checking a book number in your head, and turning a 10-digit one into 13 digits
Built as a memo rather than a table: the thing worth hanging it up for reads across the room, with the full reference in smaller type below it.
Three sizes in one archive — from a sheet on the fridge to a poster on the wall.
Above each digit is its weight, below it the product. The number on this sheet is only an example.
In the 10-digit number all ten weights differ and 11 is prime, so swapping two different digits always shifts the sum by something that is not a multiple of 11. The 13-digit number has only two weights, 1 and 3: neighbours 1 and 6 swapped shift the sum by 2 × 5 = 10, and the check sees nothing. The price of modulus 11 was an eleventh symbol, X.
Why the numbers can be trusted. Every countable number here is computed from data rather than typed in, and the sheet must pass 2 independent checks before it is allowed to build — how many items there are, the order they come in, and the claim in the highlighted box itself. If one fails, there is no file.
ten tasks, the year of each, the system, the figure — and the human it was measured against
all 128 positions: the column is the three high bits, the row is the four low ones
who published each standard, when, what it does to the sound, and how many bits per second it allows
forty bits to a quantum: five bytes, eight characters and five padding cases