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CRC-16-OpenSafety-A safety fieldbus [35] 0x5935 0xAC9A 0x5935 0xAC9A [13] odd CRC-16-OpenSafety-B safety fieldbus [35] 0x755B 0xDAAE 0xB55D 0xBAAD [13] odd CRC-16-Profibus: fieldbus networks [50] 0x1DCF 0xF3B8 0xE771 0x8EE7 odd Fletcher-16 Used in Adler-32 A & B Checksums Often confused to be a CRC, but actually a checksum; see Fletcher's ...
So CRC method can be used to correct single-bit errors as well (within those limits, e.g. 32,767 bits with optimal generator polynomials of degree 16). Since all odd errors leave an odd residual, all even an even residual, 1-bit errors and 2-bit errors can be distinguished.
BSD checksum (Unix) 16 bits sum with circular rotation SYSV checksum (Unix) 16 bits sum with circular rotation sum8 8 bits sum Internet Checksum: 16 bits sum (ones' complement) sum24 24 bits sum sum32 32 bits sum fletcher-4: 4 bits sum fletcher-8: 8 bits sum fletcher-16: 16 bits sum fletcher-32: 32 bits sum Adler-32: 32 bits sum xor8: 8 bits ...
The checksum algorithms most used in practice, such as Fletcher's checksum, Adler-32, and cyclic redundancy checks (CRCs), address these weaknesses by considering not only the value of each word but also its position in the sequence. This feature generally increases the cost of computing the checksum.
When the data word is divided into 8-bit blocks, as in the example above, two 8-bit sums result and are combined into a 16-bit Fletcher checksum. Usually, the second sum will be multiplied by 256 and added to the simple checksum, effectively stacking the sums side-by-side in a 16-bit word with the simple checksum at the least significant end.
Below is the relevant part of the GNU sum source code (GPL licensed). It computes a 16-bit checksum by adding up all bytes (8-bit words) of the input data stream. In order to avoid many of the weaknesses of simply adding the data, the checksum accumulator is circular rotated to the right by one bit at each step before the new char is added.
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 rolling hash (also known as recursive hashing or rolling checksum) is a hash function where the input is hashed in a window that moves through the input.. A few hash functions allow a rolling hash to be computed very quickly—the new hash value is rapidly calculated given only the old hash value, the old value removed from the window, and the new value added to the window—similar to the ...