Binary prefix - Stage One Wiki

In computing, a binary prefix is a set of letters that precede a unit of measure (such as a byte) to indicate multiplication by a power of two. In certain contexts in computing, such as computer memory sizes, units of information storage and communication traffic (Byte) have traditionally been reported in multiples of powers of two. The term binary prefix is intended to differentiate usage of certain symbolic abbreviations (for example, k or kilo) from the SI prefixes, which are always decimal (power of 10) multiples.<ref name="bipm">Template:Cite web</ref>

The first few binary multipliers, e.g., 1024 (2¹⁰), Template:Gaps (2²⁰), are close in value to SI prefixes, such as kilo (1000 = 10³) and mega (Template:Gaps = 10⁶), respectively. Therefore it became common practice amongst computer professionals to use these prefixes for the binary multiples – for example, to use the symbol M (mega) to mean Template:Gaps instead of Template:Gaps. However, when used with SI units and in some other contexts, these prefixes retain their decimal meanings. Certain disciplines of computing have always used these prefixes as decimal multipliers, for example, when specifying quantities of bits transmitted on a serial transmission medium. This has led to ambiguity in intended use of these prefixes.<ref name="NIST"/>

In 1999, following recommendations by the International Union of Pure and Applied Chemistry (IUPAC) in 1995<ref name="iupac">IUCr 1995 Report - IUCr IUPAC Interdivisional Committee on Nomenclature and Symbols (IDCNS)</ref> and National Institute of Standards and Technology (NIST), the standards organization known as the International Electrotechnical Commission (IEC) adopted a set of distinct prefixes (cf. IEC 60027), e.g., kibi (symbol Ki, from "kilobinary")<ref name="NIST"/> and mebi (symbol Mi, from "megabinary"), to indicate binary multipliers. The system used the multiplier 1024 (2¹⁰), rather than 1000 (10³) as in the SI system, to arrive at successively larger prefixes. Under this recommendation, the SI prefixes should only be used in the decimal sense: kilobyte and megabyte denote one thousand bytes and one million bytes respectively, while kibibyte and mebibyte denote 1024 bytes and Template:Gaps bytes respectively. This recommendation has since been adopted by some other leading national and international standards bodies, that now prescribe that the prefixes k, M and G should always refer to powers of ten, even in the context of information technology.<ref name="BIPM"/><ref name="NIST"/><ref name="IEEE1541"/><ref name="ieee260">Template:Cite book</ref> Notwithstanding the availability of the new binary prefixes and their unambiguous meaning, they have seen limited adoption in practice; the use of K (or k), M and G as binary multipliers when denoting the capacity of solid‑state memory like random access memory (RAM) remains a ubiquitous industry practice.<ref>Hewlett-Packard, Dell, Sony, Apple Inc., Toshiba, Gateway
Sun Microsystems, 4AllMemory.com</ref>

Contents 1 History 1.1 Early usage 1.2 Suggestions for new prefixes 2 Prefixes 2.1 SI prefix names in binary use 2.2 IEC standard prefixes 2.3 Errors between binary and decimal interpretations 3 Usage notes 3.1 Pronunciation 3.2 Files 3.3 Computer memory 3.4 Hard disk drives 3.5 Flash drives 3.6 Floppy drives 3.7 Optical discs 3.8 Buses 3.9 Software 4 Consumer confusion 5 Legal disputes 5.1 Willem Vroegh v. Eastman Kodak Company 5.2 Orin Safier v. Western Digital Corporation 6 See also 6.1 Specific units of IEC 60027-2 A.2 7 References 8 Further reading 9 External links 9.1 Converters

History

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Early usage

Early computers used one of two addressing methods to access the system memory; binary (base-2) or decimal (base-10). For instance, the IBM 701 (1952) used binary and could address 2,048 36-bit words, while the IBM 702 (1953) used decimal and could address 10,000 7-bit words.

