Binary prefix


A binary prefix is a unit prefix for multiples of units in data processing, data transmission, and digital information, notably the bit and the byte, to indicate multiplication by a power of 2.
The computer industry has historically used the units kilobyte, megabyte, and gigabyte, and the corresponding symbols KB, MB, and GB, in at least two slightly different measurement systems. In citations of main memory capacity, gigabyte customarily means bytes. As this is a power of 1024, and 1024 is a power of two, this usage is referred to as a binary measurement.
In most other contexts, the industry uses the multipliers kilo, mega, giga, etc., in a manner consistent with their meaning in the International System of Units, namely as powers of 1000. For example, a 500 gigabyte hard disk holds bytes, and a 1 Gbit/s Ethernet 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.
The use of the same unit prefixes with two different meanings has caused confusion. Starting around 1998, the International Electrotechnical Commission and several other standards and trade organizations addressed 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 requires that SI prefixes only be used in the decimal sense: kilobyte and megabyte denote one thousand bytes and one million bytes respectively, while new terms such as kibibyte, mebibyte and gibibyte, having the symbols KiB, MiB, and GiB, denote 1024 bytes, bytes, and bytes, respectively. In 2008, the IEC prefixes were incorporated into the international standard system of units used alongside the International System of Quantities.

History

Main memory

Early computers used one of two addressing methods to access the system memory; binary or decimal.
For example, the IBM 701 used binary and could address 2048 words of 36 bits each, while the IBM 702 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 210, or 1024. As storage capacities increased, several different methods were developed to abbreviate these quantities.
The method most commonly used today uses prefixes such as kilo, mega, giga, and corresponding symbols K, M, and G, which the computer industry originally adopted from the metric system. 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 after the International System of Units, 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.
Gene Amdahl's seminal 1964 article on IBM System/360 used "1K" to mean 1024.
This style was used by other computer vendors, the CDC 7600 System Description 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".
This style was used from about 1965 to 1975.
These two styles were used loosely around the same time, sometimes by the same company. In discussions of binary-addressed memories, the exact size was evident from context. The HP 21MX real-time computer denoted as "196K" and as "1M",
while the HP 3000 business computer 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 10242 bytes, and later "gigabyte" for 10243 bytes. For example, a "512 megabyte" RAM module is 512×10242 bytes, 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 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-11/70
and gigabyte the 30-bit addressing DEC VAX-11/780.
In 1998, the International Electrotechnical Commission IEC introduced the binary prefixes kibi, mebi, gibi... to mean 1024, 10242, 10243 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 in 2009.

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, 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. It was introduced in September 1956.
In the 1960s most disk drives used IBM's variable block length format, called Count Key Data.
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 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 and 1440 sectors 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" = 210 × 103 = 1 024 000 bytes.
In contrast, hard disk drive manufacturers used megabytes or MB, meaning 106 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 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, 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 and extensively advertised and reported as a "10 MB" 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 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 . Operating systems such as Microsoft Windows that display hard drive sizes using the customary binary prefix "GB" would display this as "279.4 GB". On the other hand, macOS has since version 10.6 shown hard drive size using decimal prefixes.
However, other usages still occur. Seagate has specified data transfer rates in select manuals of some hard drives in both IEC and decimal units.
"Advanced Format" drives using 4096-byte sectors are described as having "4K sectors."

Information transfer and clock rates

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.
Similarly, digital information transfer rates are quoted using decimal prefixes:
By the mid-1970s it was common to see K meaning 1024 and the occasional M meaning for words or bytes of main memory 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 hard disk drive was introduced in 2007.
The dual usage of the kilo, mega, and giga 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
defined dual uses for kilo and mega.
The binary units Kbyte and Mbyte were formally defined in ANSI/IEEE Std 1212–1991.
Many dictionaries have noted the practice of using traditional prefixes to indicate binary multiples.
Oxford online dictionary defines, for example, megabyte as: "Computing: a unit of information equal to one million or bytes."
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 or 230 bytes.
Kilobyte, Kbyte, and KB are equivalent units and all are defined in the obsolete standard, IEEE 100–2000.
The hardware industry measures system memory using the binary meaning while magnetic disk storage uses the SI definition. However, many exceptions exist. Labeling of diskettes uses the megabyte to denote 1024×1000 bytes. In the optical disks market, compact discs use MB to mean 10242 bytes while DVDs 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 21% for the yotta prefix.

