#Formula to calculate the check digit for a 13 digit identity number

According to the provisions of the Identification Amendment Act, 2000 (Act No. 28 of 2000,
which was promulgated on 13 October 2000) all forms of identity documents other than the
green bar-coded identity document are invalid.
## [my observation: the following algorithm appears to work for the older 'blue'-book id numbers as well].
In accordance with the legislation,
the control figure which is the 13th digit of all identity numbers which have 08 and 09 is
calculated as follows using ID Number 800101 5009 087 as an example:

- Add all the digits in the odd positions (excluding last digit).
  8 + 0 + 0 + 5 + 0 + 0 = 13...................[1]
- Move the even positions into a field and multiply the number by 2.
  011098 x 2 = 22196
- Add the digits of the result in b).
  2 + 2 + 1 + 9 + 6 = 20.........................[2]
- Add the answer in [2] to the answer in [1].
  13 + 20 = 33
- Subtract the second digit (i.e. 3) from 10.
- The number must tally with the last number in the ID Number. If the result is 2 digits, the last digit is used to compare against the last number in the ID Number.
- If the answer differs, the ID number is invalid.