By the mid 1960s, binary addressing had become the standard architecture in computer design. The computer system documentation would specify the memory size with an exact number such as 32768, 65536 or 131072 words of storage (all powers of 2). There were several methods used to abbreviate these quantities. The use of K in the binary sense as in a "32K core" can be found as early as 1959<ref name = "32K 1959">Template:Cite journal Note: the IBM 704 core memory units had 4096 36-bit words. Up to 32,768 words could be installed </ref><ref name = "32K 1960">Template:Cite journal "The 8K core stores were getting fairly common in this country in 1954. The 32K store started mass production in 1956; it is the standard now for large machines and at least 200 machines of the size (or its equivalent in the character addressable machines) are in existence today (and at least 100 were in existence in mid-1959)." Note: The IBM 1401 was a character addressable computer.</ref> Gene Amdahl's seminal 1964 article on IBM System/360 used 1K to mean 1024.<ref name="IBM360">Template:Cite journal Figure 1 gives storage (memory) capacity ranges of the various models in "Capacity 8 bit bytes, 1 K = 1024"</ref> This style was used by other computer vendors, the CDC 7600 System Description (1968) made extensive use of K as 1024.<ref name = "CDC7600">Template:Cite book</ref> Another style was to truncate the last 3 digits and append K. The exact values Template:Gaps, Template:Gaps and Template:Gaps would then become 32K, 65K and 131K.<ref name = "CDC6600">Template:Cite book</ref> (If Template:Gaps were instead rounded off, it would be 33K; if K = 1024 were used, 65,536 would become "64K".) 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 as 196K and Template:Gaps as 1 M,<ref name ="HP21MX">Template:Cite journal</ref> while the HP 3000 business computer (1973) could have 64K, 96K, or 128K bytes of memory.<ref name="HP3000"> Template:Citation</ref>

The terms Kbit, Kbyte, Mbit and Mbyte started to be used as binary units in the early 1970s.<ref name= "Mbyte1972"> Template:Cite journal</ref> Most memory capacities were 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."<ref name="IBM370">Template:Cite journal</ref> Megabyte was used to describe the 22-bit addressing of DEC PDP-11/70 (1975)<ref name="PDP11">Template:Cite journal</ref> and gigabyte the 30-bit addressing DEC VAX-11/780 (1977).

By the mid 1970s it was common to see K (e.g. Kbyte) meaning 1024 and the occasional M (e.g. Mbyte) as 1048576 for words or bytes of computer memory (RAM) while K and M were commonly used with their decimal meaning for disk storage. In the 1980s the term G (e.g. GB) with decimal meaning was commonly applied to disk storage while M in its binary meaning became common for computer memory. In the 1990s G in its binary meaning became common usage for computer memory. The first TB hard disk drive (terabyte, decimal meaning) was introduced in 2007.<ref>PC World - Hitachi Introduces 1-Terabyte Hard Drive</ref>

The dual use of these prefixes as both decimal and binary quantities was defined in standards and dictionaries. The 1986 ANSI/IEEE Std 1084-1986<ref name="IEEE1084"> Template:Cite book</ref> defined dual uses for kilo and mega. Template:Quote The binary units Kbyte and Mbyte were formally defined in ANSI/IEEE Std 1212-1991.<ref name = "IEEE1212"> Template:Cite book</ref> The terms 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 Template:Gaps or 2³⁰ bytes.<ref name = "IEEE610"> Template:Cite book</ref> Kilobyte, Kbyte, and KB are equivalent units and all are defined in the current standard, IEEE 100-2000.<ref name = "IEEE100">Template:Cite book "kB See kilobyte." "Kbyte Kilobyte. Indicates 2¹⁰ bytes." "Kilobyte Either 1000 or 2¹⁰ or 1024 bytes." The standard also defines megabyte and gigabyte. There is a note that an alternative notation for base-2 is under development.</ref>

The industry has coped with the dual definitions because system memory (RAM) typically uses the binary meaning while disk storage uses the decimal meaning. There are exceptions like diskettes and CDs. There are no SI units for computer storage capacity but the decimal prefix meanings of KB, MB, and GB are often referred to as SI prefixes.

