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                                 Binary prefix

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   This article is about unit prefixes, notably prefixes of units of digital
   information like bit and byte. For the syntactical elements used to
   declare the radix of a given integer literal in program code, see Integer
   literal § Affixes.
   Link: mw-deduplicated-inline-style
   For guidelines on using binary prefixes on Wikipedia, see Wikipedia:Manual
   of Style/Dates and numbers § Quantities of bytes and bits.

               Prefixes for multiples of bits (bit) or bytes (B)
   Decimal        Binary                
   Value  SI      Value  IEC     Legacy 
   1000   k kilo  1024   Ki kibi K kilo 
   1000^2 M mega  1024^2 Mi mebi M mega 
   1000^3 G giga  1024^3 Gi gibi G giga 
   1000^4 T tera  1024^4 Ti tebi T tera 
   1000^5 P peta  1024^5 Pi pebi –      
   1000^6 E exa   1024^6 Ei exbi –      
   1000^7 Z zetta 1024^7 Zi zebi –      
   1000^8 Y yotta 1024^8 Yi yobi –      
     * v          
     * t          
     * e          

   A binary prefix is a unit prefix for multiples of units in data
   processing, data transmission, and digital information, principally in
   association with the bit and the byte, to indicate multiplication by a
   power of 2. As shown in the table to the right there are two sets of
   symbols for binary prefixes, one set established by International
   Electrotechnical Commission (IEC) and several other standards and trade
   organizations using two letter symbols, e.g. Mi indicating 1,048,576 with
   a second set established by semiconductor industry convention using one
   letter symbols, e.g., M also indicating 1,048,576.

   In most contexts, industry uses the multipliers kilo (k), mega (M), giga
   (G), etc., in a manner consistent with their meaning in the International
   System of Units (SI), namely as powers of 1000. For example, a
   500-gigabyte hard disk holds 500000000000 bytes, and a 1 Gbit/s (gigabit
   per second) Ethernet connection transfers data at nominal speed of
   1000000000 bit/s. In contrast with the binary prefix usage, this use is
   described as a decimal prefix, as 1000 is a power of 10 (10^3).

   The computer industry has historically in citations of main memory (RAM)
   capacity used the units kilobyte, megabyte, and gigabyte, and the
   corresponding symbols KB, MB, and GB, in a binary sense: gigabyte
   customarily means 1073741824 bytes. As this is a power of 1024, and 1024
   is a power of two (2^10), this usage is referred to as a binary
   measurement.

   The use of the same unit prefixes with two different meanings has caused
   confusion. Starting around 1998, the IEC and several other standards and
   trade organizations attempted to address the ambiguity by publishing
   standards and recommendations for a set of binary prefixes that refer
   exclusively to powers of 1024. Accordingly, the US National Institute of
   Standards and Technology (NIST) requires that SI prefixes be used only in
   the decimal sense:^[1] kilobyte and megabyte denote one thousand bytes and
   one million bytes respectively (consistent with SI), while new terms such
   as kibibyte, mebibyte, and gibibyte, having the symbols KiB, MiB, and GiB,
   denote 1024 bytes, 1048576 bytes, and 1073741824 bytes, respectively.^[2]
   In 2008, the IEC prefixes were incorporated into the International System
   of Quantities alongside the decimal prefixes of the international standard
   system of units (see ISO/IEC 80000).

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 Early cases
               * 2.3.2 Willem Vroegh v. Eastman Kodak Company
               * 2.3.3 Orin Safier v. Western Digital Corporation
               * 2.3.4 Cho v. Seagate Technology (US) Holdings, Inc.
               * 2.3.5 Dinan et al. v. SanDisk LLC
     * 3 Unique binary prefixes
          * 3.1 Early suggestions
          * 3.2 IEC prefixes
          * 3.3 Adoption by IEC, NIST and ISO
          * 3.4 Other standards bodies and organizations
     * 4 Current practice
          * 4.1 Operating systems
          * 4.2 Software
          * 4.3 Computer hardware
               * 4.3.1 Computer memory
               * 4.3.2 Hard disk drives
               * 4.3.3 Flash drives
               * 4.3.4 Floppy drives
               * 4.3.5 Optical discs
               * 4.3.6 Tape drives and media
               * 4.3.7 Data transmission and clock rates
          * 4.4 Use by industry
     * 5 See also
     * 6 Definitions
     * 7 References
     * 8 Further reading
     * 9 External links

