A binary prefix is a
unit prefix A unit prefix is a specifier or mnemonic that is prepended to units of measurement to indicate multiples or fractions of the units. Units of various order of magnitude, sizes are commonly formed by the use of such prefixes. The Metric prefix, prefi ...
for multiples of
units
Unit may refer to:
Arts and entertainment
* UNIT, a fictional military organization in the science fiction television series ''Doctor Who''
* Unit of action, a discrete piece of action (or beat) in a theatrical presentation
Music
* Unit (album), ...
. It is most often used in data processing, data transmission, and digital information, principally in association with the
bit
The bit is the most basic unit of information in computing and digital communications. The name is a portmanteau of binary digit. The bit represents a logical state with one of two possible values. These values are most commonly represente ...
and the
byte
The byte is a unit of digital information that most commonly consists of eight bits. Historically, the byte was the number of bits used to encode a single character of text in a computer and for this reason it is the smallest addressable unit ...
, 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
The International Electrotechnical Commission (IEC; in French: ''Commission électrotechnique internationale'') is an international standards organization that prepares and publishes international standards for all electrical, electronic and r ...
(IEC) and several other standards and trade organizations using two-letter symbols, e.g. ''Mi'' indicating with a second set established by semiconductor industry convention using one-letter symbols, e.g., ''M'' also indicating .
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
The International System of Units, known by the international abbreviation SI in all languages and sometimes pleonastically as the SI system, is the modern form of the metric system and the world's most widely used system of measurement. E ...
(SI), namely as powers of 1000. For example, a 500-gigabyte hard disk holds bytes, and a 1 Gbit/s (gigabit per second)
Ethernet
Ethernet () is a family of wired computer networking technologies commonly used in local area networks (LAN), metropolitan area networks (MAN) and wide area networks (WAN). It was commercially introduced in 1980 and first standardized in 198 ...
connection transfers data at nominal speed of bit/s. In contrast with the ''binary prefix'' usage, this use is described as a ''decimal prefix'', as 1000 is a
power of 10
A power of 10 is any of the integer exponentiation, powers of the number 10 (number), ten; in other words, ten multiplication, multiplied by itself a certain number of times (when the power is a positive integer). By definition, the number one is ...
(10
3).
The computer industry has historically in citations of main memory (
RAM
Ram, ram, or RAM may refer to:
Animals
* A male sheep
* Ram cichlid, a freshwater tropical fish
People
* Ram (given name)
* Ram (surname)
* Ram (director) (Ramsubramaniam), an Indian Tamil film director
* RAM (musician) (born 1974), Dutch
* ...
) capacity used the units ''kilobyte'', ''megabyte'', and ''gigabyte'', and the corresponding symbols ''KB'', ''MB'', and ''GB'', in a binary sense: ''gigabyte'' customarily means bytes. As this is a power of 1024, and 1024 is a
power of two
A power of two is a number of the form where is an integer, that is, the result of exponentiation with number two as the base and integer as the exponent.
In a context where only integers are considered, is restricted to non-negative ...
(2
10), these three usages are referred to as a binary prefixes; they were defined by the
Joint Electron Device Engineering Council
A joint or articulation (or articular surface) is the connection made between bones, ossicles, or other hard structures in the body which link an animal's skeletal system into a functional whole.Saladin, Ken. Anatomy & Physiology. 7th ed. McGraw- ...
(JEDEC) for
semiconductor
A semiconductor is a material which has an electrical resistivity and conductivity, electrical conductivity value falling between that of a electrical conductor, conductor, such as copper, and an insulator (electricity), insulator, such as glas ...
s and are used by some
operating system
An operating system (OS) is system software that manages computer hardware, software resources, and provides common services for computer programs.
Time-sharing operating systems schedule tasks for efficient use of the system and may also in ...
s.
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
The National Institute of Standards and Technology (NIST) is an agency of the United States Department of Commerce whose mission is to promote American innovation and industrial competitiveness. NIST's activities are organized into physical sci ...
(NIST) requires that
SI prefix
The International System of Units, known by the international abbreviation SI in all languages and sometimes pleonastically as the SI system, is the modern form of the metric system and the world's most widely used system of measurement. E ...
es be used only in the decimal sense:
kilobyte
The kilobyte is a multiple of the unit byte for digital information.
The International System of Units (SI) defines the prefix ''kilo'' as 1000 (103); per this definition, one kilobyte is 1000 bytes.International Standard IEC 80000-13 Quantiti ...
and
megabyte
The megabyte is a multiple of the unit byte for digital information. Its recommended unit symbol is MB. The unit prefix ''mega'' is a multiplier of (106) in the International System of Units (SI). Therefore, one megabyte is one million bytes o ...
denote one thousand bytes and one million bytes respectively (consistent with SI), while new terms such as
kibibyte
The byte is a unit of digital information that most commonly consists of eight bits. Historically, the byte was the number of bits used to encode a single character of text in a computer and for this reason it is the smallest addressable unit ...
,
mebibyte
The byte is a unit of digital information that most commonly consists of eight bits. Historically, the byte was the number of bits used to encode a single character of text in a computer and for this reason it is the smallest addressable unit ...
, and
gibibyte
The byte is a unit of digital information that most commonly consists of eight bits. Historically, the byte was the number of bits used to encode a single character of text in a computer and for this reason it is the smallest addressable unit ...
, having the symbols KiB, MiB, and GiB, denote 1024 bytes, bytes, and bytes, respectively.
In 2008, the IEC prefixes were incorporated into the
ISO/IEC 80000
ISO 80000 or IEC 80000 is an international standard introducing the International System of Quantities (ISQ).
It was developed and promulgated jointly by the International Organization for Standardization (ISO) and the International Electrote ...
standard alongside the decimal prefixes of the international standard
system of units
A system of measurement is a collection of units of measurement and rules relating them to each other. Systems of measurement have historically been important, regulated and defined for the purposes of science and commerce. Systems of measurement i ...
.
In response to litigation over the use of metric prefixes, the
includes a judicial notice that "the U.S. Congress has deemed the decimal definition of gigabyte to be the 'preferred' one for the purposes of 'U.S. trade and commerce.
History
Early prefixes
The original
metric system
The metric system is a system of measurement that succeeded the Decimal, decimalised system based on the metre that had been introduced in French Revolution, France in the 1790s. The historical development of these systems culminated in the d ...
adopted by France in 1795 included two binary prefixes named ''
double
A double is a look-alike or doppelgänger; one person or being that resembles another.
Double, The Double or Dubble may also refer to:
Film and television
* Double (filmmaking), someone who substitutes for the credited actor of a character
* Th ...
-'' (2×) and ''
demi
Demi is a feminine given name with Greek and Latin roots. It was originally a nickname of Demetria, the feminine form of the masculine name Demetrius, which is itself the Latin and English spelling of the Greek name Demetrios.
It is also an Alba ...
-'' (×).
