Binary prefix

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Prefixes for decimal and binary multiples
Decimal
Value SI
1000103k kilo
10002106M mega
10003109G giga
100041012T tera
100051015P peta
100061018E exa
100071021Z zetta
100081024Y yotta
100091027R ronna
1000101030Q quetta
Binary
Value IEC JEDEC
1024210Ki kibi Kkilo
10242220Mi mebi Mmega
10243230Gi gibi Ggiga
10244240Ti tebi Ttera
10245250Pi pebi —
10246260Ei exbi —
10247270Zi zebi —
10248280Yi yobi —
—
—

A binary prefix is a unit prefix that indicates a multiple of a unit of measurement by an integer power of two. The most commonly used binary prefixes are kibi (symbol Ki, meaning 210 = 1024), mebi (Mi, 220 = 1048576), and gibi (Gi, 230 = 1073741824). They are most often used in information technology as multipliers of bit and byte, when expressing the capacity of storage devices or the size of computer files.

Contents

The binary prefixes "kibi", "mebi", etc. were defined in 1999 by the International Electrotechnical Commission (IEC), in the IEC 60027-2 standard (Amendment 2). They were meant to replace the metric (SI) decimal power prefixes, such as "kilo" (k, 103 = 1000), "mega" (M, 106 = 1000000) and "giga" (G, 109 = 1000000000), [1] that were commonly used in the computer industry to indicate the nearest powers of two. For example, a memory module whose capacity was specified by the manufacturer as "2 megabytes" or "2 MB" would hold 2 × 220 = 2097152 bytes, instead of 2 × 106 = 2000000.

On the other hand, a hard disk whose capacity is specified by the manufacturer as "10 gigabytes" or "10 GB", holds 10 × 109 = 10000000000 bytes, or a little more than that, but less than 10 × 230 = 10737418240 and a file whose size is listed as "2.3 GB" may have a size closer to 2.3 × 230 ≈ 2470000000 or to 2.3 × 109 = 2300000000, depending on the program or operating system providing that measurement. This kind of ambiguity is often confusing to computer system users and has resulted in lawsuits. [2] [3] The IEC 60027-2 binary prefixes have been incorporated in the ISO/IEC 80000 standard and are supported by other standards bodies, including the BIPM, which defines the SI system, [1] : p.121  the US NIST, [4] [5] and the European Union.

Prior to the 1999 IEC standard, some industry organizations, such as the Joint Electron Device Engineering Council (JEDEC), attempted to redefine[ citation needed ] the terms kilobyte, megabyte, and gigabyte, and the corresponding symbols KB, MB, and GB in the binary sense, for use in storage capacity measurements. However, other computer industry sectors (such as magnetic storage) continued using those same terms and symbols with the decimal meaning. Since then, the major standards organizations have expressly disapproved the use of SI prefixes to denote binary multiples, and recommended or mandated the use of the IEC prefixes for that purpose, but the use of SI prefixes in this sense has persisted in some fields.

Definitions

Specific units of IEC 60027-2 A.2 and ISO/IEC 80000:13-2008
IEC prefixRepresentations
NameSymbolBase 2Base 1024ValueBase 10
kibiKi210102411024= 1.024×103
mebiMi220102421048576≈ 1.049×106
gibiGi230102431073741824≈ 1.074×109
tebiTi240102441099511627776≈ 1.100×1012
pebiPi250102451125899906842624≈ 1.126×1015
exbiEi260102461152921504606846976≈ 1.153×1018
zebiZi270102471180591620717411303424≈ 1.181×1021
yobiYi280102481208925819614629174706176≈ 1.209×1024

In 2022, the International Bureau of Weights and Measures (BIPM) adopted the decimal prefixes ronna for 10009 and quetta for 100010. [6] [7] In analogy to the existing binary prefixes, a consultation paper of the International Committee for Weights and Measures' Consultative Committee for Units (CCU) suggested the prefixes robi (Ri, 10249) and quebi (Qi, 102410) for their binary counterparts, [8] but as of 2022, no corresponding binary prefixes have been adopted. [9]

Comparison of binary and decimal prefixes

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.

PrefixBinary ÷ DecimalDecimal ÷ Binary
kilokibi1.024 (+2.4%)
 
0.9766 (−2.3%)
 
megamebi1.049 (+4.9%)
 
0.9537 (−4.6%)
 
gigagibi1.074 (+7.4%)
 
0.9313 (−6.9%)
 
teratebi1.100 (+10.0%)
 
0.9095 (−9.1%)
 
petapebi1.126 (+12.6%)
 
0.8882 (−11.2%)
 
exaexbi1.153 (+15.3%)
 
0.8674 (−13.3%)
 
zettazebi1.181 (+18.1%)
 
0.8470 (−15.3%)
 
yottayobi1.209 (+20.9%)
 
0.8272 (−17.3%)
 
ronna—1.238 (+23.8%)
 
0.8078 (−19.2%)
 
quetta—1.268 (+26.8%)
 
0.7889 (−21.1%)
 

History

Early prefixes

The original metric system adopted by France in 1795 included two binary prefixes named double- (2×) and demi- (⁠1/2⁠×). [10] However, these were not retained when the SI prefixes were internationally adopted by the 11th CGPM conference in 1960.