HistoryEdit

   Link: mw-deduplicated-inline-style
   See also: Timeline of binary prefixes

  Main memoryEdit

   Early computers used one of two addressing methods to access the system
   memory; binary (base 2) or decimal (base 10).^[3] For example, the IBM 701
   (1952) used binary and could address 2048 words of 36 bits each, while the
   IBM 702 (1953) used decimal and could address ten thousand 7-bit words.

   By the mid-1960s, binary addressing had become the standard architecture
   in most computer designs, 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 two, and furthermore are small multiples of 2^10, 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
   originally adopted from the metric system. The prefixes kilo- and mega-,
   meaning 1000 and 1000000 respectively, were commonly used in the
   electronics industry before World War II.^[4] Along with giga- or G-,
   meaning 1000000000, they are now known as SI prefixes^[defn. 1] after the
   International System of Units (SI), introduced in 1960 to formalize
   aspects of the metric system.

   The International System of Units does not define units 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 is manufactured in sizes that
   were easily expressed as multiples of 1024, kilobyte, when applied to
   computer memory, came to be used to mean 1024 bytes instead of 1000. This
   usage is not consistent with the SI. Compliance with the SI requires that
   the prefixes take their 1000-based meaning, and that they are not to be
   used as placeholders for other numbers, like 1024.^[5]

   The use of K in the binary sense as in a "32K core" meaning 32 × 1024
   words, i.e., 32768 words, 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 three digits and append K,
   essentially using K as a decimal prefix^[defn. 3] similar to SI, but
   always truncating to the next lower whole number instead of rounding to
   the nearest. The exact values 32768 words, 65536 words and 131072 words
   would then be described as "32K", "65K" and "131K".^[10] (If these values
   had been rounded to nearest 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. (For
   memory sizes of "41K" and below, there is no difference between the two
   styles.) 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, and use of the lowercase k did
   persist.^[13]^[14]^[15] Nevertheless, the practice of using the
   SI-inspired "kilo" to indicate 1024 was later extended to "megabyte"
   meaning 1024^2 (1048576) bytes, and later "gigabyte" for 1024^3
   (1073741824) bytes. For example, a "512 megabyte" RAM module is 512×1024^2
   bytes (512 × 1048576, or 536870912), rather than 512000000.

   The symbols 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.^[16] 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."^[17]

   Megabyte was used to describe the 22-bit addressing of DEC PDP-11/70
   (1975)^[18] and gigabyte the 30-bit addressing DEC VAX-11/780 (1977).

   In 1998, the International Electrotechnical Commission IEC introduced the
   binary prefixes kibi, mebi, gibi ... to mean 1024, 1024^2, 1024^3 etc., so
   that 1048576 bytes could be referred to unambiguously as 1 mebibyte. The
   IEC prefixes were defined for use alongside the International System of
   Quantities (ISQ) in 2009.

  Disk drivesEdit

   The disk drive industry has followed a different pattern. Disk drive
   capacity is generally specified with unit prefixes with decimal meaning,
   in accordance to SI practices. Unlike computer main memory, disk
   architecture or construction does not mandate or make it convenient to use
   binary multiples. Drives can have any practical number of platters or
   surfaces, and the count of tracks, as well as the count of sectors per
   track may vary greatly between designs.

   The first commercially sold disk drive, the IBM 350, had fifty physical
   disk platters containing a total of 50,000 sectors of 100 characters each,
   for a total quoted capacity of 5 million characters.^[19] It was
   introduced in September 1956.

   In the 1960s most disk drives used IBM's variable block length format,
   called Count Key Data (CKD).^[20] 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 80- and 96-character 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.

