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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.
big_endian_table[0] := 0 crc := 0x8000 // Assuming a 16-bit polynomial i := 1 do { if crc and 0x8000 { crc := (crc leftShift 1) xor 0x1021 // The CRC polynomial} else { crc := crc leftShift 1 } // crc is the value of big_endian_table[i]; let j iterate over the already-initialized entries for j from 0 to i−1 { big_endian_table[i + j] := crc ...
The result for that iteration is the bitwise XOR of the polynomial divisor with the bits above it. The bits not above the divisor are simply copied directly below for that step. The divisor is then shifted right to align with the highest remaining 1 bit in the input, and the process is repeated until the divisor reaches the right-hand end of ...
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.
The first weakness of the simple checksum is that it is insensitive to the order of the blocks (bytes) in the data word (message). If the order is changed, the checksum value will be the same and the change will not be detected. The second weakness is that the universe of checksum values is small, being equal to the chosen modulus.
XOR/table Paul Hsieh's SuperFastHash [1] 32 bits Buzhash: variable XOR/table Fowler–Noll–Vo hash function (FNV Hash) 32, 64, 128, 256, 512, or 1024 bits xor/product or product/XOR Jenkins hash function: 32 or 64 bits XOR/addition Bernstein's hash djb2 [2] 32 or 64 bits shift/add or mult/add or shift/add/xor or mult/xor PJW hash / Elf Hash ...
The result of that XOR calculation yields Drive 2's contents. 11010100 is then stored on Drive 2, fully repairing the array. XOR logic is also equivalent to even parity (because a XOR b XOR c XOR ... may be treated as XOR(a,b,c,...), which is an n-ary operator that is true if and only if an odd number of arguments is true). So the same XOR ...
Many protocols use an XOR-based longitudinal redundancy check byte (often called block check character or BCC), including the serial line interface protocol (SLIP, not to be confused with the later and well-known Serial Line Internet Protocol), [8] the IEC 62056-21 standard for electrical-meter reading, smart cards as defined in ISO/IEC 7816, and the ACCESS.bus protocol.