# 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.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.

## 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.
References in periodicals archive ?
With the introduction of Ultra160 SCSI, three key technologies were introduced and include dual-edge clocking, domain validation, and cyclic redundancy check (CRC).
It provides the header information and 8-bit/10-bit encoding/decoding, along with cyclic redundancy check (CRC) and scrambling.
CRC (Cyclic redundancy check): CRC is an algorithm that provides improved data reliability for the parallel SCSI bus.
Ultra3 SCSI has six new features in its specification, including Double Transition Clocking (DTC), Cyclic Redundancy Check (CRC), Domain Validation, Protection for Asynchronous Information Phase (AIP), Packetization, and Quick Arbitration and Selection (QAS).

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