Suggestions for new prefixes

While computer scientists typically used k to mean 1000, they recognized the convenience that would result from working with powers of 1024 and the confusion that resulted from using the same abbreviation for two definitions.<ref name="Morrison">Letters to the editor: Abbreviations for computer and memory sizes. Donald R. Morrison, Sandia Corp, Communications of the ACM, Volume 11, Issue 3 (March 1968) Page: 150 Template:DOI</ref> Several proposals for unique symbols were made in 1968. (At the time, memory size was small, and only K was in widespread use.) Donald Morrison proposed to use the Greek letter κ to denote 1024, κ² to denote 1024×1024, and so on.<ref name="Morrison"/> 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.<ref>Letters to the editor: proposed abbreviation for 1024: bK, Wallace Givens, Applied National Lab, Communications of the ACM archive, Volume 11, Issue 6 (June 1968), Page: 391 Template:DOI</ref> Bruce A. Martin further proposed that the units be abandoned altogether, and the letter B be used as a binary exponent, similar to E notation, to create shorthands like 3B20 for 3×2²⁰<ref>Letters to the editor: On binary notation, Bruce A. Martin, Associated Universities Inc., Communications of the ACM, Volume 11, Issue 10 (October 1968) Page: 658 Template:DOI</ref> None of these gained much acceptance, and capitalization of the letter K became the de facto standard for binary notation, though this could not be extended to higher powers. Later, as the discrepancy between the two systems increased, more proposals for unique units were made. In 1996, Markus Kuhn proposed a system of units with di prefixes, like the "dikilobyte" (K₂B or K2B).<ref>Standardized units for use in information technology, Markus Kuhn, 1996-12-29</ref>

The binary set of prefixes seem to have been first proposed<ref name="Knuth-webpage"/> by the IUPAC Interdivisional Committee on Nomenclature and Symbols 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".<ref name="iupac"/> The proposal was not accepted at the time.

The IEEE had begun to collaborate with the ISO and IEC to find acceptable names for binary prefixes. The IEC proposed "kibi", "mebi", "gibi" and "tebi", with the prefixes "Ki", "Mi", "Gi" and "Ti" respectively, in 1996.<ref name="iucr-96">1996 IUCr IUPAC Interdivisional Committee on Nomenclature and Symbols (IDCNS) report</ref> The IEEE decided that IEEE standards would use the prefixes "kilo" etc. with their metric definitions, allowing the base-two definitions to be used in an interim period as long as such usage was explicitly pointed out on a case-by-case basis.<ref name="ieee-standards">Bruce Barrow, "A Lesson in Megabytes," IEEE Standards Bearer, January 1997, page 5</ref>

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).<ref>"These prefixes for binary multiples, which were developed by IEC Technical Committee (TC) 25, Quantities and units, and their letter symbols, with the strong support of the International Committee for Weights and Measures (CIPM) and the Institute of Electrical and Electronics Engineers (IEEE), were adopted by the IEC as Amendment 2 to IEC International Standard IEC 60027-2: Letter symbols to be used in electrical technology - Part 2: Telecommunications and electronics."</ref><ref>IUCR 1999 report on IUPAC Interdivisional Committee on Nomenclature and Symbols</ref>

Proposals for alternative sets of prefixes have continued following the introduction of these prefixes as well. Donald Knuth, who uses decimal notation like 1 MB = 1000 kB,<ref name="Knuth">The Art of Computer Programming Volume 1, Donald Knuth, pp. 24 and 94</ref> has 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").<ref name="Knuth-webpage">Knuth: Recent News (1999)</ref><ref name="Knuth"/>

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Prefixes

IEC prefix		Representations				SI prefix names in binary use
Name	Symbol	Base 2	Base 1024	Value	Base 10	Name	Symbol
kibi	Ki	210	10241	Template:Gaps	~Template:Gaps	kilo	k, K
mebi	Mi	220	10242	Template:Gaps	~Template:Gaps	mega	M
gibi	Gi	230	10243	Template:Gaps	~Template:Gaps	giga	G
tebi	Ti	240	10244	Template:Gaps	~Template:Gaps	tera	T
pebi	Pi	250	10245	Template:Gaps	~Template:Gaps	peta	P
exbi	Ei	260	10246	Template:Gaps	~Template:Gaps	exa	E
zebi	Zi	270	10247	Template:Gaps	~Template:Gaps	zetta	Z
yobi	Yi	280	10248	Template:Gaps	~Template:Gaps	yotta	Y

SI prefix names in binary use

Quantities that are multiples of the unit by a power of 2 are indicated using similarly-valued SI prefixes, such as using kilo (the SI prefix for 1000) to indicate 2¹⁰=1024. Byte multiples using binary powers up to yottabyte are given by the on-line computing dictionary FOLDOC.<ref>Free on-line Dictionary of Computing</ref>

The one-letter symbols are identical to SI prefixes, except for "K", which is used interchangeably with "k" (in SI, only the lower-case "k" represents 1000).

