Binary prefix

Prefixes for bit and byte multiples
Decimal Value SI 1000 k kilo 10002 M mega 10003 G giga 10004 T tera 10005 P peta 10006 E exa 10007 Z zetta 10008 Y yotta	Binary Value IEC JEDEC 1024 Ki kibi K kilo 10242 Mi mebi M mega 10243 Gi gibi G giga 10244 Ti tebi 10245 Pi pebi 10246 Ei exbi 10247 Zi zebi 10248 Yi yobi

In computing, a binary prefix is a specifier or mnemonic that is prepended to the units of digital information, the bit and the byte, to indicate multiplication by a power of 2. In practice the powers used are multiples of 10, so the prefixes denote powers of 1024 = 2¹⁰.

The computer industry uses terms such as "kilobyte," "megabyte," and "gigabyte," and corresponding abbreviations "KB", "MB", and "GB", in two different ways. In citations of main memory or RAM capacity, "gigabyte" customarily means 1073741824 bytes. This is a power of 2, specifically 2³⁰, so this usage is referred to as a "binary unit" or "binary prefix."

In other contexts, the industry uses "kilo", "mega", "giga", etc., in a manner consistent with their meaning in the International System of Units (SI): as powers of 1000. For example, a "500 gigabyte" hard drive holds 500000000000 bytes, and a "100 megabit per second" Ethernet connection runs at 100000000 bit/s.

Starting in about 2000, a number of standards and trade organizations approved standards and recommendations for a new set of binary prefixes, proposed earlier by the International Electrotechnical Commission (IEC), that would refer unambiguously to powers of 1024. According to these, the SI prefixes would only be used in the decimal sense, even when referring to data storage capacities: kilobyte and megabyte would denote one thousand bytes and one million bytes respectively (consistent with SI), while new terms such as kibibyte, mebibyte and gibibyte, abbreviated KiB, MiB, and GiB, would denote 1024 bytes, 1048576 bytes, and 1073741824 bytes respectively.^[1]

In practice, the IEC binary prefixes have seen little use by the press or the US computing industry and marketplace. However, they are starting to appear in the EU computing industry and marketplace (as required by EU law since 2007),^[2][3] certain US and International Government contexts (as required by contract or internal policy),^[4] and popular free and open source software such as Linux.^[5]

Contents 1 History 1.1 Main memory 1.2 Disk drives 1.3 Information transfer and clock rates 1.4 Standardization of dual definitions 2 Inconsistent use of units 2.1 Deviation between powers of 1024 and powers of 1000 2.2 Consumer confusion 2.3 Legal disputes 2.3.1 Willem Vroegh v. Eastman Kodak Company 2.3.2 Orin Safier v. Western Digital Corporation 3 Unique binary prefixes 3.1 Early suggestions 3.2 IEC prefixes 3.3 Adoption by IEC and NIST 3.4 Specific units of IEC 60027-2 A.2 and ISO/IEC 80000 3.5 Other standards bodies and organizations 3.6 Dissent 4 Current practice 4.1 Software 4.1.1 Files 4.2 Computer hardware 4.2.1 Computer memory 4.2.2 Hard disk drives 4.2.3 Flash drives 4.2.4 Floppy drives 4.2.5 Optical discs 4.2.6 Tape drives and media 4.2.7 Data transmission and clock rates 5 See also 6 Definitions 7 References 8 Further reading 9 External links

History

Main memory

Early computers used one of two addressing methods to access the system memory; binary (base-2) or decimal (base-10). For example, the IBM 701 (1952) used binary and could address 2048 36-bit words, while the IBM 702 (1953) used decimal and could address 10000 7-bit words.

By the mid 1960s, binary addressing had become the standard architecture in computer design, and main memory sizes were most commonly powers of two. 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 block of memory with contiguous addresses.

Early computer system documentation would specify the memory size with an exact number such as 4096, 8192, or 16384 words of storage. These are all powers of 2, and furthermore are small multiples of 2¹⁰, or 1024. As storage capacities increased, several different methods were developed to abbreviate these quantities.

The method most commonly used today uses prefixes such as kilo, mega, giga, and corresponding symbols K, M, and G, which the computer industry adapted from the International System of Units (SI). These are known as the SI prefixes.^{[defn. 1]} They are defined as indicating multipliers that are powers of 1000: A kilogram is 1000 grams, one megahertz is 1000000 hertz, and so on.

The International System of Units defines no units such as "bytes" for digital information but notes that the SI prefixes may be applied outside the contexts where base units or derived units would be used. But as computer main memory in a binary-addressed system naturally came in sizes that were easily expressed as multiples of 1024, "kilobyte" when applied to computer memory was commonly used to mean 1024 bytes instead of 1000.