Consumer confusion

In the early days of 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.
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 "160 GB" as "149.05 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 MS-DOS or PC DOS CHKDSK command.

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.

Recent cases

The most recent cases did not settle and are currently on appeal. Notably, the defendant persuaded the district court of the Northern District of California to enter judgment in its favor by citing to a publication from the National Institute of Technology from 1998, which was published at a time that USB Drives did not exist and memory storage in gigabytes was not commercially feasible for the average consumer. However, the 1998 NIST publication was superseded in a 2008 NIST publication. The superseding publication does not maintain the same positions regarding the definition of gigabyte and megabyte as the 1998 publication. Additionally, NIST's 2008 Guide for the Use of the International System of Units makes clear that confusion of use of units is to be avoided, even if traditional units of must be used. Guide at p. 2. Thus, the litigation has not ended in favor of the manufacturers, and will not end until the appeals conclude along with any other suits that may be filed.

Early cases

Earlier cases 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 Company, Kingston Technology Company, Inc., Memorex Products, Inc.; PNY Technologies Inc., SanDisk Corporation, Verbatim Corporation, and Viking Interworks alleging that their descriptions of the capacity of their flash memory cards were false and misleading.
Vroegh claimed that a 256 MB Flash Memory Device had only 244 MB of accessible memory. "Plaintiffs allege that Defendants marketed the memory capacity of their products by assuming that one megabyte equals one million bytes and one gigabyte equals one billion bytes."
The plaintiffs wanted the defendants to use the traditional values of 10242 for megabyte and 10243 for gigabyte.
The plaintiffs acknowledged that the IEC and IEEE standards define a MB as one million bytes but stated that the industry has largely ignored the IEC standards.
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 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 $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.

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

A lawsuit was filed against Seagate Technology, alleging that Seagate overrepresented the amount of usable storage by 7% on hard drives sold between March 22, 2001 and September 26, 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.

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 were made in 1968. Donald Morrison proposed to use the Greek letter kappa to denote 1024, κ2 to denote 10242, and so on.
Wallace Givens 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 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 3×220, 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". Donald Knuth, who uses decimal notation like 1 MB = 1000 kB, expressed "astonishment" that the IEC proposal was adopted, calling them "funny-sounding" and opining that proponents were assuming "that standards are automatically adopted just because they are there." Knuth proposed that the powers of 1024 be designated as "large kilobytes" and "large megabytes". Double prefixes were already abolished from SI, however, having a multiplicative meaning, 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", were first proposed by the International Union of Pure and Applied Chemistry's Interdivisional Committee on Nomenclature and Symbols in 1995. At that time, it was proposed that the terms kilobyte and megabyte be used only for 103 bytes and 106 bytes, respectively. The new prefixes kibi, mebi, gibi and tebi 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 began to collaborate with the International Organization for Standardization and International Electrotechnical Commission 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 therefore identical to the corresponding SI prefixes, except for "K", which is used interchangeably with "k", whereas in SI, only the lower-case k represents 1000.
The IEEE decided that their standards would use the prefixes kilo, etc. with their metric definitions, but allowed the binary definitions to be used in an interim period as long as such usage was explicitly pointed out on a case-by-case basis.