These prefixes are in common use in contexts such as file and memory sizes. The names and values of the SI prefixes were defined in the 1960 SI standard, with powers-of-1000 values. Standard dictionaries do recognize the binary use of these prefixes.<ref name="webster">Template:Cite web</ref><ref name="metadict">Template:Cite web</ref> Oxford online dictionary defines, for example, megabyte as: "Computing a unit of information equal to one million or (strictly) Template:Gaps."<ref name="oxford">Template:Cite web</ref>

IEC standard prefixes

In January 1999, the International Electrotechnical Commission introduced in an addendum to IEC 60027-2 the prefixes kibi (kibibyte), mebi, gibi, etc., and the symbols Ki, Mi, Gi, etc. to specify binary multiples of a quantity and eliminate the ambiguity with their SI meanings.<ref name="NIST-biprefix">Template:Cite web</ref> The names for the new standard are derived from the original SI prefixes followed by "binary", such as "kilobinary", and can be shortened to a prefix like "kibi". The new standard also clarifies that, from the point of view of the IEC, the SI prefixes will remain to have their base-10 meaning and never have a base-2 meaning.

The second edition of the standard<ref>IEC 60027-2 (2000-11) Ed. 2.0</ref> defined them only up to exbi,<ref>Template:Cite journal</ref> but in 2005, the third edition added prefixes zebi and yobi, thus matching all SI prefixes with their binary counterparts.<ref>Template:Cite press release</ref>

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.<ref>Template:Cite web</ref> Nevertheless, Template:As of, the IEEE Publications division does not use the IEC prefixes in its major magazines such as Spectrum<ref name = " Spectrum 2008">Template:Cite journal "A lot can happen in a decade. You can hold the Nokia N800 in your hand, yet it’s a near-exact match for a high-end desktop PC from 10 years ago. It has a 320-megahertz processor, 128 megabytes of RAM, and a few gigabytes of available mass storage." </ref> or Computer.<ref name = "Computer June 2007">Template:Cite journal "The processor has a memory subsystem with separate first-level 32-Kbyte instruction and data caches, and a 512-Kbyte unified second-level cache." Authors are with IBM.</ref>

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. <ref>niso, New Specs and Standards</ref>

BIPM (the International Bureau of Weights and Measures which maintains SI) expressly prohibits the use of SI prefixes to denote powers of two, and recommends the use of the IEC prefixes as an alternative since computing units are not included in SI.<ref name="BIPM"> Template:Cite book </ref>. The binary definition of the prefixes k, M, G etc is not permitted by the United States National Institute of Standards and Technology (NIST).<ref name="sp330">Template:Cite book </ref>

Errors between binary and decimal interpretations

The relative difference between the values in the binary and decimal interpretations increases, when using the SI prefixes, from 2.4% for kilo to over 20% for the yotta prefix.

This makes differentiating between the two unit interpretations increasingly important as larger data storage and transmission technologies are developed.

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%

Example: 300 GB (300×10⁹ B) ≅ 300×0.9313 GiB ≅ 279.4 GiB

Usage notes

In this section, the phrase "decimal unit" is used to denote "SI designation understood in its standard, decimal, power-of-1000 sense" and "binary unit" means "SI designation understood in its binary, power-of-1024 sense." B is the symbol for bytes (as per computer-industry standard IEEE 1541 and IEC 60027), while both bit (as per ISO/IEC 80000) and b (as per IEEE 1541-2002) are used as the symbol for bits.

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 Template:Gaps 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 Template:Gaps (125 kB, approx 122 KiB) per second, assuming an 8-bit byte, and no overhead.<ref>Binary vs. Decimal Measurements</ref>

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."<ref name="NIST"/>

Files

Prior to the release of Mac OS (1984), file sizes were typically reported by the operating system in decimal digits without prefixes of any sort.Template:Fact Today, most operating systems are capable of reporting 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. Microsoft Windows reports file sizes in binary units but does not use IEC standard prefixes.

This chunk gives a history of the creation and filtering of a file. Each program that creates or modifies a file should leave a short description of what actions it took in the file history chunk. By convention this should consist of a string giving the complete command line for the program followed by optionaladditional comments in additional strings. A file should contain only one file history chunk and each filter should append its description after all the existing strings in the chunk. The file history chunk should be at the top level and preferably at the end of the file.

Computer memory

Image:Memory module DDRAM 20-03-2006.jpg

Measurements of most types of electronic memory such as RAM, 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.

