Binary prefix

The SI defines a system of prefixes (nano-, micro-, milli-, kilo-, mega-, giga- etc.) and symbols (n, µ, m, k, M, G, etc.) that denote powers of ten. When discussing things that naturally come in powers of two (mostly amounts of computer memory) one also needs names and symbols for those, but such names were first introduced rather late (1999, see below), and it was and still is common to use the decimal prefixes to denote nearby powers of two.

2¹⁰=1,024 bytes is accurately designated as 1.0 kilobytes to two significant digits. In the absence of other information, it is never clear what an author means by k (or K) for any power of 2 lower than 2¹⁵. 32k equals 32,000 according to the SI usage or 2¹⁵=32,768; the latter rounds to 33k in the SI. As storage size increased, binary meaning was also extended to higher SI prefixes, such as mega, M, and giga, G, where differences become greater.

This led to much confusion about the meaning of the SI prefixes combined with "byte" (kilobyte, megabyte, gigabyte, etc.).

History

The practice of using binary-based prefixes for computer memory arose as early as 1964;.

In January 1999, the International Electrotechnical Commission introduced the prefixes kibi-, mebi-, gibi-, etc., and the symbols Ki, Mi, Gi, etc. to specify binary multiples of a quantity and eliminate this ambiguity. The names for the new standard are derived from the first two letters of the original SI prefixes followed by bi, short for "binary". The new standard also clarifies that, from the point of view of the IEC, the SI prefixes will henceforth only have their base-10 meaning and never have a base-2 meaning.

The second edition of the standard defined them only up to exbi-, but in 2005, the third edition added prefixes zebi- and yobi-, thus matching all standard SI prefixes with their binary counterparts.

On March 19, 2005 the IEEE standard IEEE 1541-2002 (Prefixes for Binary Multiples) has been elevated to a full-use standard by the IEEE Standards Association after a two-year trial period.

Consumer confusion

In the early days of computers there was little or no consumer confusion because of the sophisticated nature of the consumers and the practice of the computer manufacturers to specify (as opposed to advertise) their products with decimal digits of sufficient places, e.g., the 1968 IBM stated System 360 "Model 91s can accommodate up to 6,291,496 bytes of main storage." The confusion appears to relate to the advent of graphical user interfaces where there was not enough space to provide sufficient digits to fully state the capacity. In such GUIs, storage capacity was reported in a mixed system of decimal digits and binary prefixes using the SI notation. Apparently, some computer programmers were unaware that disk drive manufacturers used the SI notation when specifying and/or advertising capacity of their hard disk drives. This mixed presentation appears as early as Microsoft Windows 98 which, for example, would report the space available on a 41,959,424 byte hard disk drive as 40 MB. In Microsoft Windows XP, a 30 gigabyte drive has its capacity reported both 30,064,771,072 bytes and as 28 GB. The confusion has sometimes led to litigation.

Adoption

As of 2007 the binary naming convention has not gained widespread use. However, its use is growing. It is strongly supported by many standardization bodies and technical organizations, such as IEEE, CIPM, NIST, and SAE. The new binary prefixes have also been adopted by the European Committee for Electrotechnical Standardization (CENELEC) as the harmonization document HD 60027-2:2003-03. This document will be adopted as a European standard.

Binary prefixes using SI symbols

Name	Symbol	Value	Base 16	Base 10
kilo	k/K	210 = 1,024	= 162.5	> 103
mega	M	220 = 1,048,576	= 165	> 106
giga	G	230 = 1,073,741,824	= 167.5	> 109
tera	T	240 = 1,099,511,627,776	= 1610	> 1012
peta	P	250 = 1,125,899,906,842,624	= 1612.5	> 1015
exa	E	260 = 1,152,921,504,606,846,976	= 1615	> 1018
zetta	Z	270 = 1,180,591,620,717,411,303,424	= 1617.5	> 1021
yotta	Y	280 = 1,208,925,819,614,629,174,706,176	= 1620	> 1024

The one-letter symbols are identical to SI prefixes, except for "K", which is used interchangeably with "k" (in SI, the upper-case or capital "K" stands for kelvin, and only the lower-case "k" represents 1,000).

These prefixes are in common use in contexts where accuracy is not important, such as file and memory sizes, but conflict with SI definitions. The names and values of the SI prefixes were defined in the 1960 SI standard, with powers-of-1000 values. As of 2005, standard dictionaries do not recognize the binary meanings for these prefixes.