   Floppy disks for the IBM PC and compatibles quickly standardized on
   512-byte sectors, so two sectors were easily referred to as "1K". The
   3.5-inch "360 KB" and "720 KB" had 720 (single-sided) and 1440 sectors
   (double-sided) respectively. When the High Density "1.44 MB" floppies came
   along, with 2880 of these 512-byte sectors, that terminology represented a
   hybrid binary-decimal definition of "1 MB" = 2^10 × 10^3 = 1 024 000
   bytes.

   In contrast, hard disk drive manufacturers used megabytes or MB, meaning
   10^6 bytes, to characterize their products as early as 1974.^[21] 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.^[22]

   One of the earliest hard disk drives in personal computing history, the
   Seagate ST-412, was specified as Formatted: 10.0 Megabytes.^[23] The drive
   contains four heads and active surfaces (tracks per cylinder), 306
   cylinders. When formatted with a sector size of 256 bytes and 32
   sectors/track it has a capacity of 10027008 bytes. This drive was one of
   several types installed in the IBM PC/XT^[24] and extensively advertised
   and reported as a "10 MB" (formatted) hard disk drive.^[25] The cylinder
   count of 306 is not conveniently close to any power of 1024; operating
   systems and programs using the customary binary prefixes show this as
   9.5625 MB. Many later drives in the personal computer market used 17
   sectors per track; still later, zone bit recording was introduced, causing
   the number of sectors per track to vary from the outer track to the inner.

   The hard drive industry continues to use decimal prefixes for drive
   capacity, as well as for transfer rate. For example, a "300 GB" hard drive
   offers slightly more than 300×10^9, or 300000000000, bytes, not 300 × 2^30
   (which would be about 322×10^9). 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 × 1024^3 bytes, or 279.4 × 1073741824 B). On the other hand, macOS
   has since version 10.6 shown hard drive size using decimal prefixes (thus
   matching the drive makers' packaging). (Previous versions of Mac OS X used
   binary prefixes.)

   Disk drive manufacturers sometimes use both IEC and SI prefixes with their
   standardized meanings. Seagate has specified data transfer rates in select
   manuals of some hard drives with both units, with the conversion between
   units clearly shown and the numeric values adjusted accordingly.^[26]
   "Advanced Format" drives uses the term "4K sectors", which it defines as
   having size of "4096 (4K) bytes".^[27]

  Information transfer and clock ratesEdit

   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 decimal prefixes:

     * The ATA-100 disk interface refers to 100000000 bytes per second
     * A "56K" modem refers to 56000 bits per second
     * SATA-2 has a raw bit rate of 3 Gbit/s = 3000000000 bits per second
     * PC2-6400 RAM transfers 6400000000 bytes per second
     * Firewire 800 has a raw rate of 800000000 bits per second
     * In 2011, Seagate specified the sustained transfer rate of some hard
       disk drive models with both decimal and IEC binary prefixes.^[26]

  Standardization of dual definitionsEdit

   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.^[28]

   The dual usage of the kilo (K), mega (M), and giga (G) prefixes as both
   powers of 1000 and powers of 1024 has been recorded in standards and
   dictionaries. For example, the 1986 ANSI/IEEE Std 1084-1986^[29] 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 2^10, or 1024.

     mega (M). (1) A prefix indicating one million. (2) In statements
     involving size of computer storage, a prefix indicating 2^20, or
     1048576.

   The binary units Kbyte and Mbyte were formally defined in ANSI/IEEE Std
   1212-1991.^[30]

   Many dictionaries have noted the practice of using customary prefixes to
   indicate binary multiples.^[31]^[32] Oxford online dictionary defines, for
   example, megabyte as: "Computing: a unit of information equal to one
   million or (strictly) 1048576 bytes."^[33]

   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 2^30 bytes.^[34] Kilobyte, Kbyte, and KB are equivalent
   units and all are defined in the obsolete standard, IEEE 100–2000.^[35]

   The hardware industry measures system memory (RAM) using the binary
   meaning while magnetic disk storage uses the SI definition. However, many
   exceptions exist. Labeling of one type of diskette uses the megabyte to
   denote 1024×1000 bytes.^[36] In the optical disks market, compact discs
   use MB to mean 1024^2 bytes while DVDs use GB to mean 1000^3
   bytes.^[37]^[38]

Inconsistent use of unitsEdit

  Deviation between powers of 1024 and powers of 1000Edit

   Link: mw-deduplicated-inline-style
   See also: Orders of magnitude (data)

   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 nearly 21%
   for the yotta prefix.

