Dr. John A. Robertson, CEO, InfoSight Corporation
Ideally, items that require traceability are marked with a “License Plate Number“ (LPN), which is used as an index into a database. Choosing the correct format for such LPNs can go a long way toward making a marking / reading / data collection system robust.
The LPN can be created by all numeric (digits 0 through 9 only.) It turns out that compact bar codes are best realized by using an even number of numeric digits.
Alternatively, the LPN can be created using alphanumeric characters (0 through 9 plus A through Z without I and O --- 34 in all). The bar code’s compactness is not affected by whether there are an even or odd number of alphanumeric characters.
Lets assume that each LPN includes a Check Character which can be used to verify accuracy whenever / if the LPN needs to be manually entered. See Appendix 1.
An example numeric LPN is NNNNNNNN (even number of digits [8], where last N is the check digit)
An example alphanumeric LPN is AAAAAAAAA (9 characters, where last A is the check character)
The following chart then describes the number of permutations (different LPNs) when one digit or character is used as a check:
| LPN Size | Numeric | Permutations | Alphanumeric | Permuations | |
|---|---|---|---|---|---|
| 2 | NN | 1.00E+01 | AA | 34 | |
| 3 | -- | AAA | 1.16E+03 | ||
| 4 | NNNN | 1.00E+03 | AAAA | 3.93E+04 | |
| 5 | -- | AAAAA | 1.34E+06 | ||
| 6 | NNNNNN | 1.00E+05 | AAAAAA | 4.54E+07 | |
| 7 | -- | AAAAAAA | 1.54E+09 | ||
| 8 | NNNNNNNN | 1.00E+07 | AAAAAAAA | 5.25E+10 | |
| 9 | -- | AAAAAAAAA | 1.79E+12 | ||
| 10 | NNNNNNNNNN | 1.00E+09 | AAAAAAAAAA | 6.07E+13 | |
| 11 | -- | AAAAAAAAAAA | 2.06E+15 | ||
| 12 | NNNNNNNNNNNN | 1.00E+11 | AAAAAAAAAAAA | 7.02E+16 | |
| 13 | -- | AAAAAAAAAAAAA | 2.39E+18 | ||
| 14 | NNNNNNNNNNNNNN | 1.00E+13 | AAAAAAAAAAAAAA | 8.11E+19 | |
| 15 | -- | AAAAAAAAAAAAAAA | 2.76E+21 | ||
| 16 | NNNNNNNNNNNNNNNN | 1.00E+15 | AAAAAAAAAAAAAAAA | 9.38E+22 |
Note that for instances where the number of pieces is around 10 million, one could have the checking feature by using either 8 decimal digits or 6 alphanumeric characters.
Appendix 1
What is a check digit?
Account numbers, product codes, customer reference numbers, etc. can be very long. That means that there is a high risk of error when the numbers are entered into a computer system (via the keyboard or using a scanner). The check digit system adds an extra item (a single number or character) . This extra digit or character has been calculated from the original LPN. The scanner, or computer can repeat the exact calculation that was performed to produce the extra item. If the computer matches its extra number or character with the check digit or character, then there is a very high probability that the number has been scanned or manually entered correctly.
A single check digit eliminates 9/10 of random read errors thereby providing a 90% reduction in entry errors.
A single check character eliminates 33/34 of random read errors thereby providing a 97% reduction in entry errors.
John Robertson
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