Adoption by IEC, NIST and ISO

In January 1999, the IEC published the first international standard with the new prefixes, extended up to pebi and exbi.
The IEC 60027-2 Amendment 2 also states that the IEC position is the same as that of BIPM ; 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, defined them only up to exbi, but in 2005, the third edition added prefixes zebi and yobi, thus matching all SI prefixes with binary counterparts.
The harmonized ISO/IEC IEC 80000-13:2008 standard cancels and replaces subclauses 3.8 and 3.9 of IEC 60027-2:2005. 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, 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, which is 1 kibibit."

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 supports the ISO/IEC standards for
"Prefixes for binary multiples" and has a 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 describes the IEC prefixes in its online dictionary. The JEDEC standards for semiconductor memory use the customary prefix symbols K, M and G in the binary sense.
On 19 March 2005, the IEEE standard IEEE 1541-2002 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 or Computer.
The International Bureau of Weights and Measures, which maintains the International System of Units, 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 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 adopted the IEC-recommended binary prefixes via the harmonization document HD 60027-2:2003-03.
The European Union has required the use of the IEC binary prefixes since 2007.

Current practice

Most computer hardware uses SI prefixes 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
On the other hand, flash memory, like that found in solid state drives, mostly uses SI prefixes 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 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, file sizes were typically reported by the operating system without any prefixes. Today, most operating systems report file sizes with prefixes.
, most software does not distinguish symbols for binary and decimal prefixes.
The IEC binary naming convention has been adopted by a few, but this is not 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/cfdisk, parted, and apt-get use SI prefixes with their decimal meaning.
Example of the use of IEC binary prefixes in the Linux operating system displaying traffic volume on a network interface in kibibytes and mebibytes, as obtained with the ifconfig utility:

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

Software that uses standard SI prefixes for powers of 1000, but not IEC binary prefixes for powers of 1024, includes:
Software that supports decimal prefixes for powers of 1000 and binary prefixes for powers of 1024 includes:
Software that uses IEC binary prefixes for powers of 1024 and uses standard SI prefixes for powers of 1000 includes:
Hardware types that use powers-of-1024 multipliers, such as memory, continue to be marketed with customary binary prefixes.

Computer memory

Measurements of most types of electronic memory such as RAM and ROM are given using customary binary prefixes. This includes some flash memory, like EEPROMs. For example, a "512-megabyte" memory module is 512×220 bytes.
JEDEC Solid State Technology Association, the semiconductor engineering standardization body of the Electronic Industries Alliance, continues to include the customary binary definitions of kilo, mega and giga in their Terms, Definitions, and Letter Symbols document,
and uses those definitions in later 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 ; 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 bytes of memory: "8K" pages of "4 kilobytes" each within "32 megabytes" of memory.

Hard disk drives

All hard disk drive manufacturers state capacity using SI prefixes.

Flash drives

s, flash-based memory cards like CompactFlash or Secure Digital, and flash-based SSDs use SI prefixes;
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, error correction, sparing, and metadata needed by the device's internal firmware.

Floppy drives

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 3½-inch high density. This has a formatted capacity of bytes or 1440 KB. 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". 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 earlier "1200 KB" 5¼-inch diskette sold with the IBM PC AT 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 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, leading to more irregularities.

Optical discs

The capacities of most optical disc storage media like DVD, Blu-ray Disc, HD DVD and magneto-optical are given using SI decimal prefixes.
A "4.7 GB" DVD has a nominal capacity of about 4.38 GiB. However, CD capacities are always given using customary binary prefixes. Thus a "700-MB" CD has a nominal capacity of about 700 MiB.

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, which is used to measure the clock rates of electronic components, and bit/s, used to measure data transmission speed.
Bus clock speeds and therefore bandwidths are both quoted using SI decimal prefixes.
IEC prefixes are used by Toshiba, IBM, HP to advertise or describe some of their products. According to one HP brochure, "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. The IBM Style Guide reads
To help avoid inaccuracy and potential ambiguity, the International Electrotechnical Commission in 2000 adopted a set of prefixes specifically for binary multipliers. Their use is now supported by the United States National Institute of Standards and Technology 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. 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.

Definitions