   [IMG] 
   Enlarge
   Linear-log graph of percentage of the difference between decimal and
   binary interpretations of the unit prefixes versus the storage size.

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

  Consumer confusionEdit

   In the early days of computers (roughly, prior to the advent of personal
   computers) there was little or no consumer confusion because of the
   technical sophistication of the buyers and their familiarity with the
   products. In addition, it was common for computer manufacturers to specify
   their products with capacities in full precision.^[39]

   In the personal computing era, 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. Hard drives
   are specified and sold using "GB" and "TB" in their decimal meaning: one
   billion and one trillion bytes. Many operating systems and other software,
   however, display hard drive and file sizes using "MB", "GB" or other
   SI-looking prefixes in their binary sense, just as they do for displays of
   RAM capacity. For example, many such systems display a hard drive marketed
   as "1 TB" as "931 GB". The earliest known presentation of hard disk drive
   capacity by an operating system using "KB" or "MB" in a binary sense is
   1984;^[40] earlier operating systems generally presented the hard disk
   drive capacity as an exact number of bytes, with no prefix of any sort,
   for example, in the output of the MS-DOS or PC DOS CHKDSK command.

  Legal disputesEdit

   The different interpretations of disk size prefixes has led to class
   action lawsuits against digital storage manufacturers. These cases
   involved both flash memory and hard disk drives.

    Early casesEdit

   Early cases (2004–2007) were settled prior to any court ruling with the
   manufacturers admitting no wrongdoing but agreeing to clarify the storage
   capacity of their products on the consumer packaging. Accordingly, many
   flash memory and hard disk manufacturers have disclosures on their
   packaging and web sites clarifying the formatted capacity of the devices
   or defining MB as 1 million bytes and 1 GB as 1 billion
   bytes.^[41]^[42]^[43]^[44]

    Willem Vroegh v. Eastman Kodak CompanyEdit

   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 customary values of 1024^2 for megabyte
   and 1024^3 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.^[45]

   The parties agreed that manufacturers could continue to use the decimal
   definition so long as the definition was added to the packaging and web
   sites.^[46] The consumers could apply for "a discount of ten percent off a
   future online purchase from Defendants' Online Stores Flash Memory
   Device".^[47]

    Orin Safier v. Western Digital CorporationEdit

   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.^[48]

   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.^[49]

   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.^[50]^[51]^[52]

    Cho v. Seagate Technology (US) Holdings, Inc.Edit

   A lawsuit (Cho v. Seagate Technology (US) Holdings, Inc., San Francisco
   Superior Court, Case No. CGC-06-453195) was filed against Seagate
   Technology, alleging that Seagate overrepresented the amount of usable
   storage by 7% on hard drives sold between 22 March 2001 and 26 September
   2007. The case was settled without Seagate admitting wrongdoing, but
   agreeing to supply those purchasers with free backup software or a 5%
   refund on the cost of the drives.^[53]

    Dinan et al. v. SanDisk LLCEdit

   On 22 January 2020, the district court of the Northern District of
   California ruled in favor of the defendant, SanDisk, upholding its use of
   "GB" to mean 1000000000 bytes.^[54]

Unique binary prefixesEdit

  Early suggestionsEdit

   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,
   κ^2 to denote 1024^2, and so on.^[55] (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 bK^2 for 1024^2,
   though he noted that neither the Greek letter nor lowercase letter b would
   be easy to reproduce on computer printers of the day.^[56] Bruce Alan
   Martin of Brookhaven National Laboratory further proposed that the
   prefixes be abandoned altogether, and the letter B be used for base-2
   exponents, similar to E in decimal scientific notation, to create
   shorthands like 3B20 for 3×2^20,^[57] a convention still used on some
   calculators to present binary floating point-numbers today.^[58]

   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" (K_2B or
   K2B).^[59] Donald Knuth, who uses decimal notation like 1 MB =
   1000 kB,^[60] proposed that the powers of 1024 be designated as "large
   kilobytes" and "large megabytes", with abbreviations KKB and MMB.^[61]
   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.