The use of K in the binary sense as in a "32K core" meaning 32×1024, or 32768, can be found as early as 1959^[6][7] Gene Amdahl's seminal 1964 article on IBM System/360 used 1K to mean 1024.^[8] This style was used by other computer vendors, the CDC 7600 System Description (1968) made extensive use of K as 1024.^[9] Thus the first binary prefix was born.^{[defn. 2]}

Another style was to truncate the last 3 digits and append K, essentially using K as a decimal prefix^{[defn. 3]} in accordance with SI, but always truncating to the next lower whole number instead of rounding to the nearest. The exact values 32768, 65536 and 131072 would then be described as 32K, 65K and 131K.^[10] (If these values had been rounded they would have become 33K, 66K, and 131K, respectively.) This style was used from about 1965 to 1975.

These two styles (K = 1024 and truncation) were used loosely around the same time, sometimes by the same company. In discussions of binary-addressed memories, the exact size was evident from context. The HP 21MX real-time computer (1974) denoted 196608 (which is 192×1024) as 196K and 1048576 as 1M,^[11] while the HP 3000 business computer (1973) could have 64K, 96K, or 128K bytes of memory.^[12]

The "truncation" method gradually waned. Capitalization of the letter K became the de facto standard for binary notation, although this could not be extended to higher powers. Nevertheless, the practice of using the SI-inspired "kilo" to indicate 1024 was later extended to "megabyte" meaning 1024² (1048576) bytes, and later "gigabyte" for 1024³ (1073741824) bytes. For example, a "512 megabyte" RAM module is 512×1024² bytes (512×1048576, or 536870912), rather than 512000000.

The abbreviated terms Kbit, Kbyte, Mbit and Mbyte started to be used as "binary units"—"bit" or "byte" with a multiplier that is a power of 1024—in the early 1970s.^[13] For a time, memory capacities were often expressed in K, even when M could have been used: The IBM System/370 Model 158 brochure (1972) had the following: "Real storage capacity is available in 512K increments ranging from 512K to 2,048K bytes."^[14]

Megabyte was used to describe the 22-bit addressing of DEC PDP-11/70 (1975)^[15] and gigabyte the 30-bit addressing DEC VAX-11/780 (1977).

Disk drives

The disk drive industry followed a different pattern. Industry practice, more thoroughly documented at Timeline of binary prefixes and continuing today, is to specify hard drives using SI prefixes and symbols in their SI or "decimal" interpretation. Unlike binary-addressed computer main memory, there is nothing in a disk drive that influences it to have a total capacity easily expressed using a power of 1024. The first commercially sold disk drive, the IBM 350, had 50 (not 32 or 64) physical disk "platters" containing a total of 50,000 sectors of 100 characters each, for a total quoted capacity of "5 million characters."^[16] It was introduced in September 1956.

In the 1960s most disk drives used IBM's variable block length format (called Count Key Data or "CKD").^[17] Any block size could be specified up to the maximum track length. Since the block headers occupied space, the usable capacity of the drive was dependent on the block size. 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 under conditions of 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.

Hard disk drive manufacturers used "megabytes" or "MB", meaning 10⁶ bytes, to characterize their products as early as 1974.^[18] By 1977, in its first edition, Disk/Trend, a leading hard disk drive industry marketing consultancy segmented the industry according to MBs (decimal sense) of capacity.^[19]

An early hard drive in personal computing history, the Seagate ST251, had 6 heads or active surfaces (tracks per cylinder), 17 sectors per track, and 820 cylinders; with a sector size of 512 bytes, this gives a capacity of 42823680 bytes.^[20] Seagate like other hard drive manufacturers before and since used the SI prefixes in their marketing, and labeled this as a "42 MB" drive, meaning 42000000 bytes. With the customary binary prefixes^{[defn. 4]} used for RAM, this would have been described as 40.84 megabytes.

The hard drive industry continues to use SI prefixes. Today, for example, a "300 GB" hard drive offers slightly more than 300×10⁹, or 300000000000, bytes, not 300×2³⁰ (which would be about 322×10⁹). Operating systems such as Microsoft Windows that display hard drive sizes using the customary binary prefix "GB" (as it is used for RAM) would display this as 279.4 GB (meaning 279.4×1024³, or 279.4×1073741824).

Information transfer and clock rates

Like the hard drive, there is nothing in a computer clock circuit or data transfer path that demands or even encourages that things happen at rates easily expressed using powers of 1024, or even using powers of 2.

