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The message stream may be any length. After it has been shifted through the register, followed by 8 zeroes, the result in the register is the checksum. Checking received data with checksum. The received message is shifted through the same register as used in the generator, but the received checksum is attached to it instead of zeroes.
Often confused to be a CRC, but actually a checksum; see Fletcher's checksum: CRC-17-CAN CAN FD [51] 0x1685B 0x1B42D 0x1685B 0x1B42D even CRC-21-CAN CAN FD [51] 0x102899 0x132281 0x064503 0x18144C even CRC-24 FlexRay [39] 0x5D6DCB 0xD3B6BA 0xA76D75 0xAEB6E5 even
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.
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.
“Here is a useful formula for determining how many to keep: (Number of people who use mug/water bottle ) × (number of mugs they use a day) then X that by (one + the number of days between ...
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.
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