When I first used a computer in about 1968 there were only a handful of them throughout Ireland. The bank where I worked did not have one and so I rented time on CIE’s computer in Oriel Street (now part of the IFSC). Every computer installation had a large hall where punch-card operators keyed in computer data to punched cards. The operator at the adjacent station punched the same information into a punch card verifier to check it. This process was boring and laborious, not to mention expensive.

The reason why there was so much keying in of data was due to the fact that the modern methods of data capture had not yet been invented. Every possible method had to be deployed to improve accuracy. As a result of this long-winded process, the concept of the check-sum digit was born. The check-sum digit is still incorporated into your bank account number today.

Ireland established a world lead in this technology when Professor Gordon Foster of Trinity College, Dublin (my professor) wrote a report entitled “STANDARD NUMBERING IN THE BOOK TRADE”. This work was subsequently adopted as ISO 2108 and commonly known as the ISBN number which you will see in the publication details of any book worldwide.

The concept of the check-sum states that only numbers which satisfy a pre-defined mathematical formula should be used as book numbers. Therefore, if an operator keys in a wrong number there is a high probability that it will be rejected (unless the number keyed in also happens to satisfy the formula) by the computer at a very early stage in the process. In a simple check-sum you could choose only numbers which are divisible by 11. However, Professor Foster’s scheme does somewhat better. He had carried out an analysis of the most common “keying in” errors and designed a formula which would reject as many errors as possible without massively reducing the number of valid numbers.

What the banks do?

Most banks use different formulae. The typical check-sum formula built into an 8-digit account number is that if you take the digits of the number and multiply them by the bank’s chosen weights, the result must be divisible by 11. An example would be using the account number 17134355.

The result of 715 is exactly divisible by 11. This formula may not be the exact one used by your bank, but a similar one will be used. Some banks join together the branch code (6 digits) and the account number (8 digits) to form a 14-digit code which is then checked by a check-sum formula.

A much more complex arrangement is incorporated into the IBAN (International Bank Account Number). The Irish IBAN is a 22-character number at the top of your bank statement. Since the IBAN is mainly used for cross-border transfers, it is necessary to stop as many erroneous numbers as possible before they get into the clearing system. Therefore, the chosen divisor is 97 instead of 11. The check can be described as follows:

1. Move the 4 rightmost characters from the left-end of the string to the right-end.
2. Replace each letter with a 2-digit number by adding 9 to the letter number (for A (the first letter of the alphabet) the replacement number is 10, whereas for Z the replacement number is 35). This results in a string of 28 digits.
3. Divide the resulting string by 97 (note: most popular computer systems, e.g. Microsoft Excel, cannot handle such a large number directly but can be programmed to do so).
4. If the number is valid the result of this calculation should be 1.

It should be noted that an IBAN is checked at the point of entry using this formula. It is also checked at the destination using the domestic mechanism. The IBAN should be checked by reference to the name of the destination account. The chances of an error are extremely low – but not zero. It is much better to ensure that you get the account number or IBAN correct in the first instance.