A weighted checksum works in nearly the same way as a normal checksum.
Where a normal checksum is based on the summation of the values in a
data range, however, a weighted checksum takes both data value and
position into consideration. To do this, each distinct position in
the data range is assigned a weight. Each position's weight is
multiplied by the value at the position in question to achieve the
final terms in the sum. These terms are added and the weighted
checksum value is determined based on this summation.
For instance, imagine creating a weighted checksum for telephone
numbers in the format 1234567890. If we remove the dashes from the
numbers we get something that looks like 1234567890. There are ten
places in a number of this format. A typical way to assign weights to
places is to give the nth place the weight of 7^{n}. Other values,
such as powers of nine or powers of four are also used.
place 
value 
0 
1 
1 
7 
2 
49 
3 
343 
4 
2401 
5 
16807 
6 
117649 
7 
823543 
8 
5764801 
9 
40353607 
Using such a scheme, the phone number 1234567890 would result in the
sum:
S = 1*1 + 2*7 + 3*49 + 4*343 + ... + 0*40353607
The weighted checksum would then be calculated in such a way as to
yield a meaningful result when added to the weighted sum calculated in
the manner described above. Perhaps the summation added to the
checksum would have to yield a number evenly divisible by some large
prime. Or perhaps the checksum would negate the summation and their
combination would result in zero.
