The Exbibyte Wars Are Coming

[beamjockey]

As someone whose workplace is concerned with inverse femtobarns, I am somewhat aware of the importance of standard prefixes for very small or very large numbers.

In the article about puppies killing the Internet, the reference to a "zettabyte" got me thinking about prefixes we use for big binary numbers like kilobytes and megabytes. Turns out the International Electrotechnical Commission has tried to set some standards for this sort of thing.

The IEC explains the problem:

As time has passed, kilobytes have grown into megabytes and megabytes into gigabytes. Within a few years, ordinary PC or laptop data storage could well be measured in terabytes and very large industrial or scientific systems in peta- or even exabytes. The problem is that, even at the SI tera-scale (10¹²), the discrepancy with the binary equivalent (2⁴⁰) is not the 2,4 % at kilo-scale but rather approaching 10 %. At exa-scale (10¹⁸ and 2⁶⁰), it is nearer 20 %. The niceties of mathematics dictate that the bigger the number of bytes, the bigger the differential, so the inaccuracies – for engineers, marketing staff and public alike – are set to grow more and more significant. This is one good reason for the IEC to have standardized prefixes for binary multiples.

The other primary reason is that different parts of the IT industry had started to confuse themselves. In the computing world, for example, the major disk-drive manufacturers tend to mean what they say in kilobytes, megabytes, gigabytes and so on of storage, i.e. precisely 1 000 B, 1 000 000 B and 1 000 000 000 B respectively, according to the decimal prefix. Memory, on the other hand, is described using the decimal prefix but actually supplied in binary quantities, so 512 MB of RAM bought on the high street generally means 536 870 912 B and, as shown in the table, should more properly be described as 512 MiB (mebibytes) or 537 MB.

I made a chart to illustrate the difference between 2^10N and 10^3N running up to a decigoogol (10⁹⁹). I normalized the difference two different ways:
Binary: (2^10N - 10^3N)/(2^10N)
Decimal: (2^10N - 10^3N)/(10^3N)

The difference is a few percent in the kiloscale to gigascale range, but it hits 20% around 2¹⁰⁰ and becomes a positively embarrassing 50% around 2³⁰⁰--a number which is more than twice the size of 10⁹⁰.

The IEC's solution is to offer a family of alternative prefixes which express powers of 2 precisely.

I don't think I am likely to stop saying "terabyte" and start saying "tebibyte" anytime soon, but it's nice to know that the distinction exists, and that I can adopt it if I have a need to express these numbers more precisely.

Moore's Law does suggest that we are headed for an era when the distinction will really matter in specifications and advertising of computer hardware. Mark my words, we will live to see the Exbibyte Wars.

Prefixes for binary multiples

Factor  Name  Symbol  Origin Derivation   210 kibi Ki kilobinary: (210)1 kilo: (103)1  220 mebi Mi megabinary: (210)2  mega: (103)2  230 gibi Gi gigabinary: (210)3 giga: (103)3  240 tebi Ti terabinary: (210)4 tera: (103)4  250 pebi Pi petabinary: (210)5 peta: (103)5  260 exbi Ei exabinary: (210)6 exa: (103)6

Comments

[whl.livejournal.com]

I have occasionally used the binary prefixes; everyone that hears me either giggles or rolls their eyes...

And the root of the problem was advertising and the hard drive industry, who wanted to make their drives sound bigger.

[mmcirvin.livejournal.com]

Yeah, while the strictly decimal prefixes are SI-consistent, I never heard anyone use the terms that way until disk manufacturers started doing it, which makes it grating that that mildly fraudulent use is now being enshrined as the correct one.