Binary prefix

Large quantities of bytes, bits, or bits per second (bit/s) are often given using prefixes derived from the SI prefixes, so the prefixes K, M, and G are used for kilobyte, megabyte, gigabyte. For example, a 50 byte text string, 100 KB (kilobytes) files, 128 MB (megabytes) of RAM, or 30 GB (gigabytes) of disk storage.

As popularly used, these prefixes often indicate multiples that are similar, but not equal to, factors denoted by their SI counterparts. Specifically, popular usage in computing often denotes whole powers of two, while SI prefixes are powers of ten. The exact numbers are listed below:

Prefixes in colloquial computing usage

Name	Abbr	Factor	SI size
kilo	K	210 = 1024	103 = 1000
mega	M	220 = 1 048 576	106 = 1 000 000
giga	G	230 = 1 073 741 824	109 = 1 000 000 000
tera	T	240 = 1 099 511 627 776	1012 = 1 000 000 000 000
peta	P	250 = 1 125 899 906 842 624	1015 = 1 000 000 000 000 000
exa	E	260 = 1 152 921 504 606 846 976	1018 = 1 000 000 000 000 000 000
zetta	Z	270 = 1 180 591 620 717 411 303 424	1021 = 1 000 000 000 000 000 000 000
yotta	Y	280 = 1 208 925 819 614 629 174 706 176	1024 = 1 000 000 000 000 000 000 000 000

These are identical to SI prefixes, except for "K", which is lowercase in SI.

It is widely regarded as confusing that common usage of kilobyte means 1024 bytes, while the "correct" value is 1000 bytes. Hard disk manufacturers are the only group in computing that habitually uses the lower SI factors, so what is advertised as a 30 GB hard disk will actually only hold about 28 × 2³⁰ bytes. Telecommunications also uses the SI factors, so a 1 Mbit/s connection transfers 10⁶ bits per second. Floppy disk manufacturers are even more confusing. The prefix "M" means (1000 × 1000) in SI, and (1024 × 1024) in standard computing. However, the standard "1.44 MB" floppy holds (1.44 × 1000 × 1024) bytes.

In the days of 32K RAM computers, this confusion was not serious, since the different between 2¹⁰ and 10³ was approximately 2%. However, as computing equipment have become increasingly capable, these differences have become an increasingly large error when expressed as percentages.

In 1999, the International Electrotechnical Commission (IEC) published Amendment 2 to "IEC 60027-2: Letter symbols to be used in electrical technology - Part 2: Telecommunications and electronics". This standard, which had been approved in 1998, introduced the prefixes kibi-, mebi-, gibi-, tebi-, pebi-, exbi-, to be used in specifying binary multiples of a quantity. The names come from shortened versions of the original SI prefixes and bi which is short for binary. It also clarifies that, from the point of view of the IEC, the SI prefixes only have their base-10 meaning and never have a base-2 meaning.

New IEC Standard Prefixes

Name	Abbr	Factor
kibi	Ki	210 = 1024
mebi	Mi	220 = 1 048 576
gibi	Gi	230 = 1 073 741 824
tebi	Ti	240 = 1 099 511 627 776
pebi	Pi	250 = 1 125 899 906 842 624
exbi	Ei	260 = 1 152 921 504 606 846 976

As of 2002 this naming convention has not yet gained widespread use. The IEC did not give names for the prefixes beyond exa-, but if they had given them names, they would probably be zebi- and yobi-.

See Also:

• Integral data type
• Terabyte
• Petabyte
• Exabyte
• Zettabyte
• Yottabyte

External Links:

• http://physics.nist.gov/cuu/Units/binary.html
• http://www.quinion.com/words/turnsofphrase/tp-kib1.htm
• http://www.nist.gov/public_affairs/techbeat/tb9903.htm
• http://www.iec.ch/online_news/etech/arch_2003/etech_0503/focus.htm