However, these were not retained when the
SI prefix
The International System of Units, known by the international abbreviation SI in all languages and sometimes pleonastically as the SI system, is the modern form of the metric system and the world's most widely used system of measurement. E ...
es were internationally adopted by the 11th
CGPM conference in 1960.
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
The IBM 701 Electronic Data Processing Machine, known as the Defense Calculator while in development, was IBM’s first commercial scientific computer and its first series production mainframe computer, which was announced to the public on May ...
(1952) used binary and could address 2048
words
A word is a basic element of language that carries an objective or practical meaning, can be used on its own, and is uninterruptible. Despite the fact that language speakers often have an intuitive grasp of what a word is, there is no consen ...
of 36
bit
The bit is the most basic unit of information in computing and digital communications. The name is a portmanteau of binary digit. The bit represents a logical state with one of two possible values. These values are most commonly represente ...
s each, while the
IBM 702
The IBM 702 was an early generation tube-based digital computer produced by IBM in the early to mid-1950s. It was the company's response to Remington Rand's UNIVAC—the first mainframe computer to use magnetic tapes. As these machines wer ...
(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 line
In computer architecture, a bus (shortened form of the Latin '' omnibus'', and historically also called data highway or databus) is a communication system that transfers data between components inside a computer, or between computers. This ex ...
s 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 words of storage. These are all
powers of two
A power of two is a number of the form where is an integer, that is, the result of exponentiation with number two as the base and integer as the exponent.
In a context where only integers are considered, is restricted to non-negative ...
, 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 metric system is a system of measurement that succeeded the Decimal, decimalised system based on the metre that had been introduced in French Revolution, France in the 1790s. The historical development of these systems culminated in the d ...
. The prefixes ''kilo-'' and ''mega-'', meaning 1000 and respectively, were commonly used in the electronics industry before World War II. Along with ''giga-'' or G-, meaning , they are now known as
SI prefixes
A metric prefix is a unit prefix that precedes a basic unit of measure to indicate a multiple or submultiple of the unit. All metric prefixes used today are decadic. Each prefix has a unique symbol that is prepended to any unit symbol. The pre ...
after the
International System of Units
The International System of Units, known by the international abbreviation SI in all languages and sometimes pleonastically as the SI system, is the modern form of the metric system and the world's most widely used system of measurement. E ...
(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.
The use of K in the binary sense as in a "32K core" meaning words, i.e., words, can be found as early as 1959.
[ Note: the IBM 704 core memory units had 4096 36-bit words. Up to words could be installed][ "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
The IBM 1401 is a variable-wordlength decimal computer that was announced by IBM on October 5, 1959. The first member of the highly successful IBM 1400 series, it was aimed at replacing unit record equipment for processing data stored on pu ...
was a character addressable computer.
Gene Amdahl
Gene Myron Amdahl (November 16, 1922 – November 10, 2015) was an American computer architect and high-tech entrepreneur, chiefly known for his work on mainframe computers at IBM and later his own companies, especially Amdahl Corporation ...
's seminal 1964 article on
IBM System/360
The IBM System/360 (S/360) is a family of mainframe computer systems that was announced by IBM on April 7, 1964, and delivered between 1965 and 1978. It was the first family of computers designed to cover both commercial and scientific applica ...
used "1K" to mean 1024.
[ Figure 1 gives storage (memory) capacity ranges of the various models in "Capacity 8-bit bytes, 1 K = 1024"] This style was used by other computer vendors, the
CDC 7600
The CDC 7600 was the Seymour Cray-designed successor to the CDC 6600, extending Control Data's dominance of the supercomputer field into the 1970s. The 7600 ran at 36.4 MHz (27.5 ns clock cycle) and had a 65 Kword primary memory (with a 6 ...
''System Description'' (1968) made extensive use of K as 1024.
Thus the first binary prefix was born.
Another style was to truncate the last three digits and append K, essentially using K as a decimal prefix
similar to
SI, but always truncating to the next lower whole number instead of rounding to the nearest. The exact values words, words and words would then be described as "32K", "65K" and "131K".
(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 (which is 192×1024) as "196K" and as "1M",
while the
HP 3000
The HP 3000 series is a family of 16-bit and 32-bit minicomputers from Hewlett-Packard. It was designed to be the first minicomputer with full support for time-sharing in the hardware and the operating system, features that had mostly been limite ...
business computer (1973) could have "64K", "96K", or "128K" bytes of memory.
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.
[
] Nevertheless, the practice of using the SI-inspired "kilo" to indicate 1024 was later extended to "megabyte" meaning 1024
2 () bytes, and later "gigabyte" for 1024
3 () bytes. For example, a "512 megabyte" RAM module is bytes (512 × , or ), rather than .
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.
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."
Megabyte was used to describe the 22-bit addressing of DEC
PDP-11
The PDP-11 is a series of 16-bit minicomputers sold by Digital Equipment Corporation (DEC) from 1970 into the 1990s, one of a set of products in the Programmed Data Processor (PDP) series. In total, around 600,000 PDP-11s of all models were sold, ...
/70 (1975)
and gigabyte the 30-bit addressing DEC
VAX-11/780
The VAX-11 is a discontinued family of 32-bit superminicomputers, running the Virtual Address eXtension (VAX) instruction set architecture (ISA), developed and manufactured by Digital Equipment Corporation (DEC). Development began in 1976. In ad ...
(1977).
In 1998, the
International Electrotechnical Commission
The International Electrotechnical Commission (IEC; in French: ''Commission électrotechnique internationale'') is an international standards organization that prepares and publishes international standards for all electrical, electronic and r ...
IEC introduced the binary prefixes kibi, mebi, gibi, etc., to mean 1024, 1024
2, 1024
3 etc., so that 1048576 bytes could be referred to unambiguously as 1
mebibyte
The byte is a unit of digital information that most commonly consists of eight bits. Historically, the byte was the number of bits used to encode a single character of text in a computer and for this reason it is the smallest addressable unit ...
. The IEC prefixes were defined for use alongside the
International System of Quantities
The International System of Quantities (ISQ) consists of the quantities used in physics and in modern science in general, starting with basic quantities such as length and mass, and the relationships between those quantities. This system underlie ...
(ISQ) in
2009
File:2009 Events Collage V2.png, From top left, clockwise: The vertical stabilizer of Air France Flight 447 is pulled out from the Atlantic Ocean; Barack Obama becomes the first African American to become President of the United States; 2009 Iran ...
.
Disk drives
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
IBM manufactured magnetic disk storage devices from 1956 to 2003, when it sold its hard disk drive business to Hitachi. Both the hard disk drive (HDD) and floppy disk drive (FDD) were invented by IBM and as such IBM's employees were responsible fo ...
, had fifty physical disk platters containing a total of sectors of 100 characters each, for a total quoted capacity of 5 million characters. It was introduced in September 1956.
In the 1960s most disk drives used IBM's variable block length format, called
Count Key Data
Count key data (CKD) is a direct-access storage device (DASD) data recording format introduced in 1964, by IBM with its IBM System/360 and still being emulated on IBM mainframes. It is a self-defining format with each data record represented by a ...
