The Ashton projectA cyclic redundancy check on 1,319 postcodes
First measure how often a slip goes unnoticed, then write three checks and try to fool each one.
Ordnance Survey publishes every postcode in Great Britain as open data in Code-Point Open. The learner loads the OL file with Python's csv module and keeps the 1,319 postcodes in districts OL6 and OL7. Then comes the damage. Each character of each postcode is replaced, in turn, by every other letter and digit, and each pair of neighbouring characters is swapped. After every change the program asks one question: is the result still a real postcode?
Typing slips applied to the OL6 and OL7 postcodes, and how many land on another real postcode (our Python run on Code-Point Open)| Kind of slip | Slips tried | Still a real postcode |
|---|
| One character replaced | 276,990 | 41,866 (15.1%) |
| Two neighbouring characters swapped | 6,309 | 983 (15.6%) |
About one slip in seven goes straight through a lookup, because the wrong postcode exists. The danger is not spread evenly. A mistake in the final letter lands on a real postcode 43.1% of the time, and in the letter before it 29.0%. Swaps do the same: OL6 6AD and OL6 6DA are both in the file. So the learner writes three checks that travel with the postcode. The first adds up the character codes and keeps the last eight bits. The second and third are cyclic redundancy checks of 8 and 16 bits. Each one treats the postcode as a long string of bits, shifts through it one bit at a time with the << operator, and uses ^, Python's exclusive-or, to subtract a fixed pattern whenever the top bit is set. What is left at the end is the check value.
Errors each check failed to notice| Check | Replaced characters missed | Swaps missed | Pairs of different postcodes with the same check value |
|---|
| Lookup in the real list | 41,866 of 276,990 | 983 of 6,309 | Does not apply |
| Sum of character codes, 8 bits | 0 | 6,309 of 6,309 | 22,503 of 869,221 |
| CRC-8 | 0 | 0 | 3,855 of 869,221 |
| CRC-16 | 0 | 0 | 0 of 869,221 |
The sum catches every replaced character and not one swap, since adding numbers gives the same total in any order. A CRC is a remainder after division, and in division position matters, so both kinds of slip change it. The last column is the honest limit. Eight bits can hold only 256 values, so some unrelated postcodes are bound to share one: 3,855 pairs for CRC-8, or about 1 in 225. The sum is far worse at 1 in 39, because the 1,319 postcodes produce only 55 different totals. Sixteen bits left no pair matching. As a final test the learner writes CRC-32 the same way and compares it with zlib.crc32 from Python's standard library. The two agree on all 1,319 postcodes.
Ages 8 to 11
Add a check digit to a six-digit number, swap two digits, and see whether the check notices.
Ages 11 to 15
Write the character-sum check in Python, then hunt for two postcodes that fool it.
Ages 15 and up
Code CRC-8 with shifts and exclusive-or, prove it against a published test value, and match zlib on CRC-32.
Data note and caveats
Contains OS data © Crown copyright and database right 2026, and Royal Mail data © Royal Mail copyright and database right 2026, from Code-Point Open. The slips are simulated and the counts are ours; no real address or delivery was involved. Postcodes are created and withdrawn over time, so a later release would shift the figures. A CRC detects accidents. It offers no defence against someone changing data on purpose.
