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The checksum field is the 16 bit one's complement of the one's complement sum of all 16 bit words in the header. For purposes of computing the checksum, the value of the checksum field is zero. If there is no corruption, the result of summing the entire IP header, including checksum, and then taking its one's complement should be zero.
The ones' complement of a binary number is the value obtained by inverting (flipping) all the bits in the binary representation of the number. The name "ones' complement" [1] refers to the fact that such an inverted value, if added to the original, would always produce an "all ones" number (the term "complement" refers to such pairs of mutually additive inverse numbers, here in respect to a ...
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.
Therefore, ones' complement and two's complement representations of the same negative value will differ by one. Note that the ones' complement representation of a negative number can be obtained from the sign–magnitude representation merely by bitwise complementing the magnitude (inverting all the bits after the first). For example, the ...
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 ...
So, the simple checksum is computed by adding together all the 8-bit bytes of the message, dividing by 255 and keeping only the remainder. (In practice, the modulo operation is performed during the summation to control the size of the result.) The checksum value is transmitted with the message, increasing its length to 137 bytes, or 1096 bits.
The nines' complement of a decimal digit is the number that must be added to it to produce 9; the nines' complement of 3 is 6, the nines' complement of 7 is 2, and so on, see table. To form the nines' complement of a larger number, each digit is replaced by its nines' complement.
Checksum is the 16-bit ones' complement of the ones' complement sum of a pseudo header of information from the IP header, the UDP header, and the data, padded with zero octets at the end (if necessary) to make a multiple of two octets. [7] In other words, all 16-bit words are summed using ones' complement arithmetic. Add the 16-bit values up.