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# When is a kilobyte a kibibyte? And an MB an MiB?

Quite often is the short answer. But what are kibibytes, and indeed mebibytes, gibibytes, tebibytes, pebibytes and exbibytes? The answers are all in IEC 60027-2, developed by TC 25 (Quantities and units, and their letter symbols), published in November 2000 and now gradually being adopted in the IT world. Essential details of the new units, their derivations, symbols and approximate relation to commonly, if sometimes incorrectly, used metric equivalents in the Système international d'unités (SI), are shown in the accompanying table.

How do these new standardized units differ from those that have become so familiar during the last two or three decades’ explosion in personal computing? And does it really matter? After all, most people probably think they know quite as much as they need to about kilobytes or megabytes when they start running out of memory, resources or hard-disk capacity on their PC. Or when the numbers, time and therefore cost don’t seem to add up when downloading files over a modem via their Internet Service Provider (ISP).

The fact is that, while it may not have mattered much to the average PC user until the last few years, a kilobyte is not necessarily the 103 or 1 000 bytes that its SI prefix ‘kilo’ would seem to indicate. SI is a decimal (base ten) system, but computers essentially only recognize whether an electrical signal is on or off, represented by a 1 or a 0. Mathematically speaking, they are binary (base two) systems. When it comes to scientists and engineers in the IT and telecommunications industries, such sources of confusion and potential incompatibility certainly do matter, and increasingly so as the numbers that computers crunch get ever bigger.

The second edition of IEC 60027-2 (Letter symbols to be used in electrical technology – Part 2: Telecommunications and electronics, to give it its full title) was developed specifically to meet industry’s expressed needs in data processing and data transmission. It eliminates confusion by setting out the prefixes and symbols for the binary, as opposed to decimal, multiples that most often apply in these fields.

Bits and bytes
A ‘bit’ is a binary digit and a ‘byte’ is a group of bits, usually eight (hence, incidentally, the French ‘octet’ for a byte). Years ago, at a time when entire computer capacities barely matched the few tens of kilobytes represented by this single page of web text, computer engineers noticed that the binary 210 (1 024) was very nearly equal to the decimal 103 (1 000) and, purely as a matter of convenience, they began referring to 1 024 bytes as a kilobyte. It was, after all, only a 2,4 % difference and all the professionals generally knew what they were talking about among themselves.

Despite its inaccuracy and the inappropriate use of the decimal SI prefix, the term was also easy for salesmen and shops to use, and it caught on with the public. Take, for example, the ubiquitous and so-called 3,5 inch floppy disk, which is said to have a capacity of 1,44 MB (megabytes). This is wrong on at least three counts: first, the word floppy no longer really applies as it did to the 5,25 inch predecessor; secondly, the physical size is 90 mm, not 3,5 inches; but more significantly, the capacity, originally described as 1 440 kB (kilobytes) before being “translated” to 1,44 MB, is in fact a little over 2 % inaccurate because of the double misuse of a decimal prefix.

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.

To make matters worse, there has traditionally been inconsistency among operating systems and system applications as to how they actually treat the prefixes, leading to apparent anomalies and incompatibilities.

Similar confusions have arisen between the computing and the telecommunications sectors of the IT world, where data transmission rates have grown enormously over the past few years. Network designers have generally used megabits per second (Mbit/s) to mean 1 048 576 bit/s, while telecommunications engineers have traditionally used the same term to mean 1 000 000 bit/s. Even the usually stated bandwidth of a PCI bus, 133,3 MB/s based on it being four bytes wide and running at 33,3 MHz, is inaccurate because the M in MHz means 1 000 000 while the M in MB means 1 048 576.

As noted above, mathematics dictate that the disparities resulting from mixed and incorrect use of decimal prefixes will become increasingly significant as capacities and data rates continue to grow. In IEC 60027-2, all branches of the IT industry now have a tool with which to iron out inconsistency and achieve mathematical clarity as never before.

# Binary multiples

The new prefixes and symbols for binary multiples standardized in IEC 60027-2 are not part of the SI metric system of units. But as the table below shows, they are related to the SI prefixes and symbols for positive powers of ten in a simple way so that they are easy to remember and use.

 Factor Name Symbol Origin SI 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)6 270 zebi Zi zettabinary (210)7 zetta (103)7 280 yobi Yi yottabinary (210)8 yotta (103)8

The standard :

IEC 60027-2 Ed. 2.0 (2000-11)
Letter symbols to be used in electrical technology - Part 2: Telecommunications and electronics
ICS code: 01.060 - TC 25 - 66 pages - CHF 112,00

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