BIPM (which maintains SI) expressly prohibits the binary prefix usage, and recommends the use of the IEC prefixes as an alternative (computing units are not included in SI).

Some have suggested that "k" be used for 1,000, and "K" for 1,024, but this cannot be extended to the higher order prefixes and has never been widely recognised.

Although the prefixes denoting fractions of a bit or byte might theoretically find application in areas such as cryptography, data compression, and data transfer rates, they are not used in practice.

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 context and cannot be determined by the units alone.

IEC standard prefixes

Name	Symbol	Base 2	Base 16		Base 10
kibi	Ki	210	162.5	0x400	= 1,024	> 103
mebi	Mi	220	165	0x10 0000	= 1,048,576	> 106
gibi	Gi	230	167.5	0x4000 0000	= 1,073,741,824	> 109
tebi	Ti	240	1610	0x100 0000 0000	= 1,099,511,627,776	> 1012
pebi	Pi	250	1612.5	0x4 0000 0000 0000	= 1,125,899,906,842,624	> 1015
exbi	Ei	260	1615	0x1000 0000 0000 0000	= 1,152,921,504,606,846,976	> 1018
zebi	Zi	270	1617.5	0x40 0000 0000 0000 0000	= 1,180,591,620,717,411,303,424	> 1021
yobi	Yi	280	1620	0x1 0000 0000 0000 0000 0000	= 1,208,925,819,614,629,174,706,176	> 1024

Example: 300 GB ≅ 279.5 GiB (= 0x117.6592E GiB = 0x45D96.4B8 MiB = 0x1176592E KiB = 0x45D964B800 bytes).

Approximate ratios between binary and decimal prefixes

As the order of magnitude increases, the percentage difference between the binary and decimal values of a prefix increases, from 2.4% (with the kilo prefix) to over 20% (with the yotta prefix). This makes differentiating between the two increasingly important as larger and larger data storage and transmission technologies are developed.

Name	Bin ÷ Dec	Dec ÷ Bin	Example	Percentage difference
kilobyte : kibibyte	1.024	0.976	100 kB ≅ 97.6 KiB	+2.4% or −2.3%
megabyte : mebibyte	1.049	0.954	100 MB ≅ 95.4 MiB	+4.9% or −4.6%
gigabyte : gibibyte	1.074	0.931	100 GB ≅ 93.1 GiB	+7.4% or −6.9%
terabyte : tebibyte	1.100	0.909	100 TB ≅ 90.9 TiB	+10% or −9.1%
petabyte : pebibyte	1.126	0.888	100 PB ≅ 88.8 PiB	+12.6% or −11.2%
exabyte : exbibyte	1.153	0.867	100 EB ≅ 86.7 EiB	+15.3% or −13.3%
zettabyte : zebibyte	1.181	0.847	100 ZB ≅ 84.7 ZiB	+18.1% or −15.3%
yottabyte : yobibyte	1.209	0.827	100 YB ≅ 82.7 YiB	+20.9% or −17.3%

Usage notes

The phrase "decimal unit" will be used to denote "SI designation understood in its standard, decimal, power-of-1000 sense" and "binary unit" will mean "SI designation understood in its binary, power-of-1024 sense." B will be used as the symbol for byte as per computer-industry standard (IEEE 1541 and IEC 60027; B is also the symbol for bel, a common non-SI unit used for ratio measurement).

Certain units are always understood as decimal even in computing contexts. For example, hertz (Hz), which is used to measure clock rates of electronic components, and bit/s, used to measure bit rate. So a 1 GHz processor performs 1,000,000,000 clock ticks per second, a 128 kbit/s MP3 stream consumes 128,000 bits (16 kB, 15.625 KiB) per second, and a 1 Mbit/s Internet connection can transfer 1,000,000 bits (125 kB, approx 122 KiB) per second, assuming an 8-bit byte, and no overhead.

Pronunciation

It is suggested that in English, the first syllable of the name of the binary-multiple prefix should be pronounced in the same way as the first syllable of the name of the corresponding SI prefix, and that the second syllable should be pronounced as "bee."

Computer memory

Measurements of most types of electronic memory such as RAM and ROM and Flash (large scale disk-like flash is sometimes an exception) are given in binary units, as they are made in power-of-two sizes. This is the most natural configuration for memory, as all combinations of their address lines map to a valid address, allowing easy aggregation into a larger contiguous block of memory.