  IEC prefixesEdit

   Link: mw-deduplicated-inline-style
   "Gibi" redirects here. For other uses, see Gibi (disambiguation).

   The set of binary prefixes that were eventually adopted, now referred to
   as the "IEC prefixes",^[defn. 4] 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 10^3 bytes and 10^6
   bytes, respectively. The new prefixes kibi (kilobinary), mebi
   (megabinary), gibi (gigabinary) and tebi (terabinary) were also proposed
   at the time, and the proposed symbols for the prefixes were kb, Mb, Gb and
   Tb respectively, rather than Ki, Mi, Gi and Ti.^[62] The proposal was not
   accepted at the time.

   The Institute of Electrical and Electronics Engineers (IEEE) began to
   collaborate with the International Organization for Standardization (ISO)
   and International Electrotechnical Commission (IEC) to find acceptable
   names for binary prefixes. IEC proposed kibi, mebi, gibi and tebi, with
   the symbols Ki, Mi, Gi and Ti respectively, in 1996.^[63]

   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 that "k" is capitalised to "K".

   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.^[64]

  Adoption by IEC, NIST and ISOEdit

   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).^[65]^[66]

   The IEC 60027-2 Amendment 2 also states that the IEC position is the same
   as that of BIPM (the body that regulates 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 "466 GiB", while 536870912 bytes of RAM would
   be displayed as "512 MiB".

   The second edition of the standard, published in 2000,^[67] defined them
   only up to exbi,^[68] but in 2005, the third edition added prefixes zebi
   and yobi, thus matching all SI prefixes with binary counterparts.^[69]

   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.^[70] In 2009, the prefixes kibi-, mebi-,
   etc. were defined by ISO 80000-1 in their own right, independently of the
   kibibyte, mebibyte, and so on.

   The BIPM standard JCGM 200:2012 "International vocabulary of metrology –
   Basic and general concepts and associated terms (VIM), 3rd edition" lists
   the IEC binary prefixes and states "SI prefixes refer strictly to powers
   of 10, and should not be used for powers of 2. For example, 1 kilobit
   should not be used to represent 1024 bits (2^10 bits), which is 1
   kibibit."^[71]

          Specific units of IEC 60027-2 A.2 and ISO/IEC 80000:13-2008
   IEC prefix  Representations
   Name Symbol Base 2 Base 1024 Value                     Base 10       
   kibi Ki     2^10   1024^1                         1024 = 1.024×10^3  
   mebi Mi     2^20   1024^2                      1048576 ≈ 1.049×10^6  
   gibi Gi     2^30   1024^3                   1073741824 ≈ 1.074×10^9  
   tebi Ti     2^40   1024^4                1099511627776 ≈ 1.100×10^12 
   pebi Pi     2^50   1024^5             1125899906842624 ≈ 1.126×10^15 
   exbi Ei     2^60   1024^6          1152921504606846976 ≈ 1.153×10^18 
   zebi Zi     2^70   1024^7       1180591620717411303424 ≈ 1.181×10^21 
   yobi Yi     2^80   1024^8    1208925819614629174706176 ≈ 1.209×10^24 

  Other standards bodies and organizationsEdit

   The IEC standard 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.^[2] NIST has stated the SI prefixes
   "refer strictly to powers of 10" and that the binary definitions "should
   not be used" for them.^[72]

   The microelectronics industry standards body JEDEC describes the IEC
   prefixes in its online dictionary with a note: "The definitions of kilo,
   giga, and mega based on powers of two are included only to reflect common
   usage."^[73] The JEDEC standards for semiconductor memory use the
   customary prefix symbols K, M and G in the binary sense.^[74]

