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To compute an n-bit binary CRC, line the bits representing the input in a row, and position the (n + 1)-bit pattern representing the CRC's divisor (called a "polynomial") underneath the left end of the row. In this example, we shall encode 14 bits of message with a 3-bit CRC, with a polynomial x 3 + x + 1.
// Initialize CRC-32 to starting value crc32 ← 0xFFFFFFFF for each byte in data do nLookupIndex ← (crc32 xor byte) and 0xFF crc32 ← (crc32 shr 8) xor CRCTable[nLookupIndex] // CRCTable is an array of 256 32-bit constants // Finalize the CRC-32 value by inverting all the bits crc32 ← crc32 xor 0xFFFFFFFF return crc32
The simplest checksum algorithm is the so-called longitudinal parity check, which breaks the data into "words" with a fixed number n of bits, and then computes the bitwise exclusive or (XOR) of all those words. The result is appended to the message as an extra word.
Download QR code; Print/export Download as PDF; Printable version; In other projects Wikidata item; ... CRC with length appended CRC-8: 8 bits CRC: CRC-16: 16 bits ...
Both ends must preset their division circuitry to all-ones, the transmitter must add the trailing inversion pattern to the result, and the receiver must expect this pattern when checking the CRC. If the receiver checks the CRC by full-length division, the remainder because the CRC of a full codeword that already includes a CRC is no longer zero.
CRC Handbook of Chemistry and Physics, a science reference handbook published by CRC Press; CRC Standard Mathematical Tables, a mathematics reference handbook published by CRC Press; Cyclic redundancy check, a type of hash function used to produce a checksum in order to detect errors in data storage or transmission
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Parity in this form, applied across multiple parallel signals, is known as a transverse redundancy check. This can be combined with parity computed over multiple bits sent on a single signal, a longitudinal redundancy check. In a parallel bus, there is one longitudinal redundancy check bit per parallel signal.