JEDEC Solid State Technology Association, the semiconductor engineering standardization body of the Electronic Industries Alliance (EIA) in Standard 100B.01[6]<ref name="JEDEC">Template:Citation</ref> continues to include definitions in the binary sense K, M and G as prefixes to units of semiconductor memory (see JEDEC memory standards), noting that these definitions are "only included to reflect common usage" and noting that "IEEE/ASTM SI 10-1997 states 'This practice frequently leads to confusion and is deprecated.'" All standards published by JEDEC use the common usage, including end-user packaging recommendations for memory chips.

Many computer programming tasks naturally reference memory in terms of powers of two. For example, a 16-bit pointer can reference at most 65,536 items (bytes, words, or other objects), or an operating system might map memory in terms of 4096-byte pages, in which case exactly 8192 pages could be allocated within Template:Gaps of hardware memory. It is convenient to informally express these numbers, respectively, as 64K items, or as 8K pages of 4 Kbytes (KiB) each within 32 MBytes (MiB) of memory. A programmer can easily mentally calculate that "8K × 4K is 32 meg" and get it exactly right, within this powers-of-two context. This convenience is likely one source of originally adapting "kilo" and "mega" into shorthand for 1024 and 1048576 as jargon within a segment of the industry.

Hard disk drives

HDD manufacturers mostly 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 million 6 bit characters organized in 100 character sectors (i.e., blocks). This predates the SI system.
• In the 1960s most disk drives used IBM's variable block length format (called, Count Key Data or "CKD").<ref>IBM invented the disk drive in 1956 and until the late 1960s its drives and their clones were dominant. See, e.g. US vs. IBM antitrust litigation (Jan 1969), especially IBM analyses of Memorex and other disk drive companies.</ref> 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 (12.75×10⁶ B) and with the Xebec controller and 512 byte blocks it formatted to and was advertised as a 10.0 MB (10.0×10⁶ B) 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.

Template:As of, most, if not all, HDD manufacturers continue to use decimal prefixes to identify capacity.<ref> On 6 January 2007, a check of the websites of Fujitsu, HGST, Samsung, Seagate, Toshiba and Western Digital showed these companies (representing virtually all of the HDD industry by unit volume) specify capacity with the SI prefix definitions. </ref>

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, a "256 MB" card provides at least 256 million bytes (Template:Gaps), not 256×1024×1024 (Template:Gaps).<ref name="sd-cap-disclaimer">Template:Cite web</ref> Although the devices usually have at least the expected byte capacity, each manufacturer allocates different portions of the device's ultimate capacity for such things as wear levelling.

Floppy drives

Floppy disk drive and media manufacturers use decimal units for unformatted recording capacity while most computer operating systems use binary units to measure the formatted capacity. The original IBM Personal Computer (1981) used a Tandon TM100 5¼ inch floppy disk drive. The single sided drive was rated at 250 kilobytes (unformatted) and the double sided version was rated at 500 kilobytes.<ref>Template:Cite book</ref>

A 5¼ inch diskette recorded at double density (MFM) will hold 6,250 bytes per track and has 40 tracks per side, yielding 250,000 bytes per side. To make it practical to record smaller blocks of data, the tracks are formatted into sectors with gaps between them. The gaps allow individual sectors to be recorded without overwriting adjacent sectors. Each sector also has additional header bytes to identify the sector.

With IBM PC-DOS 1.0 and 1.1, each track has 8 sectors of 512 bytes and this provides 163,840 bytes per side (8 × 512 × 40). The IBM user documentation referred to this as "160KB" for single sided diskette and "320KB" for double sided diskette.<ref name="DOS 1.1">Template:Cite book Some software applications "used with DOS 1.10, will operate with either two 160KB drives or two 320KB drives. Both drives MUST be of the same type..." </ref> Starting with PC-DOS 2.0 (1983), each track had 9 sectors of 512 bytes. The formatted capacity was increased to 184,320 bytes per side or 368,640 bytes per diskette. The IBM documentation referred to these as "180KB" and "360KB" diskettes. The same drives and media can have different capacities depending on format.<ref name = "DOS 2.0">Template:Cite book "Beginning with DOS Version 2.00, DOS formats diskettes at 9 sectors per track, which increases capacity from 163,840 to 184,320 characters of information for single-sided diskettes and from 327,680 to 368,640 characters for dual-sided diskettes. The smaller capacity diskettes created by DOS Version 1.00 or DOS Version 1.10 (8 sectors per track) are also usable with DOS Version 2.00."</ref>

On all diskettes the capacity available to the user will be smaller that the total number of sectors because some are reserved by the operating system for boot records or directory tables.