(CKD). 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 bytes.
Floppy disks
A floppy disk or floppy diskette (casually referred to as a floppy, or a diskette) is an obsolescent type of disk storage composed of a thin and flexible disk of a magnetic storage medium in a square or nearly square plastic enclosure lined w ...
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
A hard disk drive (HDD), hard disk, hard drive, or fixed disk is an electro-mechanical data storage device that stores and retrieves digital data using magnetic storage with one or more rigid rapidly rotating platters coated with magnet ...
drive manufacturers used ''megabytes'' or ''MB'', meaning 10
6 bytes, to characterize their products as early as 1974. 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.
One of the earliest hard disk drives in personal computing history, the Seagate
ST-412, was specified as ''Formatted: 10.0 Megabytes''. 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 . This drive was one of several types installed in the
IBM PC/XT
The IBM Personal Computer XT (model 5160, often shortened to PC/XT) is the second computer in the IBM Personal Computer line, released on March 8, 1983. Except for the addition of a built-in Hard disk drive, hard drive and extra expansion slots, ...
and extensively advertised and reported as a "10 MB" (formatted) hard disk drive. 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 In computer storage, zone bit recording (ZBR) is a method used by disk drives to optimise the tracks for increased data capacity. It does this by placing more sectors per zone on outer tracks than on inner tracks. This contrasts with other approach ...
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 , or , bytes, not (which would be about ). Operating systems such as
Microsoft Windows
Windows is a group of several proprietary graphical operating system families developed and marketed by Microsoft. Each family caters to a certain sector of the computing industry. For example, Windows NT for consumers, Windows Server for serv ...
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 bytes, or ). On the other hand,
macOS
macOS (; previously OS X and originally Mac OS X) is a Unix operating system developed and marketed by Apple Inc. since 2001. It is the primary operating system for Apple's Mac computers. Within the market of desktop and lapt ...
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.
[Seagate Savvio 10K.5 SAS Product Manual]
100628561, Rev D, March 2011, sec 5.2.3, p. 10 (18th page of the pdf), states the drive's sustained transfer speed as "89 to 160 MiB/s" on one line, and "93 to 168 MB/s" on the next line.
"Advanced Format" drives uses the term "4K sectors", which it defines as having size of "4096 (4K) bytes".
Information transfer and clock rates
Computer
clock
A clock or a timepiece is a device used to measure and indicate time. The clock is one of the oldest human inventions, meeting the need to measure intervals of time shorter than the natural units such as the day, the lunar month and the ...
frequencies are always quoted using SI prefixes in their decimal sense. For example, the internal clock frequency of the original
IBM PC
The IBM Personal Computer (model 5150, commonly known as the IBM PC) is the first microcomputer released in the IBM PC model line and the basis for the IBM PC compatible de facto standard. Released on August 12, 1981, it was created by a team ...
was 4.77 MHz, that is . Similarly, digital information transfer rates are quoted using decimal prefixes:
* The ATA-100 disk interface refers to bytes per second
* A "56K" modem refers to bits per second
* SATA-2 has a raw bit rate of 3 Gbit/s = bits per second
* PC2-6400
RAM
Ram, ram, or RAM may refer to:
Animals
* A male sheep
* Ram cichlid, a freshwater tropical fish
People
* Ram (given name)
* Ram (surname)
* Ram (director) (Ramsubramaniam), an Indian Tamil film director
* RAM (musician) (born 1974), Dutch
* ...
transfers bytes per second
* Firewire 800 has a raw rate of bits per second
* In 2011, Seagate specified the sustained transfer rate of some hard disk drive models with both decimal and IEC binary prefixes.
[
]
Historical standardization of dual definitions
By the mid-1970s it was common to see K meaning 1024 and the occasional M meaning 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, bytes) hard disk drive was introduced in 2007.
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 obsolete standard ANSI/IEEE Std 1084-1986 defined dual uses for kilo and mega.
The binary units Kbyte and Mbyte were formally defined in the obsolete standard ANSI/IEEE Std 1212-1991.
Many dictionaries have noted the practice of using customary prefixes to indicate binary multiples.
Oxford online dictionary historically defined, for example, megabyte as: "Computing: a unit of information equal to one million or (strictly) bytes."
The units Kbyte, Mbyte, and Gbyte were found in the trade press and in IEEE journals. Gigabyte was formally defined in obsolete standard IEEE Std 610.10-1994 as either or 230 bytes.
Kilobyte, Kbyte, and KB were all defined in the obsolete standard IEEE 100–2000.[ "kB See kilobyte." "Kbyte Kilobyte. Indicates 210 bytes." "Kilobyte Either 1000 or 210 or 1024 bytes." The standard also defines megabyte and gigabyte with a note that an alternative notation for base 2 is under development.]
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
A floppy disk or floppy diskette (casually referred to as a floppy, or a diskette) is an obsolescent type of disk storage composed of a thin and flexible disk of a magnetic storage medium in a square or nearly square plastic enclosure lined w ...
uses the megabyte to denote bytes. In the optical disks market, compact disc
The compact disc (CD) is a Digital media, digital optical disc data storage format that was co-developed by Philips and Sony to store and play digital audio recordings. In August 1982, the first compact disc was manufactured. It was then rele ...
s use ''MB'' to mean 10242 bytes while DVD
The DVD (common abbreviation for Digital Video Disc or Digital Versatile Disc) is a digital optical disc data storage format. It was invented and developed in 1995 and first released on November 1, 1996, in Japan. The medium can store any kind ...
s use ''GB'' to mean 10003 bytes.
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 nearly 27% for the quetta prefix. Although the prefixes ronna and quetta have been defined, as of 2022 no names have been officially assigned to the corresponding binary prefixes.
Consumer confusion
In the early days of computers (roughly, prior to the advent of personal computers) there was little or no consumer confusion
Consumer confusion is a state of mind that leads to consumers making imperfect purchasing decisions or lacking confidence in the correctness of their purchasing decisions.
Confusion
Confusion occurs when a consumer fails to correctly understand o ...
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.
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
A hard disk drive (HDD), hard disk, hard drive, or fixed disk is an electro-mechanical data storage device that stores and retrieves digital data using magnetic storage with one or more rigid rapidly rotating platters coated with magneti ...
are specified and sold using "GB" and "TB" in their decimal meaning: one billion
Billion is a word for a large number, and it has two distinct definitions:
*1,000,000,000, i.e. one thousand million, or (ten to the ninth power), as defined on the short scale. This is its only current meaning in English.
* 1,000,000,000,000, i.e ...
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; 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 DOS
DOS is shorthand for the MS-DOS and IBM PC DOS family of operating systems.
DOS may also refer to:
Computing
* Data over signalling (DoS), multiplexing data onto a signalling channel
* Denial-of-service attack (DoS), an attack on a communicat ...
command 'CHKDSK
In computing, CHKDSK (short for "check disk") is a system tool and command in DOS, Digital Research FlexOS, IBM/Toshiba 4690 OS, IBM OS/2, Microsoft Windows and related operating systems. It verifies the file system integrity of a volume and at ...