Computer clock frequencies are always quoted using SI prefixes in their decimal sense. For example, the internal clock frequency of the original IBM PC was 4.77 MHz, that is, 4770000 Hz.

Similarly, digital information transfer rates are quoted using SI prefixes:

• The ATA-100 disk interface refers to 100000000bytes/s.
• 1x CD-ROM speed is 150K or 150000bytes/s
• A "56K" modem refers to 56000bits/s
• SATA-2 has a raw bit rate of 3Gb/s = 3000000000bits/s
• PC2-6400 ram transfers 6400000000bytes/s
• Firewire 800 has a raw rate of 800000000bits/s

Standardization of dual definitions

By the mid 1970s it was common to see K meaning 1024 and the occasional M meaning 1048576 for words or bytes of main memory (RAM) while K and M were commonly used with their decimal meaning for disk storage. In the 1980s, as capacities of both types of devices increased, the SI prefix G, with SI meaning, was commonly applied to disk storage, while M in its binary meaning, became common for computer memory. In the 1990s, the prefix G, in its binary meaning, became commonly used for computer memory capacity. The first terabyte (SI prefix, 1000000000000 bytes) hard disk drive was introduced in 2007.^[21]

The dual usage of the kilo, mega, and giga prefixes and their corresponding symbols K, M, and G as both powers of 1000 and powers of 1024 was recorded in standards and dictionaries. For example, the 1986 ANSI/IEEE Std 1084-1986^[22] defined dual uses for kilo and mega.

kilo (K). (1) A prefix indicating 1000. (2) In statements involving size of computer storage, a prefix indicating 2¹⁰, or 1024.

mega (M). (1) A prefix indicating one million. (2) In statements involving size of computer storage, a prefix indicating 2²⁰, or 1048576.

The binary units Kbyte and Mbyte were formally defined in ANSI/IEEE Std 1212-1991.^[23]

Many dictionaries have noted, often incorrectly stated, the practice of using prefixes borrowed from SI to indicate binary multiples.^[24][25] Oxford online dictionary defines, for example, megabyte as: "Computing: a unit of information equal to one million or (strictly) 1048576bytes."^[26]

The units Kbyte, Mbyte, and Gbyte are found in the trade press and in IEEE journals. Gigabyte was formally defined in IEEE Std 610.10-1994 as either 1000000000 or 2³⁰ bytes.^[27] Kilobyte, Kbyte, and KB are equivalent units and all are defined in the current standard, IEEE 100-2000.^[28] Byte multiples using powers of 1024 up to yottabyte are given by the on-line computing dictionary FOLDOC (Free On-Line Dictionary of Computing).^[29]

The hardware industry has coped with the dual definitions because of relative consistency: system memory (RAM) typically uses the binary meaning while magnetic disk storage uses the SI meaning. There are, however, exceptions and special cases. Diskettes use yet another "megabyte" equal to 1024×1000 bytes.^[30] In optical disks, Compact Disks use MB to mean 1024² bytes while DVDs use GB to mean 1000³ bytes.^[31][32]

Inconsistent use of units

Deviation between powers of 1024 and powers of 1000

Computer storage has become cheaper per unit and thereby larger, by many orders of magnitude since "K" was first used to mean 1024. Because both the SI and "binary" meanings of kilo, Mega, etc., are based on powers of 1000 or 1024 rather than simple multiples, the difference between 1M "binary" and 1M "decimal" is proportionally larger than that between 1K "binary" and 1k "decimal," and so on up the scale. The relative difference between the values in the binary and decimal interpretations increases, when using the SI prefixes as the base, from 2.4% for kilo to over 20% for the yotta prefix.

Prefix	Bin ÷ Dec	Dec ÷ Bin	Percentage difference
kilo	1.024	0.9766	+2.4% or −2.3%
mega	1.049	0.9537	+4.9% or −4.6%
giga	1.074	0.9313	+7.4% or −6.9%
tera	1.100	0.9095	+10.0% or −9.1%
peta	1.126	0.8882	+12.6% or −11.2%
exa	1.153	0.8674	+15.3% or −13.3%
zetta	1.181	0.8470	+18.1% or −15.3%
yotta	1.209	0.8272	+20.9% or −17.3%

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 computer manufacturers to specify their products with capacities in full precision. For example, in 1965 IBM stated about the System/360 Model 75 that "Its main memory operated at 750 nanoseconds and was available in three sizes up to 1,048,576 characters of information."^[33]

One source of consumer confusion is the difference in the way many operating systems display hard drive sizes, compared to the way hard drive manufacturers describe them. As noted previously, hard drives are described and sold using "GB" or "TB" in their SI meaning: one billion and one trillion bytes. Many current operating systems and other software however display hard drive and file sizes using "MB", "GB" or other SI-looking prefixes in their "binary" meaning, just as they do for displays of RAM capacity. (This is fairly recent. The presentation of hard disk drive capacity by an operating system using "MB" in a binary sense appears no earlier than Macintosh Finder after 1984. Prior to that, on the systems that had a hard disk drive, capacity was presented in decimal digits with no prefix of any sort (e.g., MS/PC DOS CHKDSK command).)