Hard disk drives

HDD manufacturers state capacity in decimal units. This usage has a long tradition, even predating the SI system of decimal prefixes adopted in 1960, as follows:

• The first disk drive the IBM 350 (1950s) had 5,000,000 6 bit characters organized in 100 character sectors (i.e., blocks). This predates the SI system.
• In the 1960s virtually all disk drives used IBM's variable block length format (called, Count Key Data or "CKD"). Any block size could be specified up to the maximum track length. Blocks ("records" in IBM's terminology) of 88, 96, 880 and 960 were often used because they related to the fixed block size of punch cards. The drive capacity was usually stated in full track record blocking, for example, the 100 Megabyte 3336 disk pack only achieved that capacity with a full track block size of 13,030 bytes.
• CKD continued into the 1990s and perhaps into this day. In the 1970s and 1980s most drives were specified with unformatted tracks (the unformatted capacity) with the particular block size and formatted capacity a function of the controller design. For example, the ST412 of IBM PC/XT fame had an unformatted capacity of 12.75 MB (not MiB) and with the Xebec controller and 512 byte blocks it formatted to and was advertised as a 10.0 MB (not MiB) HDD. Other controllers supported other block sizes resulting in other formatted capacities.
• The advent of intelligent interfaces (SCSI and IDE) in the early 1990s took the block size decision into the drive and virtually all chose 512 bytes, for no reason other than that was what IBM had chosen when they picked the Xebec controller for the PC/XT. Capacity continued to be specified by the HDD manufacturers with SI prefix definitions.

Regardless of the HDD manufacturer's continuous practice of specifying with conventional SI prefixes, some systems GUI's took the HDD capacity, reported by the operating system as a binary number without prefixes, and reported the HDD capacity in a mixed decimal number/binary prefix leading to some confusion. As of January 2007, most, if not all, HDD manufacturers continue to use decimal prefixes to identify capacity.

Flash drives

USB Flash Drive and Flash-based memory cards like CompactFlash and Secure Digital are typically classified in "powers of two" multiples of decimal megabytes, for example: 32 MB, 64 MB, 128 MB, 256 MB, 512 MB. Although the devices usually have at least the expected byte capacity as defined by the "decimal" calculation (256 million bytes for a 256 MB classified device), each manufacturer allocates different portions of the device's ultimate capacity for such things as wear levelling.

Floppy drives

The confused usage of decimal prefixes may have started in floppy drives where the drive and media manufacturers stated their unformatted capacity while various systems houses published differing formatted capacities as a consequence of their varying controller designs. It appears that some system manufacturers and OS vendors began reporting in what we now know as Ki bytes. A very confusing hybrid system developed with the double sided high density 3½" floppy disk, in which a "megabyte" means a thousand 1024-byte "kilobytes". Thus, as of 2005, manufacturers universally use the designation "1.44 MB diskette" for a product which holds neither 1.44×2²⁰ bytes nor 1.44×10⁶ bytes, but rather 1.44×1000×1024 bytes (approximately 1.406 MiB, or 1.475 MB). This is probably because some marketing person decided that this was best advertised as a double capacity version of the prior generation 720 KB product (of course, it was 720 KiB).

CD and DVD

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.

Buses

Bus bandwidth is given in decimal units. This is not because hard drive capacities use the decimal versions, nor because bit rates do, but because clock speeds do. For example, "PC3200" memory runs on a double pumped 200 MHz bus, transferring 8 bytes per cycle, and hence has a bandwidth of 200,000,000×2×8 = 3,200,000,000 byte/s.

Legal disputes

The implicit use of decimal units to describe the capacity of storage devices has become a source of confusion as these devices are increasingly marketed to non-technical consumers. When a user buys a device advertised using decimal units, and installs it in a system that shows the available space in binary units, a misinformed user may be disturbed by the apparent discrepancy. As a result, there have been several lawsuits against companies who sell hard drives, flash memory devices, and computer systems that list drive capacities.