'.
Legal disputes
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 cases
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.
''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
The Eastman Kodak Company (referred to simply as Kodak ) is an American public company that produces various products related to its historic basis in analogue photography. The company is headquartered in Rochester, New York, and is incorpor ...
Company, Kingston Technology Company, Inc., Memorex
Memorex Corp. began as a computer tape producer and expanded to become both a consumer media supplier and a major IBM plug compatible peripheral supplier. It was broken up and ceased to exist after 1996 other than as a consumer electronics bran ...
Products, Inc.; PNY Technologies
PNY Technologies, Inc., doing business as PNY, is an American manufacturer of flash memory cards, USB flash drives, solid state drives, memory upgrade modules, portable battery chargers, computer locks, cables, chargers, adapters, and consumer an ...
Inc., SanDisk Corporation
SanDisk is a brand for flash memory products, including memory cards and readers, USB flash drives, solid-state drives, and digital audio players, manufactured and marketed by Western Digital. The original company, SanDisk Corporation was acquire ...
, Verbatim Corporation
Verbatim is a brand for storage media and flash memory products currently owned by CMC Magnetics Corporation (CMC), a Taiwanese company that is known for optical disc manufacturing. Formerly a subsidiary of Mitsubishi Chemical, the global busi ...
, and Viking Interworks
Sanmina Corporation is an American electronics manufacturing services (EMS) provider headquartered in San Jose, California that serves original equipment manufacturers in communications and computer hardware fields. The firm has nearly 80 manufa ...
alleging that their descriptions of the capacity of their flash memory
Flash memory is an electronic non-volatile computer memory storage medium that can be electrically erased and reprogrammed. The two main types of flash memory, NOR flash and NAND flash, are named for the NOR and NAND logic gates. Both us ...
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 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.
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. The consumers could apply for "a discount of ten percent off a future online purchase from Defendants' Online Stores Flash Memory Device".
''Orin Safier v. Western Digital Corporation''
On 7 July 2005, an action entitled ''Orin Safier v. Western Digital
Western Digital Corporation (WDC, commonly known as Western Digital or WD) is an American computer drive manufacturer and data storage company, headquartered in San Jose, California. It designs, manufactures and sells data technology produc ...
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.
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.
Western Digital offered to compensate customers with a free download of backup and recovery software valued at US$30. They also paid $ 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.[
]
''Cho v. Seagate Technology (US) Holdings, Inc.''
A lawsuit (''Cho v. Seagate Technology (US) Holdings, Inc.'', San Francisco Superior Court, Case No. CGC-06-453195) was filed against Seagate Technology
Seagate Technology Holdings plc is an American data storage company. It was incorporated in 1978 as Shugart Technology and commenced business in 1979. Since 2010, the company has been incorporated in Dublin, Ireland, with operational headquart ...
, 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.
''Dinan et al. v. SanDisk LLC''
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 .
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[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 10242 bytes of RAM, one "gigabyte" of RAM is 10243 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.] were made in 1968. Donald Morrison proposed to use the Greek letter kappa ( κ) to denote 1024, κ2 to denote 10242, and so on. (At the time, memory size was small, and only K was in widespread use.) Wallace Givens James Wallace Givens, Jr. (December 14, 1910 – March 5, 1993) was a mathematician and a pioneer in computer science. He is the eponym of the well-known Givens rotations. Born the son of two teachers in Alberene, Virginia (a small town near Cha ...
responded with a proposal to use bK as an abbreviation for 1024 and bK2 or bK2 for 10242, though he noted that neither the Greek letter nor lowercase letter b would be easy to reproduce on computer printers of the day. Bruce Alan Martin
The English language name Bruce arrived in Scotland with the Normans, from the place name Brix, Manche in Normandy, France, meaning "the willowlands". Initially promulgated via the descendants of king Robert the Bruce (1274−1329), it has been ...
of Brookhaven National Laboratory
Brookhaven National Laboratory (BNL) is a United States Department of Energy national laboratory located in Upton, Long Island, and was formally established in 1947 at the site of Camp Upton, a former U.S. Army base and Japanese internment c ...
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 , a convention still used on some calculators to present binary floating point-numbers today.
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).[
] Donald Knuth
Donald Ervin Knuth ( ; born January 10, 1938) is an American computer scientist, mathematician, and professor emeritus at Stanford University. He is the 1974 recipient of the ACM Turing Award, informally considered the Nobel Prize of computer sc ...
, who uses decimal notation like 1 MB = 1000 kB,
The Art of Computer Programming
'' Volume 1, Donald Knuth
Donald Ervin Knuth ( ; born January 10, 1938) is an American computer scientist, mathematician, and professor emeritus at Stanford University. He is the 1974 recipient of the ACM Turing Award, informally considered the Nobel Prize of computer sc ...
, pp. 24 and 94 proposed that the powers of 1024 be designated as "large kilobytes" and "large megabytes", with abbreviations KKB and MMB. 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 prefixes
The set of binary prefixes that were eventually adopted, now referred to as the "IEC prefixes",[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
The International Electrotechnical Commission (IEC; in French: ''Commission électrotechnique internationale'') is an international standards organization that prepares and publishes international standards for all electrical, electronic and r ...
(IEC). Such prefixes are commonly used with the units bits or bytes (or less commonly, 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 10242 bytes of RAM, one gibibyte or 1 GiB of RAM is 10243 bytes, and so on. were first proposed by the International Union of Pure and Applied Chemistry
The International Union of Pure and Applied Chemistry (IUPAC ) is an international federation of National Adhering Organizations working for the advancement of the chemical sciences, especially by developing nomenclature and terminology. It is ...
'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), ''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. The proposal was not accepted at the time.
The Institute of Electrical and Electronics Engineers
The Institute of Electrical and Electronics Engineers (IEEE) is a 501(c)(3) professional association for electronic engineering and electrical engineering (and associated disciplines) with its corporate office in New York City and its operation ...
(IEEE) began to collaborate with the International Organization for Standardization
The International Organization for Standardization (ISO ) is an international standard development organization composed of representatives from the national standards organizations of member countries. Membership requirements are given in Ar ...
(ISO) and International Electrotechnical Commission
The International Electrotechnical Commission (IEC; in French: ''Commission électrotechnique internationale'') is an international standards organization that prepares and publishes international standards for all electrical, electronic and r ...
(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.
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 identical to the corresponding SI prefix, 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.
Adoption by IEC, NIST and ISO
In January 1999, the IEC published the first international standard (IEC 60027-2
The International Electrotechnical Commission (IEC; in French: ''Commission électrotechnique internationale'') is an international standards organization that prepares and publishes international standards for all electrical, electronic and ...
Amendment 2) with the new prefixes, extended up to ''pebi'' (Pi) and ''exbi'' (Ei).
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 bytes () 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 , 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 bytes of RAM would be displayed as "512 MiB".