The following three images show the discrepancy of reporting the identical disk capacity on the manufacturer's packaging (160 GB = 160×1000³), the Windows XP disk manager (149.05 GB = 149.05×1024³), and the drive properties display (152625MB = 152625×1024²).

Disk drive packaging specifies a disk capacity of 160×109 bytes using standard SI prefixes.

Windows XP disk management application lists the capacity of a 160×109 byte disk drive as 149.05 GB

Windows XP drive properties display lists the capacity of a 160×109 byte disk drive as 152625 MB.

Legal disputes

The different interpretations of disk size prefixes has led to two significant class action lawsuits against digital storage manufacturers. One case involved flash memory and the other involved hard disk drives. Both were settled with the manufactures admitting no wrongdoing but agreeing to clarify the storage capacity of their products on the consumer packaging. Flash memory and hard disk manufacturers now have disclaimers on their packaging and web sites clarifying the formatted capacity of the devices^[34] or defining MB as 1 million bytes and 1 GB as 1 billion bytes.^[35]

Willem Vroegh v. Eastman Kodak Company

On 20 February 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.

Vroegh claimed that a 256 MB Flash Memory Device had only 244 MB of accessible memory. "Plaintiffs allege that Defendants marketed the memory capacity of their products by assuming that one megabyte equals one million bytes and one gigabyte equals one billion bytes." The plaintiffs wanted the defendants to use the traditional values of 1024² for megabyte and 1024³ for gigabyte. The plaintiffs acknowledged that the IEC and IEEE standards define a MB as one million bytes but stated that the industry has largely ignored the IEC standards.^[36]

The manufacturers agreed to clarify the flash memory card capacity on the packaging and web sites.^[37] The consumers could apply for "a discount of ten percent off a future online purchase from Defendants' Online Stores Flash Memory Device".^[38]

Orin Safier v. Western Digital Corporation

On 7 July 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.^[39]

Although Western Digital maintained that their usage of units is consistent with "the indisputably correct industry standard for measuring and describing storage capacity", and that they "cannot be expected to reform the software industry", they agreed to settle in March 2006 with 14 June 2006 as the Final Approval hearing date.^[40]

Western Digital offered to compensate customers with a free download of backup and recovery software valued at US$30. They also paid $500,000 in fees and expenses to San Francisco lawyers Adam Gutride and Seth Safier, who filed the suit. The settlement called for Western Digital to add a disclaimer to their later packaging and advertising.^[41][42][43]

Unique binary prefixes

Early suggestions

While early computer scientists typically used k to mean 1000, some recognized the convenience that would result from working with multiples of 1024 and the confusion that resulted from using the same prefixes for two different meanings.

Several proposals for unique binary prefixes^{[defn. 2]} were made in 1968. Donald Morrison proposed to use the Greek letter kappa (κ) to denote 1024, κ² to denote 1024×1024, and so on.^[44] (At the time, memory size was small, and only K was in widespread use.) Wallace Givens responded with a proposal to use bK as an abbreviation for 1024 and bK2 or bK² for 1024×1024, though he noted that neither the Greek letter nor lowercase letter b would be easy to reproduce on computer printers of the day.^[45] Bruce A. Martin further proposed that the prefixes be abandoned altogether, and the letter B be used as a binary exponent, similar to E notation, to create shorthands like 3B20 for 3×2^20[46]

None of these gained much acceptance, and capitalization of the letter K became the de facto standard for indicating a factor of 1024 instead of 1000, although this could not be extended to higher powers.