   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.^[75]^[76] However, as of
   April 2008, the IEEE Publications division does not require the use of IEC
   prefixes in its major magazines such as Spectrum^[77] or Computer.^[78]

   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.^[79]^[80]

   The Society of Automotive Engineers (SAE) 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.^[81]

   The European Committee for Electrotechnical Standardization (CENELEC)
   adopted the IEC-recommended binary prefixes via the harmonization document
   HD 60027-2:2003-03.^[82] The European Union (EU) has required the use of
   the IEC binary prefixes since 2007.^[83]

Current practiceEdit

   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.

   Capacities of main memory and cache memory are usually expressed with
   customary binary prefixes^[defn. 5]^[84]^[85]^[86] On the other hand,
   flash memory, like that found in solid state drives, mostly uses SI
   prefixes^[defn. 1] to state capacity.

   Some 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.

   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.

  Operating systemsEdit

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

     * The Linux kernel uses standards-compliant decimal and binary prefixes
       when booting up.^[87]^[88] However, many Unix-like system utilities,
       such as the ls command, use powers of 1024 indicated as K/M (customary
       binary prefixes) if called with the "-h" option. They give the exact
       value in bytes otherwise. The GNU versions will also use powers of 10
       indicated with k/M if called with the "
       Link: mw-deduplicated-inline-style
       --si" option.
          * The Ubuntu Linux distribution uses the IEC prefixes for base-2
            numbers as of the 10.10 release.^[89]^[90]
     * 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.
     * iOS 10 and earlier, Mac OS X Leopard and earlier and watchOS use the
       binary system (1 GB = 1073741824 bytes). Apple product specifications,
       iOS and macOS (including Mac OS X Snow Leopard: version 10.6) now
       report sizes using SI decimal prefixes (1 GB = 1000000000
       bytes).^[91]^[92]

  SoftwareEdit

   As of February 2010, most software did not distinguish symbols for binary
   and decimal prefixes.^[defn. 3] The IEC binary naming convention is not
   yet used universally.

   One of the stated goals of the introduction of the IEC prefixes was "to
   preserve the SI prefixes as unambiguous decimal multipliers."^[75]
   Programs such as fdisk/cfdisk, parted, and apt-get use SI prefixes with
   their decimal meaning.

     * [IMG] 

       GNOME's partition editor uses IEC prefixes to display partition sizes.
       The total capacity of the 120×10^9-byte disk is displayed as
       "111.79 GiB"

     * [IMG] 

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

     * [IMG] 

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

     * [IMG] 

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

   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 [...]
           RX packets:254804 errors:0 dropped:0 overruns:0 frame:0
           TX packets:756 errors:0 dropped:0 overruns:0 carrier:0
           [...]
           RX bytes:18613795 (17.7 MiB)  TX bytes:45708 (44.6 KiB)

   Software that uses IEC binary prefixes for powers of 1024 and uses
   standard SI prefixes for powers of 1000 includes:

     * GNU Core Utilities^[93]
     * GParted^[94]
     * FreeDOS-32^[95]
     * ifconfig^[96]
     * GNOME Network^[97]
     * SLIB^[98]
     * Cygwin/X^[99]
     * HTTrack^[100]
     * Pidgin (IM client)^[101]
     * Deluge^[102]
     * yafc^[103]
     * tnftp^[104]
     * WinSCP^[105]
     * MediaInfo^[106]

   Software that uses standard SI prefixes for powers of 1000, but not IEC
   binary prefixes for powers of 1024, includes:

     * Mac OS X v10.6 and later for hard drive and file sizes^[107]^[108]

   Software that supports decimal prefixes for powers of 1000 and binary
   prefixes for powers of 1024 (but does not follow SI or IEC nomenclature
   for this) includes:

     * 4DOS (uses lowercase letters as decimal and uppercase letters as
       binary prefixes)^[109]^[110]

  Computer hardwareEdit

   Hardware types that use powers-of-1024 multipliers, such as memory,
   continue to be marketed with customary binary prefixes.