The second edition of the standard, published in 2000,[IEC 60027-2 (2000-11) Ed. 2.0
] defined them only up to ''exbi'', but in 2005, the third edition added prefixes ''zebi'' and ''yobi'', thus matching all then-defined SI prefixes with binary counterparts.
The harmonized ISO
ISO is the most common abbreviation for the International Organization for Standardization.
ISO or Iso may also refer to: Business and finance
* Iso (supermarket), a chain of Danish supermarkets incorporated into the SuperBest chain in 2007
* Iso ...
/IEC
The International Electrotechnical Commission (IEC; in French: ''Commission électrotechnique internationale'') is an international standards organization that prepares and publishes international standards for all electrical, electronic and r ...
IEC 80000-13
ISO 80000 or IEC 80000 is an international standard introducing the International System of Quantities (ISQ).
It was developed and promulgated jointly by the International Organization for Standardization (ISO) and the International Electrote ...
: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. 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 bits (210 bits), which is 1 kibibit."
The additional decimal prefixes ''ronna-
A metric prefix is a unit prefix that precedes a basic unit of measure to indicate a multiple or submultiple of the unit. All metric prefixes used today are decadic. Each prefix has a unique symbol that is prepended to any unit symbol. The pre ...
'' for 10009 and ''quetta-
A metric prefix is a unit prefix that precedes a basic unit of measure to indicate a multiple or submultiple of the unit. All metric prefixes used today are decadic. Each prefix has a unique symbol that is prepended to any unit symbol. The pre ...
'' for 100010 were adopted by the International Bureau of Weights and Measures
The International Bureau of Weights and Measures (french: Bureau international des poids et mesures, BIPM) is an intergovernmental organisation, through which its 59 member-states act together on measurement standards in four areas: chemistry, ...
(BIPM) in 2022. The natural binary counterparts to ''ronna-'' and ''quetta-'' were suggested in a consultation paper of the International Committee for Weights and Measures
The General Conference on Weights and Measures (GCWM; french: Conférence générale des poids et mesures, CGPM) is the supreme authority of the International Bureau of Weights and Measures (BIPM), the intergovernmental organization established i ...
' Consultative Committee for Units (CCU) as ''robi-'' (Ri, 10249) and ''quebi-'' (Qi, 102410). , no corresponding binary prefixes have been adopted by the IEC and ISO.
Other standards bodies and organizations
The IEC standard binary prefixes are now supported by other standardization bodies and technical organizations.
The United States National Institute of Standards and Technology
The National Institute of Standards and Technology (NIST) is an agency of the United States Department of Commerce whose mission is to promote American innovation and industrial competitiveness. NIST's activities are organized into physical sci ...
(NIST) supports the ISO/IEC standards for
"Prefixes for binary multiples" and has a web page 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''. NIST has stated the SI prefixes "refer strictly to powers of 10" and that the binary definitions "should not be used" for them.
The microelectronics industry standards body JEDEC
The JEDEC Solid State Technology Association is an independent semiconductor engineering trade organization and standardization body headquartered in Arlington County, Virginia, United States.
JEDEC has over 300 members, including some of the w ...
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." The JEDEC standards for semiconductor memory use the customary prefix symbols K, M and G in the binary sense.[ Free registration required to download the standard.]
On 19 March 2005, the IEEE standard IEEE 1541-2002
IEEE 1541-2002 is a standard issued in 2002 by the Institute of Electrical and Electronics Engineers (IEEE) concerning the use of prefixes for binary multiples of units of measurement related to digital electronics and computing.
While the Interna ...
("Prefixes for Binary Multiples") was elevated to a full-use standard by the IEEE Standards Association after a two-year trial period.[
] However, , the IEEE Publications division does not require the use of IEC prefixes in its major magazines such as ''Spectrum''[ ''"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."''] or ''Computer''.[ "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.]
The International Bureau of Weights and Measures
The International Bureau of Weights and Measures (french: Bureau international des poids et mesures, BIPM) is an intergovernmental organisation, through which its 59 member-states act together on measurement standards in four areas: chemistry, ...
(BIPM), which maintains the International System of Units
The International System of Units, known by the international abbreviation SI in all languages and sometimes pleonastically as the SI system, is the modern form of the metric system and the world's most widely used system of measurement. E ...
(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.
The Society of Automotive Engineers
SAE International, formerly named the Society of Automotive Engineers, is a United States-based, globally active professional association and standards developing organization for engineering professionals in various industries. SAE Internatio ...
(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.
The European Committee for Electrotechnical Standardization (CENELEC
CENELEC (french: Comité Européen de Normalisation Électrotechnique; en, European Committee for Electrotechnical Standardization) is responsible for European standardization in the area of electrical engineering. Together with ETSI (telecommun ...
) adopted the IEC-recommended binary prefixes via the harmonization document HD 60027-2:2003-03. The European Union (EU) has required the use of the IEC binary prefixes since 2007.
Current practice in information technology
Most computer hardware uses SI prefixes
A metric prefix is a unit prefix that precedes a basic unit of measure to indicate a multiple or submultiple of the unit. All metric prefixes used today are decadic. Each prefix has a unique symbol that is prepended to any unit symbol. The pre ...
to state capacity and define other performance parameters such as data rate. Main
Main may refer to:
Geography
* Main River (disambiguation)
**Most commonly the Main (river) in Germany
* Main, Iran, a village in Fars Province
*"Spanish Main", the Caribbean coasts of mainland Spanish territories in the 16th and 17th centuries
...
and cache
Cache, caching, or caché may refer to:
Places United States
* Cache, Idaho, an unincorporated community
* Cache, Illinois, an unincorporated community
* Cache, Oklahoma, a city in Comanche County
* Cache, Utah, Cache County, Utah
* Cache County ...
memories are notable exceptions.
Capacities of main memory
Computer data storage is a technology consisting of computer components and recording media that are used to retain digital data. It is a core function and fundamental component of computers.
The central processing unit (CPU) of a computer ...
and cache memory
In computing, a cache ( ) is a hardware or software component that stores data so that future requests for that data can be served faster; the data stored in a cache might be the result of an earlier computation or a copy of data stored elsewher ...
are usually expressed with customary binary prefixes[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 prefix
The International System of Units, known by the international abbreviation SI in all languages and sometimes pleonastically as the SI system, is the modern form of the metric system and the world's most widely used system of measurement. E ...
es but used to denote a power of 1024. On the other hand, flash memory
Flash memory is an electronic non-volatile computer memory storage medium that can be electrically erased and reprogrammed. The two main types of flash memory, NOR flash and NAND flash, are named for the NOR and NAND logic gates. Both us ...
, like that found in solid state drives, mostly uses SI prefixes
A metric prefix is a unit prefix that precedes a basic unit of measure to indicate a multiple or submultiple of the unit. All metric prefixes used today are decadic. Each prefix has a unique symbol that is prepended to any unit symbol. The pre ...