As the discrepancy between the two systems increased in the higher order powers, more proposals for unique prefixes were made. In 1996, Markus Kuhn proposed a system with di prefixes, like the "dikilobyte" (K₂B or K2B).^[47]

IEC prefixes

The set of binary prefixes that were eventually adopted, now referred to as the "IEC prefixes,"^{[defn. 5]} were first proposed by the International Union of Pure and Applied Chemistry's (IUPAC) Interdivisional Committee on Nomenclature and Symbols (IDCNS) in 1995. At that time, it was proposed that the terms kilobyte and megabyte be used only for 10³ bytes and 10⁶ bytes, respectively. The new prefixes kibi (kilobinary), mebi (megabinary) and gibi (gigabinary) were also proposed at the time, and the proposed symbols for the prefixes were kb, Mb and Gb respectively, rather than Ki, Mi and Gi.^[48] The proposal was not accepted at the time.

The Institute of Electrical and Electronic Engineers (IEEE) began to collaborate with the International Organization for Standardization (ISO) and International Electrotechnical Commission (IEC) to find acceptable names for binary prefixes. The IEC proposed kibi, mebi, gibi and tebi, with the symbols Ki, Mi, Gi and Ti respectively, in 1996.^[49]

The names for the new prefixes are derived from the original SI prefixes combined with the term binary, but contracted, by taking the first two letters of the SI prefix and 'bi' from binary. The first letter of each such prefix is therefore identical to the corresponding SI prefixes, except for "K", which is used interchangeably with "k", whereas in SI, only the lower-case k represents 1000.

The IEEE decided that their standards would use the prefixes kilo, etc. with their metric definitions, but allowed the binary definitions to be used in an interim period as long as such usage was explicitly pointed out on a case-by-case basis.^[50]

Adoption by IEC and NIST

In January 1999, the IEC published the first international standard (IEC 60027-2 Amendment 2) with the new prefixes, extended up to pebi (Pi) and exbi (Ei).^[51][52]

The IEC 60027-2 Amendment 2 also states that the IEC position is the same as that of BIPM (the body who regulate the SI system); the SI prefixes retain their definitions in powers of 1000 and are never used to mean a power of 1024.

In usage, products and concepts typically described using powers of 1024 would continue to be, but with the new IEC prefixes. For example, a memory module of 536870912 bytes (512×1048576) would be referred to as 512 MiB or 512 mebibytes instead of 512 MB or 512 megabytes. Conversely, since hard drives have historically been marketed using the SI convention that "giga" means 1000000000, a "500 GB" hard drive would still be labeled as such. According to these recommendations, operating systems and other software would also use binary and SI prefixes in the same way, so the purchaser of a "500 GB" hard drive would find the operating system reporting either "500 GB" or "477 GiB", while 536870912 bytes of RAM would be displayed as "512 MiB".

The second edition of the standard, published in 2000,^[53] defined them only up to exbi,^[54] but in 2005, the third edition added prefixes zebi and yobi, thus matching all SI prefixes with binary counterparts.^[55]

The harmonized ISO/IEC IEC 80000-13:2008 standard cancels and replaces subclauses 3.8 and 3.9 of IEC 60027-2:2005 (those defining prefixes for binary multiples). The only significant change is the addition of explicit definitions for some quantities.^[56]

Specific units of IEC 60027-2 A.2 and ISO/IEC 80000

IEC prefix		Representations				Customary prefix
Name	Symbol	Base 2	Base 1024	Value	Base 10	Name	Symbol
kibi	Ki	210	10241	1024	~1.02×10^3	kilo	k, K
mebi	Mi	220	10242	1048576	~1.05×10^6	mega	M
gibi	Gi	230	10243	1073741824	~1.07×10^9	giga	G
tebi	Ti	240	10244	1099511627776	~1.10×10^12	tera	T
pebi	Pi	250	10245	1125899906842624	~1.13×10^15	peta	P
exbi	Ei	260	10246	1152921504606846976	~1.15×10^18	exa	E
zebi	Zi	270	10247	1180591620717411303424	~1.18×10^21	zetta	Z
yobi	Yi	280	10248	1208925819614629174706176	~1.21×10^24	yotta	Y

Other standards bodies and organizations

The IEC-proposed binary prefixes are now supported by other standardization bodies and technical organizations.