The IBM Personal Computer/AT (1984) had a new 5¼ inch disk drive that had 80 tracks per side, rotated at 360 rpm (versus 300 rpm) and had a new diskette media. The formatted capacity was 1228800 bytes or 1200 KB. (80 tracks × 15 sectors × 512 bytes × 2 sides)

The IBM PC Convertible (1986) used the 3½ inch diskettes. These were similar in recording technology to the original 5¼ inch drives except they had 80 tracks per side. The formatted capacity was 737,280 bytes or 720 KB. Apple used the same disk with a different recording technology, GCR, that gave a formatted capacity of 819,200 bytes or 800 KB. Apple referred to this as an "800K" disk.<ref name="Apple 800K">Template:Cite web "This article gives the specifications for the 800K floppy disks and the 1.4MB floppy disks." 800K Disk has 1600 sectors and 1.4MB Disk has 2880 sectors. A sector is 512 bytes. </ref>

The last widely adopted diskette was the 3½ inch high density. This has twice the capacity as the 720 KB diskettes, 1474560 bytes or 1440 KB. The drive was marketed as 1.44 MB when a more accurate value would have been 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.<ref name="Apple 800K"/><ref name="Microsoft 121839"> Template:Cite web "The 1.44-megabyte (MB) value associated with the 3.5-inch disk format does not represent the actual size or free space of these disks. Although its size has been popularly called 1.44 MB, the correct size is actually 1.40 MB." </ref> The 1200 KB 5¼ inch diskette was marketed as 1.2 MB (1.171875 MiB) without any controversy.

Optical discs

CD capacities are always given in binary units. A "700 MB" (or "80 minute") CD has a nominal capacity of about 700 MiB (approx 730 MB).<ref>Data capacity of CDs</ref> However, the capacities of other optical disc storage media like DVD, Blu-ray Disc, HD DVD are given in decimal units. A "4.7 GB" DVD has a nominal capacity of about 4.38 GiB.<ref>Understanding Recordable and Rewritable DVD</ref>

Buses

Bus clock speeds and therefore bandwidths are both given in decimal units. For example, "PC3200" memory on a double pumped bus, transferring 8 bytes per cycle running with a clock speed of 200 MHz = 200,000,000 cycles per second has a bandwidth of 200,000,000 × 2 × 8 = 3,200,000,000 B/s = 3.2 GB/s (about 2.98 GiB/s).

A bus may be defined as an electronic pathway that is used to transfer information. It carries the information from one part of the computer to another. There are normally a few different buses inside a CPU. The size of the bus determines how much information can be transferred at any one time.

Software

Template:As of, most software does not distinguish symbols for binary and decimal units. The IEC binary naming convention has been adopted by some, but is not used universally.

The binary convention is supported by standardization bodies and technical organizations such as IEEE, CIPM, NIST, and SAE.<ref name="BIPM"/><ref name="NIST"> Prefixes for Binary Multiples — The NIST Reference on Constants, Units, and Uncertainty </ref><ref name="IEEE1541"> Template:Cite paper </ref><ref name="SAE"> Rules for SAE Use of SI (Metric) Units — Section C.1.12 — SI prefixes </ref> 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.<ref name="EUHD">HD 60027-2:2003 Information about the harmonization document (obtainable on order)</ref> This document will be adopted as a European standard.<ref>prEN 60027-2:2006 Information about the EN standardization process</ref>

Examples of software that use IEC standard prefixes (along with standard SI prefixes) include:

Template:Col-begin Template:Col-3

• The Linux kernel<ref>Template:Cite web</ref><ref>ESR post on LKML</ref>
• GNU Core Utilities<ref>Template:Cite web</ref>
• Flyspray<ref>Flyspray</ref>
• bugs.mysql.com<ref>bugs.mysql.com</ref>
• GParted<ref>Template:Cite web</ref>
• DFSee<ref>DFSee</ref>
• disktype<ref>disktype</ref>

Template:Col-3

• raidutil<ref>Mac OS X Manual Page For raidutil(8)</ref>
• FreeDOS-32<ref>FreeDOS-32 - Standards Compliance</ref>
• ifconfig<ref>Template:Cite web</ref>
• GNOME Network<ref>GNOME Network</ref>
• SLIB<ref>SLIB</ref>
• Cygwin/X<ref>Cygwin/XFree86</ref>
• HTTrack<ref>Re: minor typo - HTTrack Website Copier Forum</ref>

