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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.
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.
The ITU-T G.hn standard also uses CRC-32C to detect errors in the payload (although it uses CRC-16-CCITT for PHY headers). CRC-32C computation is implemented in hardware as an operation ( CRC32 ) of SSE4.2 instruction set, first introduced in Intel processors' Nehalem microarchitecture.
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 effect of a checksum algorithm that yields an n-bit checksum is to map each m-bit message to a corner of a larger hypercube, with dimension m + n. The 2 m + n corners of this hypercube represent all possible received messages. The valid received messages (those that have the correct checksum) comprise a smaller set, with only 2 m corners.
The cyclic redundancy check (CRC) is a check of the remainder after division in the ring of polynomials over GF(2) (the finite field of integers modulo 2). That is, the set of polynomials where each coefficient is either zero or one, and arithmetic operations wrap around.
The Internet checksum, [1] [2] also called the IPv4 header checksum is a checksum used in version 4 of the Internet Protocol (IPv4) to detect corruption in the header of IPv4 packets. It is carried in the IPv4 packet header, and represents the 16-bit result of the summation of the header words. [3] The IPv6 protocol does not use header checksums.
A checksum of a message is a modular arithmetic sum of message code words of a fixed word length (e.g., byte values). The sum may be negated by means of a ones'-complement operation prior to transmission to detect unintentional all-zero messages. Checksum schemes include parity bits, check digits, and longitudinal redundancy checks.