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[The term SI prefix or similar refers to prefixes such as kilo, mega, giga, etc., defined by the ]SI system
The International System of Units, known by the international abbreviation SI in all languages and sometimes pleonastically as the SI system, is the modern form of the metric system and the world's most widely used system of measurement. E ...
of units and ''always'' used to denote a power of 1000; in other words, always as decimal prefixes. 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 systems
Prior to the release of Macintosh System Software
Mac OS (originally System Software; retronym: Classic Mac OS) is the series of operating systems developed for the Macintosh family of personal computers by Apple Computer from 1984 to 2001, starting with System 1 and ending with Mac OS 9. T ...
(1984), file sizes were typically reported by the operating system without any prefixes. Today, most operating systems report file sizes with prefixes.
* The Linux kernel
The Linux kernel is a free and open-source, monolithic, modular, multitasking, Unix-like operating system kernel. It was originally authored in 1991 by Linus Torvalds for his i386-based PC, and it was soon adopted as the kernel for the GNU ope ...
uses standards-compliant decimal and binary prefixes when booting up. However, many Unix-like
A Unix-like (sometimes referred to as UN*X or *nix) operating system is one that behaves in a manner similar to a Unix system, although not necessarily conforming to or being certified to any version of the Single UNIX Specification. A Unix-li ...
system utilities, such as the ls command, use powers of 1024 indicated as K/M (customary binary prefixes) if called with the "" 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 "" option.
** The Ubuntu
Ubuntu ( ) is a Linux distribution based on Debian and composed mostly of free and open-source software. Ubuntu is officially released in three editions: ''Desktop'', ''Server'', and ''Core'' for Internet of things devices and robots. All the ...
Linux distribution
A Linux distribution (often abbreviated as distro) is an operating system made from a software collection that includes the Linux kernel and, often, a package management system. Linux users usually obtain their operating system by downloading one ...
uses the IEC prefixes for base-2 numbers as of the 10.10 release.
* Microsoft Windows
Windows is a group of several proprietary graphical operating system families developed and marketed by Microsoft. Each family caters to a certain sector of the computing industry. For example, Windows NT for consumers, Windows Server for serv ...
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 = ). Apple product specifications, iOS and macOS (including Mac OS X Snow Leopard
Mac OS X Snow Leopard (version 10.6) is the seventh major release of macOS, Apple's desktop and server operating system for Macintosh computers.
Snow Leopard was publicly unveiled on June 8, 2009 at Apple’s Worldwide Developers Conference. ...
: version 10.6) now report sizes using SI decimal prefixes (1 GB = bytes).
Software
, most software did not distinguish symbols for binary and decimal prefixes.[A decimal prefix is a prefix that denotes a ]power
Power most often refers to:
* Power (physics), meaning "rate of doing work"
** Engine power, the power put out by an engine
** Electric power
* Power (social and political), the ability to influence people or events
** Abusive power
Power may a ...
of 1000. For example, "kilo" denotes 1000, "mega" denotes 10002 or one million, "giga" denotes 10003 or one billion, and so on. SI prefixes are decimal prefixes. The IEC
The International Electrotechnical Commission (IEC; in French: ''Commission électrotechnique internationale'') is an international standards organization that prepares and publishes international standards for all electrical, electronic and r ...
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". Programs such as fdisk
In computing, the fdisk command-line utility provides disk-partitioning functions, preparatory to defining file systems. fdisk features in the DOS, DR FlexOS, IBM OS/2, and Microsoft Windows operating systems, and in certain ports of FreeBS ...
/cfdisk
cfdisk is a Linux partition editor, similar to fdisk, but with a different, curses-based user interface. It is part of the util-linux package of Linux utility programs.
The current cfdisk implementation utilizes the libfdisk library , parted
GNU Parted (the name being the conjunction of the two words PARTition and EDitor) is a free partition editor, used for creating and deleting partitions. This is useful for creating space for new operating systems, reorganising hard disk usage, ...
, and apt-get use SI prefixes with their decimal meaning.
Image:GParted 0.3.5 -- 2008, 06.png, GNOME
A gnome is a mythological creature and diminutive spirit in Renaissance magic and alchemy, first introduced by Paracelsus in the 16th century and later adopted by more recent authors including those of modern fantasy literature. Its characte ...
'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
The byte is a unit of digital information that most commonly consists of eight bits. Historically, the byte was the number of bits used to encode a single character of text in a computer and for this reason it is the smallest addressable unit ...
"
Image:GNOME System Monitor memory size and network rate.png, GNOME's system monitor uses IEC prefixes to show memory size and networking data rate.
Image:Bittornado screenshot showing use of IEC and SI prefixes.png, BitTornado uses standard SI prefixes for data rates and IEC prefixes for file sizes
Image:Deluge_using_Si_prefix_for_wiki_CD.png, Deluge (BitTorrent client)
Deluge BitTorrent Client is a free and open-source, cross-platform BitTorrent client written in Python. Deluge uses a front and back end architecture where libtorrent, a software library written in C++ which provides the application's netw ...
uses IEC prefixes for data rates as well as file sizes
Example of the use of IEC binary prefixes in the Linux
Linux ( or ) is a family of open-source Unix-like operating systems based on the Linux kernel, an operating system kernel first released on September 17, 1991, by Linus Torvalds. Linux is typically packaged as a Linux distribution, which ...
operating system displaying traffic volume on a network interface in kibibytes (KiB) and mebibytes (MiB), as obtained with the ifconfig
ifconfig (short for ''interface config'') is a system administration utility in Unix-like operating systems for network interface configuration.
The utility is a command-line interface tool and is also used in the system startup scripts of man ...
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
The GNU Core Utilities or coreutils is a package of GNU software containing implementations for many of the basic tools, such as cat, ls, and rm, which are used on Unix-like operating systems.
In September 2002, the ''GNU coreutils'' were cr ...
* GParted
GParted (acronym of GNOME Partition Editor) is a GTK front-end to GNU Parted and an official GNOME partition-editing application (alongside Disks). GParted is used for creating, deleting, resizing, moving, checking, and copying disk partitions ...
* FreeDOS-32
* ifconfig
ifconfig (short for ''interface config'') is a system administration utility in Unix-like operating systems for network interface configuration.
The utility is a command-line interface tool and is also used in the system startup scripts of man ...
* GNOME
A gnome is a mythological creature and diminutive spirit in Renaissance magic and alchemy, first introduced by Paracelsus in the 16th century and later adopted by more recent authors including those of modern fantasy literature. Its characte ...
Network
* SLIB
SLIB is computer software, a library for the programming language Scheme, written by Aubrey Jaffer. It uses only standard Scheme syntax and thus works on many different Scheme implementations, such as Bigloo, Chez Scheme, Extension Language Kit ...
* Cygwin/X
Cygwin/X is an implementation of the X Window System that runs under Microsoft Windows. It is part of the Cygwin project, and is installed using Cygwin's standard setup system. Cygwin/X is free software, licensed under the X11 License.
Cygwin/ ...