    Computer memoryEdit

   [IMG] 
   Enlarge
   The 536870912 byte (512×2^20) capacity of these RAM modules is stated as
   "512 MB" on the label.

   Measurements of most types of electronic memory such as RAM and 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 512×2^20 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,^[111] and
   uses those definitions in later memory
   standards^[112]^[113]^[114]^[115]^[116] (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 33554432 bytes of memory: "8K" (8192) pages of "4 kilobytes" (4096
   bytes) each within "32 megabytes" (32 MiB) of memory.

    Hard disk drivesEdit

   All hard disk drive manufacturers state capacity using SI prefixes.^[defn.
   1]^[117]^[118]^[119]^[120]^[121]

    Flash drivesEdit

   USB flash drives, flash-based memory cards like CompactFlash or Secure
   Digital, and flash-based solid-state drives (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).^[44] The flash memory chips
   inside these devices contain considerably more than the quoted capacities,
   but much like a traditional hard drive, some space is reserved for
   internal functions of the flash drive. These include wear leveling, error
   correction, sparing, and metadata needed by the device's internal
   firmware.

    Floppy drivesEdit

   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 usage creates a third definition of "megabyte" as 1000×1024
   bytes.

   Most operating systems display the capacity using "MB" in the customary
   binary sense, resulting in a display of "1.4 MB" (1.40625 MiB). Some users
   have noticed the missing 0.04 MB and both Apple and Microsoft have support
   bulletins referring to them as 1.4 MB.^[36]

   The earlier "1200 KB" (1200×1024 bytes) 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 discsEdit

   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.^[38] 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
   (approximately 730 MB).^[37]

    Tape drives and mediaEdit

   Tape drive and media manufacturers use SI decimal prefixes to identify
   capacity.^[122]^[123]

    Data transmission and clock ratesEdit

   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 to bit/s and B/s, which are 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 128000 bits (16 kilobytes, 15.6 KiB)
       per second.
     * A 1 Mbit/s Internet connection can transfer 1000000 bits 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 at nominal speed of
       1000000000 bits 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 (200000000 cycles per second) has
       a bandwidth of 200000000 × 8 × 2 = 3200000000 B/s = 3.2 GB/s (about
       3.0 GiB/s).
     * A PCI-X bus at 66 MHz (66000000 cycles per second), 64 bits per
       transfer, has a bandwidth of 66000000 transfers per second × 64 bits
       per transfer = 4224000000 bit/s, or 528000000 B/s, usually quoted as
       528 MB/s (about 503 MiB/s).

  Use by industryEdit

   IEC prefixes are used by Toshiba,^[124] IBM, HP to advertise or describe
   some of their products. According to one HP brochure, [3]^[dead link]
   "[t]o reduce confusion, vendors are pursuing one of two remedies: they are
   changing SI prefixes to the new binary prefixes, or they are recalculating
   the numbers as powers of ten." The IBM Data Center also uses IEC prefixes
   to reduce confusion.^[125] The IBM Style Guide reads^[126]

     To help avoid inaccuracy (especially with the larger prefixes) and
     potential ambiguity, the International Electrotechnical Commission (IEC)
     in 2000 adopted a set of prefixes specifically for binary multipliers
     (See IEC 60027-2). Their use is now supported by the United States
     National Institute of Standards and Technology (NIST) and incorporated
     into ISO 80000. They are also required by EU law and in certain contexts
     in the US. However, most documentation and products in the industry
     continue to use SI prefixes when referring to binary multipliers. In
     product documentation, follow the same standard that is used in the
     product itself (for example, in the interface or firmware). Whether you
     choose to use IEC prefixes for powers of 2 and SI prefixes for powers of
     10, or use SI prefixes for a dual purpose ... be consistent in your
     usage and explain to the user your adopted system.

