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Verhoeff had the goal of finding a decimal code—one where the check digit is a single decimal digit—which detected all single-digit errors and all transpositions of adjacent digits. At the time, supposed proofs of the nonexistence [ 6 ] of these codes made base-11 codes popular, for example in the ISBN check digit .
The check digit is computed as follows: Drop the check digit from the number (if it's already present). This leaves the payload. Start with the payload digits. Moving from right to left, double every second digit, starting from the last digit. If doubling a digit results in a value > 9, subtract 9 from it (or sum its digits).
The validity of a digit sequence containing a check digit is defined over a quasigroup. A quasigroup table ready for use can be taken from Damm's dissertation (pages 98, 106, 111). [3] It is useful if each main diagonal entry is 0, [1] because it simplifies the check digit calculation.
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.
Add the two results together: 42 + 11 = 53. To calculate the check digit, take the remainder of (53 / 10), which is also known as (53 modulo 10), and if not 0, subtract from 10. Therefore, the check digit value is 7. i.e. (53 / 10) = 5 remainder 3; 10 - 3 = 7. Another example: to calculate the check digit for the following food item "01010101010x".
The last modification date stamp (and with DELWATCH 2.0+ also the file deletion date stamp, and since DOS 7.0+ optionally also the last access date stamp and creation date stamp), are stored in the directory entry with the year represented as an unsigned seven bit number (0–127), relative to 1980, and thereby unable to indicate any dates in ...
A sanity test can refer to various orders of magnitude and other simple rule-of-thumb devices applied to cross-check mathematical calculations. For example: If one were to attempt to square 738 and calculated 54,464, a quick sanity check could show that this result cannot be true. Consider that 700 < 738, yet 700 2 = 7 2 × 100 2 = 490,000 ...
If Monday is the first day of the week, the days may be coded 1 to 7, for Monday through Sunday, as is practiced in ISO 8601. The day designated with 7 may also be counted as 0, by applying the arithmetic modulo 7, which calculates the remainder of a number after division by 7. Thus, the number 7 is treated as 0, the number 8 as 1, the number 9 ...