The United States National Institute of Standards and Technology (NIST) supports the ISO/IEC standards for "Prefixes for binary multiples" and has a web site documenting them, describing and justifying their use. NIST suggests 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.^[1] NIST has stated the SI prefixes "refer strictly to powers of 10" and that the binary definitions "should not be used."^[57]

In December 2002 JEDEC, a leading standards organization in the microelectronics industry, mentioned the IEC prefixes in their Terms, Definitions, and Letter Symbols for Microcomputers, Microprocessors, and Memory Integrated Circuits document. This document defines "kilo," "mega," and "giga" with binary multipliers. A "Note" to this definition then states that that definition is only presented "to reflect common usage", and quotes the IEC in describing the binary prefixes as "an alternative system".^[58] However, subsequent memory standards published by JEDEC still define and use the prefixes kilo, mega, and giga as binary multipliers.^{[59][60][61][62][63]}

On 19 March 2005 the IEEE standard IEEE 1541-2002 ("Prefixes for Binary Multiples") was elevated to a full-use standard by the IEEE Standards Association after a two-year trial period.^[64][65] However, As of April 2008^[update], the IEEE Publications division does not require the use of IEC prefixes in its major magazines such as Spectrum^[66] or Computer.^[67]

The International Bureau of Weights and Measures (BIPM), which maintains the International System of Units (SI), expressly prohibits the use of SI prefixes to denote binary multiples, and recommends the use of the IEC prefixes as an alternative since units of information are not included in SI.^[68][69]

The European Committee for Electrotechnical Standardization (CENELEC) has adopted the IEC-recommended binary prefixes via the harmonization document HD 60027-2:2003-03.^[3] This document will be adopted as a European standard.^[70]

The Society of Automotive Engineers prohibits the use of SI prefixes with anything but a power-of-1000 meaning, but does not recommend or otherwise cite the IEC binary prefixes.^[71]

Dissent

Even among proponents of unique prefixes for binary multiples, proposals for alternative sets of prefixes have continued following the introduction of Ki, Mi, etc., by the IEC. For example, Donald Knuth, who uses decimal notation like 1 MB = 1000 kB,^[72] expressed "astonishment" that the IEC proposal was adopted, calling them "funny-sounding" and opining that proponents were assuming "that standards are automatically adopted just because they are there." Knuth proposed that the powers of 1024 be designated as "large kilobytes" and "large megabytes" (abbreviated KKB and MMB, as "doubling the letter connotes both binary-ness and large-ness").^[73] Double prefixes were already abolished from SI, however, having a multiplicative meaning ("MMB" would be equivalent to "TB"), and this proposed usage never gained any traction.

Current practice

Most computer hardware uses SI prefixes^{[defn. 1]} to state capacity and define other performance parameters such as data rate. Main and cache memories are notable exceptions.

Main memory and cache memory universally use customary binary prefixes^{[defn. 4]} to state capacity.^{[74][75][76][77][78]} On the other hand, Flash memory as for example in solid state drives, uses SI prefixes.^{[defn. 1]} to state capacity.

With a few exceptions, most operating systems and other software continue to use the customary binary prefixes in displays of memory, disk storage capacity, and file size, but SI prefixes^{[defn. 1]} in other areas such as network communication speeds and processor speeds.

Nearly all articles, papers, and marketing materials in the industry continue to use the customary binary prefixes when referring to computer memory, even those published under the aegis of organizations that have shown support for the IEC prefixes.

In the following subsections, unless otherwise noted, examples are first given using the common prefixes used in each case, and then followed by interpretation using other notation where appropriate.

Software

As of February 2010^[update], most software does not distinguish symbols for binary and decimal prefixes.^{[defn. 3]} The IEC binary naming convention has been adopted by a few, but this is not used universally.

Examples of software that use IEC binary prefixes for powers of 1024 (along with standard SI prefixes for powers of 1000) include:

The Linux kernel[79][80] GNU Core Utilities[81] Flyspray[82] bugs.mysql.com[83] GParted[84] DFSee[85] disktype[86]

raidutil[87] FreeDOS-32[88] ifconfig[89] GNOME Network[90] SLIB[91] Cygwin/X[92] HTTrack[93]

Pidgin (IM client)[94] Deluge[95] zFTPServer[96] yafc[97] tnftp[98] WinSCP[99] MediaInfo[100]

One of the stated goals of the introduction of the IEC prefixes was "to preserve the SI prefixes as unambiguous decimal multipliers."^[64] Programs such as fdisk/cfdisk, parted, and apt-get use SI prefixes with their decimal meaning.

GNOME's partition editor uses IEC prefixes to display partition sizes. The total capacity of the 120×109 byte disk is displayed as "111.79 GiB"

GNOME's system monitor uses IEC prefixes to show memory size and networking data rate.