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• Pidgin (IM client)<ref>http://developer.pidgin.im/ticket/1684 Developer discussion</ref>
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• yafc<ref>SourceForge.net: Files</ref>
• tnftp<ref>archive.netbsd.se</ref>
• WinSCP<ref>WinSCP :: Recent Version History</ref>

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One of the stated goals of the introduction of the binary prefixes was "to preserve the SI prefixes as unambiguous decimal multipliers."<ref name="IEEE1541"/> 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"

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, e.g., the 1968 IBM stated System 360 "Model 91s can accommodate up to 6 291 496 bytes of main storage."<ref>System/360 Model 91</ref>

Hard disk drive manufacturers used MB, i.e. 10⁶ bytes, to characterize their products as early as 1974.<ref>The Product Line Card unambiguously uses MB to characterize HDD capacity in millions of bytes</ref> 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.<ref>1977 Disk/Trend Report - Rigid Disk Drives, published June 1977</ref>

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), the Windows XP disk manager (149.05 GB), and the drive properties display (152625 MB). Consumers are often confused by the differences in the reported values.

This disk drive can hold 160×109 bytes, and is marketed using standard SI prefixes."

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

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

Legal disputes

There have been two significant class action lawsuits against digital storage manufactures. One case involved flash memory and the other involved hard disk drives. Both were settled with the manufactures agreeing to clarify the storage capacity of their products on the consumer packaging.

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 non-standard binary values 2²⁰ for megabyte and 2³⁰ 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.<ref name="Vreogh-3rd">Template:Cite web</ref>

The manufacturers agreed to clarify the flash memory card capacity on the packaging and web sites.<ref>http://www.sandisk.com/Assets/Categories/Products/sd_capacitydisclaimer.pdf</ref> The consumers could apply for "a discount of ten percent off a future online purchase from Defendants' Online Stores Flash Memory Device".<ref name="FMsettle-faq">Template:Cite web</ref>

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.<ref name="wdc-safier-complaint">Template:Cite web</ref>

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.<ref name="wdc-safier-settle">Template:Cite web</ref>

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.<ref name="betanews">News article</ref>

Western Digital had this footnote in their settlement. "Apparently, Plaintiff believes that he could sue an egg company for fraud for labeling a carton of 12 eggs a "dozen," because some bakers would view a "dozen" as including 13 items."<ref name="Baskin-2006-02-01">Template:Cite web</ref>

The settlement called for Western Digital to add a disclaimer;<ref name="betanews"/> flash memory and hard disk manufacturers have disclaimers on their packaging and web sites clarifying the formatted capacity of the flash memory<ref name="sd-cap-disclaimer"/> or defining MB as 1 million bytes and 1 GB as 1 billion bytes.<ref name="wdc-CaviarSE16">Template:Cite web</ref>

See also

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

Specific units of IEC 60027-2 A.2

These units have individual articles:

Template:Bitrates

Template:Quantities of bytes

Template:Quantities of bits

References

Template:Reflist

Further reading

• Template:Cite web — An introduction to binary prefixes
• Template:Cite web
• Template:Cite press release
• Template:Cite web—a 1996–1999 paper on bits, bytes, prefixes and symbols
• Template:Cite web
• Template:Cite web—Another description of binary prefixes
• Template:Cite paper—White-paper on the controversy over drive capacities

External links

• 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)
• Storage Capacity Measurement Standards

Converters

• SI/Binary Prefix Converter
• Decimal-to-Binary Prefixes and Binary-to-Decimal Prefixes Converter
• Tool to convert to/from the binary and standard units (up to yobibytes)ar:رسيس بيناري

be-x-old:Двайковыя прыстаўкі bg:Двоична представка cs:Binární předpona da:Binært præfiks de:Binärpräfix es:Prefijo binario fr:Préfixe binaire gl:Prefixo binario ko:이진 접두어 ia:Prefixos pro multiplos binari it:Prefissi per multipli binari hu:Bináris prefixum ms:Awalan perduaan nl:Veelvouden van bytes ja:2進接頭辞 no:Binærprefiks pl:Przedrostek dwójkowy pt:Prefixo binário ro:Prefixe binare ru:Двоичные приставки sk:Binárny prefix sr:Јобибит uk:Двійкові префікси vi:Tiền tố nhị phân zh:二进制乘数词头

This page was last modified 20:58, 17 January 2010.

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