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Other advice about buying a computer

Data capacity specification anomaly

You go into a shop and say "I'd like a hundredweight of potatoes please", and the person in charge of the shop hands over two big sacks of potatoes and you're about to pay, and suddenly you spot the sacks are just a bit LIGHT. "Is this really a hundredweight?" you ask. "Oh yes", comes the reply "It is indeed a HUNDRED POUNDS of potatoes". But hang on a bit, a hundredweight of potatoes is 112lb (a hundred and twelve pounds)!

This sort of thing would never have happened in the old days of CWT hundredweights because everyone knew a hundredweight was 112 pounds. But what is a MEGABYTE? Surely there is no doubt? Computer bytage is measured in orders of two, so a K, a kilobyte, is 2X2X2X2X2X2X2X2X2X2 (210) bytes, or 1024 bytes. A megabyte is 1024x1024 bytes, which is 1048576 bytes. It's not a million bytes, it's about 5% more than that. So if you buy a hard disc drive and it's so-many "megabytes", it should be that many times 1048576, not times 1000000. Things get even sillier at the gigabytes level, because a gigabyte is 1073741824 bytes, so the extent to which you could be short changed is nearly 7.5%. The terabyte is almost 10% bigger than the million-million bytes, and in fact for each new Latin prefix an extra two and a half percent is added onto the difference.

So here's a summary of some levels of short change factor for data storage systems in the future:

NAME bytes power short by
Kilobyte 1024 103 2.4%
Megabyte 1048576 106 4.9%
Gigabyte 1073741824 109 7.4%
Terabyte 1099511627776 1012 10%
Petabyte 1125899906842624 1015 12.6%
Exabyte 1152921504606846976 1018 15.3%
Zettabyte 1180591620717411303424 1021 18.1%
Yottabyte 1208925819614629174706176 1024 20.9%

(Terms of reference: See SI Units. Also note that an Exabyte Tape is a rather optimistically-named item)

There comes a point where the percent exceeds 100%, ie the hypothetical futuristic disc drive is only HALF what it should be. That occurs at 1090 bytes, at which the actual size should be 2037035976334486086268445688409378161051468393665936250636140449354381299763336706183397376 bytes, but would be short-changed at less than half that!

This will be a while yet, as it is 10 million times the number of atoms in the known universe. Ie at one bit per atom it would take 80 million universes worth of atoms. (note: known universe estimates vary wildly. Some say 1079 atoms, some 1085 etc).

However, technology goes on advancing and each new era makes easy that which was previously impossible to conceive of. If superstring-memory was invented and this allowed a density of quanta to be used at the Planck-Length scale of 10-35 metres, so the memory would fit into a cube a tenth of a millimetre across.

Extra point of note: Not everyone understands what all this 10n stuff means. No problem! See exponential notation explained

Bigger Latin Prefixes? see http://www.mindspring.com/~jimvb/unitsystem.htm . Incidentally, I've been saying about the Sun being 390 yottawatts for some time now. Also see really very big numbers

Also, to get a good idea about what BYTES are, see this helpful explanation of bytes and kilobytes