BitTornado uses standard SI prefixes for data rates and IEC prefixes for file sizes

Deluge (BitTorrent client) uses IEC prefixes for data rates as well as file sizes

Linux's fdisk uses standard SI prefixes to display a 160×109 byte disk as "160.0 GB"

Example of the use of IEC binary prefixes in the Linux operating system displaying traffic volume on a network interface in kibibytes (KiB) and mebibytes (MiB), as obtained with the ifconfig utility:

eth0      Link encap:Ethernet  HWaddr 00:14:A0:B0:7A:42 
          inet6 addr: 2001:491:890a:1:214:a5ff:febe:7a42/64 Scope:Global
          inet6 addr: fe80::214:a5ff:febe:7a42/64 Scope:Link
          UP BROADCAST RUNNING MULTICAST  MTU:1500  Metric:1
          RX packets:254804 errors:0 dropped:0 overruns:0 frame:0
          TX packets:756 errors:0 dropped:0 overruns:0 carrier:0
          collisions:0 txqueuelen:1000 
          RX bytes:18613795 (17.7 MiB)  TX bytes:45708 (44.6 KiB)

Files

Prior to the release of Macintosh System Software (1984), file sizes were typically reported by the operating system without any prefixes. Today, most operating systems report file sizes with prefixes.

• Most Unix-like systems, which use the ls command to display file sizes, use powers of 1024 indicated as KB/MB (customary binary prefixes).
• In Linux, the directory listing tool (ls) has options for file size listings using SI decimal prefixes.
• Microsoft Windows reports file sizes and disk device capacities using the customary binary prefixes or, in a "Properties" dialog, using the exact value in bytes.
• Prior to the release of Mac OS X Snow Leopard, Apple's Mac OS X reported file sizes using the customary binary prefixes, but now uses SI prefixes.^[101][102]

Computer hardware

As of February 2010^[update], no examples of hardware marketed using IEC binary prefixes have been found. Even hardware types that use powers-of-1024 multipliers, such as memory, continue to be marketed with customary binary prefixes.

Computer memory

Measurements of most types of electronic memory such as RAM, ROM are given using customary binary prefixes (kilo, mega, and giga). This includes some Flash memory, like EEPROMs. For example, a "512 megabyte" memory module is 512×2²⁰ bytes (512×1048576, or 536870912).

JEDEC Solid State Technology Association, the semiconductor engineering standardization body of the Electronic Industries Alliance (EIA), continues to include the customary binary definitions of kilo, mega and giga in their Terms, Definitions, and Letter Symbols document,^[58] and uses those definitions in later memory standards^{[59][60][61][62][63]} (See also JEDEC memory standards.)

Many computer programming tasks reference memory in terms of powers of two because of the inherent binary design of current hardware addressing systems. For example, a 16-bit processor register can reference at most 65,536 items (bytes, words, or other objects); this is conveniently expressed as "64K" items. An operating system might map memory as 4096-byte pages, in which case exactly 8192 pages could be allocated within 33554432bytes of memory: 8K (8192) pages of 4 kilobytes (4096) each within 32 megabytes (32 MiB) of memory.

Hard disk drives

All hard disk drive manufacturers state capacity using SI prefixes.^{[defn. 1][103]}

Flash drives

USB Flash Drives, Flash-based memory cards like CompactFlash or Secure Digital, and flash based SSDs use SI prefixes.;^{[defn. 1]} for example, a "256 MB" flash card provides at least 256 million bytes (256000000), not 256×1024×1024 (268435456).^[34] These devices usually physically contain the binary capacities, but some space is reserved for internal functions of the flash drive. In other words, there are physically 256×1024×1024 bytes of storage on a typical "256MB" flash drive, but some space is needed for functions like wear leveling. In the case of a "256MB" flash drive, the manufacturer can allocate approximately 12MB to internal functions, and still provide 256 million usable bytes.

Floppy drives

Floppy disks have existed in numerous physical and logical formats, and have been sized inconsistently. In part, this is because the end user capacity of a particular disk is a function of the controller hardware, so that the same disk could be formatted to a variety of capacities. In many cases, the media are marketed without any indication of the end user capacity, as for example, DSDD, meaning double-sided double-density.

The last widely adopted diskette was the 3½ inch high density. This has a formatted capacity of 1474560 bytes or 1440 KB (1440×1024, using "KB" in the customary binary sense). These are marketed as "HD", or "1.44 MB" or both. This case defines a "third megabyte" of 1000×1024.

Most operating systems display the capacity using "MB" in the customary binary sense, resulting in a display of "1.4 MB" (1.40625 MB). Some users have noticed the missing 0.04 MB and both Apple and Microsoft have support bulletins referring to them as 1.4 MB.^[30]

The earlier 1200 KB (1200×1024) 5¼ inch diskette sold with the IBM PC AT was marketed as 1.2 MB (1.171875 MiB). The largest 8 inch diskette formats could contain more than a megabyte, and the capacities of those devices were often irregularly specified in megabytes, also without controversy.

