x^4 + 0*x^3 + 0*x^2 + 0*x^1 + 0*x^0. This is the "message polynomial". A second polynomial, with constant coefficients, is called the "generator polynomial". This is divided into the message polynomial, giving a quotient and remainder. The coefficients of the remainder form the bits of the final CRC. So, an order-33 generator polynomial is necessary to generate a 32-bit CRC. The exact bit-set used for the generator polynomial will naturally affect the CRC that is computed.

Most CRC implementations seem to operate 8 bits at a time by building a table of 256 entries, representing all 256 possible 8-bit byte combinations, and determining the effect that each byte will have. CRCs are then computed using an input byte to select a 16- or 32-bit value from the table. This value is then used to update the CRC.

Ethernet packets have a 32-bit CRC. Many disk formats include a CRC at some level.

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