See alsoEdit

     * Binary engineering notation
     * ISO/IEC 80000
     * Nibble
     * Octet

DefinitionsEdit

    1. ^ ^a ^b ^c ^d ^e ^f The term SI prefix or similar refers to prefixes
       such as kilo, mega, giga, etc., defined by the SI system of units and
       always used to denote a power of 1000; in other words, always as
       decimal prefixes.
    2. ^ ^a ^b A binary prefix is a prefix that denotes a power of 1024. For
       example, in the computer industry's customary practice, one "megabyte"
       of RAM is 1024^2 bytes of RAM, one "gigabyte" of RAM is 1024^3 bytes
       of RAM, and so on. In the IEC system, these would be expressed as one
       "mebibyte" and one "gibibyte," respectively. Both are "binary
       prefixes" in these usages.
    3. ^ ^a ^b A decimal prefix is a prefix that denotes a power of 1000. For
       example, "kilo" denotes 1000, "mega" denotes 1000^2 or one million,
       "giga" denotes 1000^3 or one billion, and so on. SI prefixes are
       decimal prefixes.
    4. ^ The term IEC binary prefix or IEC prefix refers to the prefixes such
       as kibi, mebi, gibi, etc., or their corresponding symbols Ki, Mi, Gi,
       etc., first adopted by the International Electrotechnical Commission
       (IEC). Such prefixes are only used with the units bits or bytes (or
       compound units derived from them such as bytes/second) and always
       denote powers of 1024; that is, they are always used as binary
       prefixes. Thus 1 mebibyte of RAM is 1024^2 bytes of RAM, one gibibyte
       or 1 GiB of RAM is 1024^3 bytes, and so on.
    5. ^ As used in this article, the term customary binary prefix or similar
       refers to prefixes such as kilo, mega, giga, etc., borrowed from the
       similarly named SI prefixes but commonly used to denote a power of
       1024.

ReferencesEdit

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       "International System of Units (SI): Prefixes for binary multiples".
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       Weik, Martin H. (March 1961). "A Third Survey of Domestic Electronic
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       is less than 1 Mbyte. For capacities of 4 Mbyte and 16 Mbyte serial
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   30. ^
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       ANSI/IEEE Std 1212-1991 IEEE Standard Control and Status Register
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Further readingEdit

     * Link: mw-deduplicated-inline-style
       "When is a kilobyte a kibibyte? And an MB an MiB?". International
       Electrotechnical Commission. 2007-02-12. Archived from the original on
       2009-04-03. – An introduction to binary prefixes
     * Link: mw-deduplicated-inline-style
       "Prefixes for binary multiples". NIST.
     * Link: mw-deduplicated-inline-style
       "Get Ready for the mebi, gibi and tebi" (Press release). NIST.
       1999-03-02. Archived from the original on 2016-08-20. Retrieved
       2017-07-13.
     * Link: mw-deduplicated-inline-style
       Kuhn, Markus (1996-12-29). "What is a Megabyte ...?".—a 1996–1999
       paper on bits, bytes, prefixes and symbols
     * Link: mw-deduplicated-inline-style
       de Boyne Pollard, Jonathan. "There is no such thing as a 1.44 MB
       standard format floppy disc". Frequently Given Answers. Archived from
       the original on 2016-10-07.
     * Link: mw-deduplicated-inline-style
       Michael Quinion (1999-08-21). "Kibibyte". World Wide Words. Archived
       from the original on 2004-06-12. Retrieved 2002-11-13.—Another
       description of binary prefixes
     * Link: mw-deduplicated-inline-style
       James Wiebe (2003-10-09). "When One Billion does not equal One
       Billion, or: Why your computer's disk drive capacity doesn't appear to
       match the stated capacity" (PDF). Archived from the original (PDF) on
       2013-12-04. Retrieved 2010-01-22. {{cite journal}}: Cite journal
       requires |journal= (help)—White-paper on the controversy over drive
       capacities

External linksEdit

     * 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 Archived 2015-01-02 at the
       Wayback Machine
   Retrieved from
   "https://en.wikipedia.org/w/index.php?title=Binary_prefix&oldid=1081274433"
   Last edited on 6 April 2022, at 12:31
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