Binary prefix

In computing, Binary prefixes are often used to quantify large numbers where powers of two are more useful than powers of ten. They are written and pronounced identically to the SI prefixes, but each successive prefix is multiplied by 1024 (2¹⁰) rather than 1000 (10³).

Whether the prefixes kilo-, mega-, giga-, etc., and their abbreviations K, M, G, etc., are being used in the binary or the decimal sense depends on context and common usage. This can cause serious confusion.

Table of values

The one-letter abbreviations are identical to SI prefixes, except for "K", which is used interchangeably with "k". (In SI, "K" stands for the Kelvin unit, and only "k" stands for 1000.) Some have suggested that "k" be used for 1000, and "K" for 1024, but this is not extended to the higher order prefixes and has never been widely recognised.

Notice that as the order of magnitude increases, the percentage difference between the binary and decimal values of a prefix increases.

Informally, the prefixes are often used on their own. Thus one might hear about "a 40K file" (40 binary kilobytes) or "a 2M internet connection" (2 decimal megabits per second). What units are being used, and whether the multipliers are decimal or binary, depends on exactly what is being measured.

Usage notes

Certain units always use the decimal versions, even in computing contexts. Most importantly, the Hz, used to measure clock rates of electronic components, and the bit/s, used to measure bitrate. So a 1 GHz processor performs 1,000,000,000 clock ticks per second, a 128 kbit/s MP3 stream consumes 128,000 bits (15.625 KiB) per second, and a 1 Mbit/s internet connection can transfer 1,000,000 bits (approx. 122 KiB) per second.

Electronic memory such as RAM and ROM always uses the binary versions, because the physical structure of the device makes it naturally come in sizes that are powers of two. This is the case whether the capacity is given in bits or bytes.

Hard disk drives use the decimal prefixes. So what is advertised as a "30 GB" hard disk will actually only hold 30 × 10^9</small> bytes, roughly equal to 28×2³⁰ bytes (i.e. 28 GiB). This makes sense because nothing about the physical structure of the disk drives makes power-of-two capacities natural: the number of platters, tracks and sectors per track are all continuously variable. Modern-day PC users, of course, regard both RAM and disk as kinds of storage and expect their capacities to be measured in the same way.

Floppy disks are even more confusing. The "1.44 MB" floppy holds neither 1.44 × 2²⁰ bytes nor 1.44 × 10⁶ bytes, but rather 1.44 × 1000 × 1024 bytes (approximately 1.406 binary MB , or 1.475 decimal MB).

CD capacities are always given in binary units. A "700 MB" (or "80 minute") CD has a nominal capacity of about 700 MiB. But DVD capacities are given in decimal units. A "4.7 GB" DVD has a nominal capacity of about 4.38 GiB.

Note that all the above media are accessed by the sector, not the individual byte. Sectors are always powers of two, and may range from 512 bytes (floppy disks) to 2048 bytes (DVDs). This has sometimes led to mixed conventions within certain specialties, in which a nominal "megabyte" refers to, e.g. 2000 sectors of 512 bytes each (2¹⁰ &times 10³).

Decimal versions are used when dealing with bus bandwidth (e.g. "Ultra SCSI has a bandwidth of 40 megabytes per second"). Interestingly, this is not because hard drive capacities use the decimal versions, or because bitrates do, but because clock speeds do.

IEC standard prefixes

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 the first two letters of the original SI prefixes followed by 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.

This amendment was included in the next edition of the standard: "IEC 60027-2 (2000-11) Ed. 2.0"

As of 2004 this naming convention has not gained widespread use.

Note that the IEC names are defined only up to exbi-, corresponding to the SI prefix exa-. The two SI prefixes zetta- (10²¹) and yotta- (10²⁴) have no corresponding IEC binary prefixes, even though the obvious continuation would be zebi-/Zi (2⁷⁰) and yobi-/Yi (2⁸⁰).

See also

• Integral data type
• Bit
• Nibble
• Byte
• Octet

External links

• IEC prefixes and symbols for binary multiples (http://members.optus.net/alexey/prefBin.xhtml)
• http://physics.nist.gov/cuu/Units/binary.html
• http://www.iec.ch/zone/si/si_bytes.htm
• http://www.quinion.com/words/turnsofphrase/tp-kib1.htm
• http://www.nist.gov/public_affairs/techbeat/tb9903.htm
• WiebeTech (drive manufacturer) white-paper on the controversy over drive capacities (http://www.wiebetech.com/pressreleases/BillionEqualBillion.pdf)

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