Several significant lawsuits have been filed:

• On June 23, 2003, a Business Tort action entitled Matthew Leffert vs. Amazon.com, INC., was filed in the Superior Court for the City and County of San Francisco, Case No. CGC-03-421769. In this case, the plaintiff complained of false advertising in relation to how MP3 player storage is marketed.
  • The case was dismissed on March 14 2005.
• In September of 2003, Lanchau Dan, Adam Selkowitz, Tim Swan and John Zahabian filed a lawsuit against Dell, Inc., Apple Computer Inc., Gateway, Inc., Hewlett-Packard Co., IBM Corp., Sharp Corporation, Sony Corp. and Toshiba Corp claiming their advertising deceptively exaggerates the real capacity of their hard drives.
• On February 20, 2004, Willem Vroegh filed a lawsuit against Lexar Media, Dane–Elec Memory, Fuji Photo Film USA, Eastman Kodak Company, Kingston Technology Company, Inc., Memorex Products, Inc.; PNY Technologies Inc., SanDisk Corporation, Verbatim Corporation, and Viking InterWorks alleging that their descriptions of the capacity of their flash memory cards were false and misleading.
• On July 7, 2005, an action entitled Orin Safier v. Western Digital Corporation, et al., was filed in the Superior Court for the City and County of San Francisco, Case No. CGC-05-442812. The case was subsequently moved to the Northern District of California, Case No. 05-03353 BZ.
  • The case was settled in March 2006 with June 14, 2006 as the Final Approval hearing date.

See also

• Integral data type
• Bit
• Nibble
• Byte
• Octet
• IEC 60027-2
• IEEE 1541
• SI prefix

Specific units of IEC 60027-2 A.2

These units have individual articles:

Bit rates (data-rate units) Name Symbol Multiple bit per second bit/s 1 1 Metric prefixes (SI) kilobit per second kbit/s 103 10001 megabit per second Mbit/s 106 10002 gigabit per second Gbit/s 109 10003 terabit per second Tbit/s 1012 10004 Binary prefixes (IEC 80000-13) kibibit per second Kibit/s 210 10241 mebibit per second Mibit/s 220 10242 gibibit per second Gibit/s 230 10243 tebibit per second Tibit/s 240 10244

Multiple-byte units Decimal Value Metric 1000 kB kilobyte 10002 MB megabyte 10003 GB gigabyte 10004 TB terabyte 10005 PB petabyte 10006 EB exabyte 10007 ZB zettabyte 10008 YB yottabyte 10009 RB ronnabyte 100010 QB quettabyte Binary Value IEC Memory 1024 KiB kibibyte KB kilobyte 10242 MiB mebibyte MB megabyte 10243 GiB gibibyte GB gigabyte 10244 TiB tebibyte TB terabyte 10245 PiB pebibyte – 10246 EiB exbibyte – 10247 ZiB zebibyte – 10248 YiB yobibyte – 10249 – – 102410 – – Orders of magnitude of data

Multiple-bit units Decimal Value Metric 1000 kbit kilobit 10002 Mbit megabit 10003 Gbit gigabit 10004 Tbit terabit 10005 Pbit petabit 10006 Ebit exabit 10007 Zbit zettabit 10008 Ybit yottabit 10009 Rbit ronnabit 100010 Qbit quettabit Binary Value IEC Memory 1024 Kibit kibibit Kbit Kb kilobit 10242 Mibit mebibit Mbit Mb megabit 10243 Gibit gibibit Gbit Gb gigabit 10244 Tibit tebibit — 10245 Pibit pebibit — 10246 Eibit exbibit — 10247 Zibit zebibit — 10248 Yibit yobibit — — — Orders of magnitude of data

External links

• "When is a kilobyte a kibibyte? And an MB an MiB?" — An introduction to binary prefixes from the IEC

• Tool to convert to/from the binary and standard units (up to yobibytes)
• What is a Megabyte ...? Markus Kuhn's 1996–1999 paper on bits, bytes, prefixes and symbols
• Prefixes for binary multiples — NIST
• Get Ready for the mebi, gibi and tebi — NIST

• Another description of binary prefixes
• White-paper on the controversy over drive capacities
• There is no such thing as a 1.44 MB standard format floppy disc
• A summary of the organizations, software, and so on that have implemented the new binary prefixes
• A plea for sanity
• KiloBytes vs. kilobits vs. Kibibytes (Binary prefixes)
• Here Come Zebi- and Yobi- IEC press release announcing new prefixes
• Decimal-to-Binary Prefixes and Binary-to-Decimal Prefixes Converter