This page shows some interactive animations of simple checksum calculators.
For more information on these and other machines, see my Calculating History site.
Select one of the tabs
nΣi=1 | w_{i} a_{i} = 0 mod p |
where_{ }^{ } | a_{i} = i^{ th} digit of the number a |
w_{i} = i^{ th} weight (integer) | |
p_{ } = an integer |
3a_{1} + 6a_{2} + 8a_{3} + 5a_{4} + 7a_{5} + 10a_{6} + 2a_{7} + 4a_{8} + 9a_{9} + a_{10} = 0 mod 11 |
a_{10} is shown in the small window at the top left.
Because p = 11, it is possible that
a_{10} = 10, which is indicated by an 'A'.
12Σi=1 | { | i is odd: a_{i} i is even: 2a_{i} mod 9 |
} | = 0 mod 10 |
Unlike the devices shown in the other tabs, the checksum algorithm derived by the Dutch mathematician
Jacobus (Koos) Verhoeff is not based on weighted-adding-modulo-some-number.
Verhoeff's algorithm uses multiplications in point group D_{5}, and a permutation.
Verhoeff's algorithm was used for
numbering
old German banknotes (Deutsche Mark).
These numbers also contain letters, which are converted to digits by the table at the right.
Select the numbers by setting the red sliders, left to right. Note that when setting the slider for a number, the next column of numbers changes.
The last column gives the rightmost digit of the banknote
number.
Try GN4480100S8 ! More info