* HTTrack
HTTrack is a free and open-source Web crawler and offline browser, developed by Xavier Roche and licensed under the GNU General Public License Version 3.
HTTrack allows users to download World Wide Web sites from the Internet to a local computer. ...
* Pidgin (IM client)
Pidgin (formerly named Gaim) is a free and open-source multi-platform
In computing, cross-platform software (also called multi-platform software, platform-agnostic software, or platform-independent software) is computer software that is des ...
* Deluge
A deluge is a large downpour of rain, often a flood.
The Deluge refers to the flood narrative in the Biblical book of Genesis.
Deluge may also refer to:
History
*Deluge (history), the Swedish and Russian invasion of the Polish-Lithuanian Comm ...
* yafc
* tnftp
tnftp (formerly lukemftp) is an File Transfer Protocol, FTP client for Unix-like operating systems. It is based on the original Berkeley Software Distribution, BSD FTP client, and is the default FTP client included with NetBSD, FreeBSD, OpenBSD, ...
* WinSCP
WinSCP (''Windows Secure Copy'') is a free and open-source SSH File Transfer Protocol (SFTP), File Transfer Protocol (FTP), WebDAV, Amazon S3, and secure copy protocol (SCP) client for Microsoft Windows. Its main function is secure file transfer ...
* MediaInfo
MediaInfo is a free, cross-platform and open-source program that displays technical information about media files, as well as tag information for many audio and video files. It is used in many programs such as XMedia Recode, MediaCoder, eMule, a ...
Software that uses standard SI prefixes for powers of 1000, and does not use any prefixes for powers of 1024, includes:
* Mac OS X v10.6 and later for hard drive and file sizes
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
4DOS is a command-line interpreter by JP Software, designed to replace the default command interpreter COMMAND.COM in Microsoft DOS and Windows. It was written by Rex C. Conn and Tom Rawson and first released in 1989. Compared to the default, ...
(uses lowercase letters as decimal and uppercase letters as binary prefixes)
Computer hardware
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
Memory is the faculty of the mind by which data or information is encoded, stored, and retrieved when needed. It is the retention of information over time for the purpose of influencing future action. If past events could not be remembered, ...
such as RAM
Ram, ram, or RAM may refer to:
Animals
* A male sheep
* Ram cichlid, a freshwater tropical fish
People
* Ram (given name)
* Ram (surname)
* Ram (director) (Ramsubramaniam), an Indian Tamil film director
* RAM (musician) (born 1974), Dutch
* ...
and ROM
Rom, or ROM may refer to:
Biomechanics and medicine
* Risk of mortality, a medical classification to estimate the likelihood of death for a patient
* Rupture of membranes, a term used during pregnancy to describe a rupture of the amniotic sac
* ...
are given using customary binary prefixes (kilo, mega, and giga). This includes some flash memory
Flash memory is an electronic non-volatile computer memory storage medium that can be electrically erased and reprogrammed. The two main types of flash memory, NOR flash and NAND flash, are named for the NOR and NAND logic gates. Both us ...
, like EEPROM
EEPROM (also called E2PROM) stands for electrically erasable programmable read-only memory and is a type of non-volatile memory used in computers, usually integrated in microcontrollers such as smart cards and remote keyless systems, or as a ...
s. For example, a "512-megabyte" memory module is bytes (512 × , or ).
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,[
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and uses those definitions in later memory standards[
][
][
][
][
] (See also JEDEC memory standards
The JEDEC memory standards are the specifications for semiconductor memory circuits and similar storage devices promulgated by the Joint Electron Device Engineering Council (JEDEC) Solid State Technology Association, a semiconductor trade and eng ...
.)
Many computer programming tasks reference memory in terms of powers of two
A power of two is a number of the form where is an integer, that is, the result of exponentiation with number two as the base and integer as the exponent.
In a context where only integers are considered, is restricted to non-negative ...
because of the inherent binary design of current hardware addressing systems. For example, a 16-bit processor register can reference at most items (bytes, words, or other objects); this is conveniently expressed as "64K" items. An operating system might map memory as 4096-byte pages
Page most commonly refers to:
* Page (paper), one side of a leaf of paper, as in a book
Page, PAGE, pages, or paging may also refer to:
Roles
* Page (assistance occupation), a professional occupation
* Page (servant), traditionally a young mal ...
, in which case exactly 8192 pages could be allocated within bytes of memory: "8K" (8192) pages of "4 kilobytes" (4096 bytes) each within "32 megabytes" (32 MiB) of memory.
Hard disk drives
All hard disk
A hard disk drive (HDD), hard disk, hard drive, or fixed disk is an electro-mechanical data storage device that stores and retrieves digital data using magnetic storage with one or more rigid rapidly rotating platters coated with magnet ...
drive manufacturers state capacity using SI prefixes
A metric prefix is a unit prefix that precedes a basic unit of measure to indicate a multiple or submultiple of the unit. All metric prefixes used today are decadic. Each prefix has a unique symbol that is prepended to any unit symbol. The pre ...
.
Flash drives
USB flash drive
A USB flash drive (also called a thumb drive) is a data storage device that includes flash memory with an integrated USB interface. It is typically removable, rewritable and much smaller than an optical disc. Most weigh less than . Since firs ...
s, flash-based memory cards like CompactFlash
CompactFlash (CF) is a flash memory mass storage device used mainly in portable electronic devices. The format was specified and the devices were first manufactured by SanDisk in 1994.
CompactFlash became one of the most successful of the e ...
or Secure Digital
Secure Digital, officially abbreviated as SD, is a proprietary format, proprietary non-volatile memory, non-volatile Flash memory, flash memory card format developed by the SD Association, SD Association (SDA) for use in portable devices.
The s ...
, and flash-based solid-state drive
A solid-state drive (SSD) is a solid-state storage device that uses integrated circuit assemblies to store data persistently, typically using flash memory, and functioning as secondary storage in the hierarchy of computer storage. It is ...
s (SSDs) use SI prefixes
A metric prefix is a unit prefix that precedes a basic unit of measure to indicate a multiple or submultiple of the unit. All metric prefixes used today are decadic. Each prefix has a unique symbol that is prepended to any unit symbol. The pre ...
;
for example, a "256 MB" flash card provides at least 256 million bytes (), not 256×1024×1024 (). 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 Wear leveling (also written as wear levelling) is a technique Wear leveling techniques for flash memory systems. for prolonging the service life of some kinds of erasable computer storage media, such as flash memory, which is used in solid-state d ...
, error correction, sparing, and metadata needed by the device's internal firmware.
Floppy drives
Floppy disk
A floppy disk or floppy diskette (casually referred to as a floppy, or a diskette) is an obsolescent type of disk storage composed of a thin and flexible disk of a magnetic storage medium in a square or nearly square plastic enclosure lined w ...
s 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 3.5-inch high density. This has a formatted capacity of 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.
When these disks were commonplace, most operating systems displayed the capacity using "MB" in the customary binary sense, resulting in a display of "1.4 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.[ "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."]