Older and smaller diskette formats were usually identified as an accurate number of (binary) KB, for example the Apple Disk II described as 140KB had a 140×1024 byte capacity, and the original "360KB" double sided, double density disk drive used on the IBM PC had a 360×1024 byte capacity.

In many cases diskette hardware was marketed based on unformatted capacity, and the overhead required to format sectors on the media would reduce the nominal capacity as well (and this overhead typically varied based on the size of the formatted sectors), leading to more irregularities.

Optical discs

The capacities of most optical disc storage media like DVD, Blu-ray Disc, HD DVD and magneto-optical (MO) are given using SI decimal prefixes. A "4.7 GB" DVD has a nominal capacity of about 4.38 GiB.^[32] However, CD capacities are always given using customary binary prefixes. Thus a "700 MB" (or "80 minute") CD has a nominal capacity of about 700 MiB (approx 730 MB).^[31]

Tape drives and media

Tape drive and media manufacturers use SI decimal prefixes to identify capacity.^[104]

Data transmission and clock rates

Certain units are always used with SI decimal prefixes even in computing contexts. Two examples are hertz (Hz), which is used to measure the clock rates of electronic components, and bit/s, used to measure data transmission speed.

• A 1 GHz processor receives 1000000000 clock ticks per second
• A sound file sampled at 44.1 kHz has 44100 samples per second
• A 128 kbit/s MP3 stream consumes 128000bits (16 kilobytes, 15.6 KiB) per second
• A 1 Mbit/s Internet connection can transfer 1000000bits per second (125000 bytes per second ~= 122 KiB/s, assuming an 8-bit byte and no overhead)
• A 1 Gbit/s Ethernet connection can transfer 1000000000bits per second (125000000 bytes per second ~= 119 MiB/s, assuming an 8-bit byte and no overhead)
• A 56K modem transfers 56000 bits per second ~= 6.8 KiB/s.

Bus clock speeds and therefore bandwidths are both quoted using SI decimal prefixes.

• PC3200 memory on a double data rate bus, transferring 8 bytes per cycle with a clock speed of 200 MHz (200000000cycles per second) has a bandwidth of 200000000×8×2 = 3200000000bytes/second = 3.2 GB/s (about 3.0 GiB/s).
• A PCI-X bus at 66 MHz (66000000cycles per second), 64 bits per transfer, has a bandwidth of 66000000transfers/second×64bits/transfer = 4224000000bits/second, or 528000000bytes/second, usually quoted as 528 MB/s (about 503 MiB/s).

See also

• Integral data type
• Bit
• Nibble
• Byte
• Octet
• Orders of magnitude (data)
• Timeline of binary prefixes
• IEC 60027-2
• ISO/IEC 80000
• IEEE 1541
• IEEE 1541-2002

Definitions

References

Further reading

• "When is a kilobyte a kibibyte? And an MB an MiB?". International Electrotechnical Commission. 2007-02-12. http://www.iec.ch/zone/si/si_bytes.htm.  — An introduction to binary prefixes
• "Prefixes for binary multiples". NIST. http://physics.nist.gov/cuu/Units/binary.html. 
• NIST (1999-03-02). "Get Ready for the mebi, gibi and tebi". Press release. http://www.nist.gov/public_affairs/techbeat/tb9903.htm#Information%20Technology. 
• Markus Kuhn (1996-12-29). "What is a Megabyte ...?". http://www.cl.cam.ac.uk/~mgk25/information-units.txt. —a 1996–1999 paper on bits, bytes, prefixes and symbols
• Jonathan de Boyne Pollard. "There is no such thing as a 1.44 MB standard format floppy disc". Frequently Given Answers. http://homepage.ntlworld.com./jonathan.deboynepollard/FGA/1mb44-is-not-a-standard-floppy-disc-size.html. 
• Michael Quinion (1999-08-21). "Kibibyte". World Wide Words. http://www.quinion.com/words/turnsofphrase/tp-kib1.htm. —Another description of binary prefixes
• James Wiebe (2003-10-09) (PDF). When One Billion does not equal One Billion, or: Why your computer's disk drive capacity doesn’t appear to match the stated capacity. http://www.wiebetech.com/pressreleases/BillionEqualBillion.pdf. Retrieved 2010-01-22. —White-paper on the controversy over drive capacities

External links

• A plea for sanity
• A summary of the organizations, software, and so on that have implemented the new binary prefixes
• KiloBytes vs. kilobits vs. Kibibytes (Binary prefixes)
• SI/Binary Prefix Converter
• Storage Capacity Measurement Standards