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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.
Thus, for example, the XMODEM-CRC extension, an early use of CRCs in software, uses an msbit-first CRC. So far, the pseudocode has avoided specifying the ordering of bits within bytes by describing shifts in the pseudocode as multiplications by x {\displaystyle x} and writing explicit conversions from binary to polynomial form.
A CRC is a checksum in a strict mathematical sense, as it can be expressed as the weighted modulo-2 sum of per-bit syndromes, but that word is generally reserved more specifically for sums computed using larger moduli, such as 10, 256, or 65535.
GxHash [10] 32, 64 or 128 bits AES block cipher pHash [11] fixed or variable see Perceptual hashing: dhash [12] 128 bits see Perceptual hashing: SDBM [2] [13] 32 or 64 bits mult/add or shift/add also used in GNU AWK: OSDB hash [14] 64 bits add komihash [15] 64 bits product/split/add/XOR
Files can become corrupted for a variety of reasons, including faulty storage media, errors in transmission, write errors during copying or moving, and software bugs. SFV verification ensures that a file has not been corrupted by comparing the file's CRC hash value to a previously calculated value. [1]
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The additional bits generated by the CRC algorithm (technically, the low-order bits in the code word) are properly called check bits or check digits. While it may be common to refer to them as "the CRC code" or "the CRC checksum" or "the CRC" in informal discussion, these terms are incorrect.
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