The earlier "1200 KB" ( bytes) 5.25-inch diskette sold with the IBM PC AT
The IBM Personal Computer/AT (model 5170, abbreviated as IBM AT or PC/AT) was released in 1984 as the fourth model in the IBM Personal Computer line, following the IBM PC/XT and its IBM Portable PC variant. It was designed around the Intel 8028 ...
was marketed as "1.2 MB" (). 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 -byte capacity, and the original "360KB" double sided, double density disk drive used on the IBM PC had a -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
In computing and optical disc recording technologies, an optical disc (OD) is a flat, usually circular disc that encodes binary data (bits) in the form of pits and lands on a special material, often aluminum, on one of its flat surfaces. ...
storage media like DVD
The DVD (common abbreviation for Digital Video Disc or Digital Versatile Disc) is a digital optical disc data storage format. It was invented and developed in 1995 and first released on November 1, 1996, in Japan. The medium can store any kind ...
, Blu-ray Disc
The Blu-ray Disc (BD), often known simply as Blu-ray, is a Digital media, digital optical disc data storage format. It was invented and developed in 2005 and released on June 20, 2006 worldwide. It is designed to supersede the DVD format, and c ...
, HD DVD
HD DVD (short for High Definition Digital Versatile Disc) is an obsolete high-density optical disc format for storing data and playback of high-definition video. Supported principally by Toshiba, HD DVD was envisioned to be the successor to th ...
and magneto-optical (MO) are given using SI decimal prefixes. A "4.7 GB" DVD has a nominal capacity of about 4.38 GiB
The byte is a unit of digital information that most commonly consists of eight bits. Historically, the byte was the number of bits used to encode a single character of text in a computer and for this reason it is the smallest addressable unit ...
.[Understanding Recordable and Rewritable DVD](_blank)
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).
Tape drives and media
Tape drive and media manufacturers use SI decimal prefixes to identify capacity.
Data transmission and clock rates
Certain units are always used with SI decimal prefixes even in computing contexts.
Two examples are hertz
The hertz (symbol: Hz) is the unit of frequency in the International System of Units (SI), equivalent to one event (or cycle) per second. The hertz is an SI derived unit whose expression in terms of SI base units is s−1, meaning that on ...
(Hz), which is used to measure the clock rate
In computing, the clock rate or clock speed typically refers to the frequency at which the clock generator of a processor can generate pulses, which are used to synchronize the operations of its components, and is used as an indicator of the pr ...
s of electronic components, and to bit/s and B/s, which are used to measure data transmission speed.
* A 1 GHz processor receives clock ticks per second.
* A sound file sampled at has samples per second.
* A MP3
MP3 (formally MPEG-1 Audio Layer III or MPEG-2 Audio Layer III) is a coding format for digital audio developed largely by the Fraunhofer Society in Germany, with support from other digital scientists in the United States and elsewhere. Origin ...
stream consumes bits (16 kilobytes, ) per second.
* A Internet connection can transfer bits per second ( bytes per second ≈ , assuming an 8-bit byte and no overhead)
* A Ethernet connection can transfer at nominal speed of bits per second ( bytes per second ≈ , assuming an 8-bit byte and no overhead)
* A 56k modem transfers bits per second ≈ .
Bus
A bus (contracted from omnibus, with variants multibus, motorbus, autobus, etc.) is a road vehicle that carries significantly more passengers than an average car or van. It is most commonly used in public transport, but is also in use for cha ...
clock speeds and therefore bandwidths are both quoted using SI decimal prefixes.
* PC3200 memory on a double data rate
In computing, a computer bus operating with double data rate (DDR) transfers data on both the rising and falling edges of the clock signal. This is also known as double pumped, dual-pumped, and double transition. The term toggle mode is used i ...
bus, transferring 8 bytes per cycle with a clock speed of ( cycles per second) has a bandwidth of = B/s = (about ).
* A PCI-X
PCI-X, short for Peripheral Component Interconnect eXtended, is a computer bus and expansion card standard that enhances the 32-bit PCI local bus for higher bandwidth demanded mostly by servers and workstations. It uses a modified protocol t ...
bus at ( cycles per second), 64 bits per transfer, has a bandwidth of transfers per second × 64 bits per transfer = bit/s, or B/s, usually quoted as (about ).
Use by industry
IEC prefixes are used by Toshiba
, commonly known as Toshiba and stylized as TOSHIBA, is a Japanese multinational conglomerate corporation headquartered in Minato, Tokyo, Japan. Its diversified products and services include power, industrial and social infrastructure system ...
, IBM, HP to advertise or describe some of their products. According to one HP brochure
" 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. The IBM Style Guide reads 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.
Other uses
The international standard ISO 80000-1 defines the prefixes kibi-, mebi-, gibi- ... without limiting their application to information technology
Information technology (IT) is the use of computers to create, process, store, retrieve, and exchange all kinds of data . and information. IT forms part of information and communications technology (ICT). An information technology system (I ...
. Uses of binary prefixes for quantities other than bits or bytes include their use to indicate binary multiples of the frequency unit hertz
The hertz (symbol: Hz) is the unit of frequency in the International System of Units (SI), equivalent to one event (or cycle) per second. The hertz is an SI derived unit whose expression in terms of SI base units is s−1, meaning that on ...
(Hz), for example the kibihertz
ISO 80000 or IEC 80000 is an international standard introducing the International System of Quantities (ISQ).
It was developed and promulgated jointly by the International Organization for Standardization (ISO) and the International Electrotech ...
(symbol KiHz) is 1024 Hz.
(22 pages)
See also
* Binary engineering notation
Engineering notation or engineering form (also technical notation) is a version of scientific notation in which the exponent of ten must be divisible by three (i.e., they are powers of a thousand, but written as, for example, 106 instead of 1000 ...
* B notation (scientific notation)
Scientific notation is a way of expressing numbers that are too large or too small (usually would result in a long string of digits) to be conveniently written in decimal form. It may be referred to as scientific form or standard index form, o ...
* ISO/IEC 80000
ISO 80000 or IEC 80000 is an international standard introducing the International System of Quantities (ISQ).
It was developed and promulgated jointly by the International Organization for Standardization (ISO) and the International Electrote ...
* Nibble
In computing, a nibble (occasionally nybble, nyble, or nybl to match the spelling of byte) is a four-bit aggregation, or half an octet. It is also known as half-byte or tetrade. In a networking or telecommunication context, the nibble is oft ...
* Octet
Octet may refer to:
Music
* Octet (music), ensemble consisting of eight instruments or voices, or composition written for such an ensemble
** String octet, a piece of music written for eight string instruments
*** Octet (Mendelssohn), 1825 compos ...
Definitions
References
Further reading
* – An introduction to binary prefixes
*
*
* —a 1996–1999 paper on bits, bytes, prefixes and symbols
*
* —Another description of binary prefixes
* —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
SI/Binary Prefix Converter
Storage Capacity Measurement Standards
{{DEFAULTSORT:Binary Prefix
Measurement
Naming conventions
Units of information
Numeral systems