Storage capacity

Main memory

Early computers used one of two addressing methods to access the system memory; binary (base 2) or decimal (base 10). [11] For example, the IBM 701 (1952) used a binary methods and could address 2048 words of 36 bits each, while the IBM 702 (1953) used a decimal system, 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 states of their address lines map to a valid address, allowing easy aggregation into a larger block of memory with contiguous addresses.

While early documentation specified those memory sizes as exact numbers such as 4096, 8192, or 16384 units (usually words, bytes, or bits), computer professionals also started using the long-established metric system prefixes "kilo", "mega", "giga", etc., defined to be powers of 10, [1] to mean instead the nearest powers of two; namely, 210 = 1024, 220 = 10242, 230 = 10243, etc. [12] [13] The corresponding metric prefix symbols ("k", "M", "G", etc.) where used with the same binary meanings. [14] [15] The symbol for 210 = 1024 could be written either in lower case ("k") [16] [17] [18] or in uppercase ("K"). The latter was often used intentionally to indicate the binary rather than decimal meaning. [19] This convention, which could not be extended to higher powers, was widely used in the documentation of the IBM 360 (1964) [19] and of the IBM System/370 (1972), [20] of the CDC 7600, [21] of the DEC PDP-11/70 (1975) [22] and of the DEC VAX-11/780 (1977).[ citation needed ]

In other documents, however, the metric prefixes and their symbols were used to denote powers of 10, but usually with the understanding that the values given were approximate, often truncated down. Thus, for example, a 1967 document by Control Data Corporation (CDC) abbreviated "216 = 64 × 1024 = 65536 words" as "65K words" (rather than "64K" or "66K"), [23] while the documentation of the HP 21MX real-time computer (1974) denoted 3 × 216 = 192 × 1024 = 196608 as "196K" and 220 = 1048576 as "1M". [24]

These three possible meanings of "k" and "K" ("1024", "1000", or "approximately 1000") were used loosely around the same time, sometimes by the same company. The HP 3000 business computer (1973) could have "64K", "96K", or "128K" bytes of memory. [25] The use of SI prefixes, and the use of "K" instead of "k" remained popular in computer-related publications well into the 21st century, although the ambiguity persisted. The correct meaning was often clear from the context; for instance, in a binary-addressed computer, the true memory size had to be either a power of 2, or a small integer multiple thereof. Thus a "512 megabyte" RAM module was generally understood to have 512 × 10242 = 536870912 bytes, rather than 512000000.

Hard disks

In specifying disk drive capacities, manufacturers have always used conventional decimal SI prefixes representing powers of 10. Storage in a rotating disk drive is organized in platters and tracks whose sizes and counts are determined by mechanical engineering constraints so that the capacity of a disk drive has hardly ever been a simple multiple of a power of 2. For example, the first commercially sold disk drive, the IBM 350 (1956), had 50 physical disk platters containing a total of 50000 sectors of 100 characters each, for a total quoted capacity of 5 million characters. [26]

Moreover, since the 1960s, many disk drives used IBM's disk format, where each track was divided into blocks of user-specified size; and the block sizes were recorded on the disk, subtracting from the usable capacity. For example, the IBM 3336 disk pack was quoted to have a 200-megabyte capacity, achieved only with a single 13030-byte block in each of its 808 × 19 tracks.

Decimal megabytes were used for disk capacity by the CDC in 1974. [27] The Seagate ST-412, [28] one of several types installed in the IBM PC/XT, [29] had a capacity of 10027008 bytes when formatted as 306 × 4 tracks and 32 256-byte sectors per track, which was quoted as "10 MB". [30] Similarly, a "300 GB" hard drive can be expected to offer only slightly more than 300×109 = 300000000000, bytes, not 300 × 230 (which would be about 322×109 bytes or "322 GB"). The first terabyte (SI prefix, 1000000000000 bytes) hard disk drive was introduced in 2007. [31] Decimal prefixes were generally used by information processing publications when comparing hard disk capacities. [32]

Some programs and operating systems, such as Microsoft Windows, still use "MB" and "GB" to denote binary prefixes even when displaying disk drive capacities and file sizes, as did Classic Mac OS. Thus, for example, the capacity of a "10 MB" (decimal "M") disk drive could be reported as "9.56 MB", and that of a "300 GB" drive as "279.4 GB". Some operating systems, such as Mac OS X, [33] Ubuntu, [34] and Debian, [35] have been updated to use "MB" and "GB" to denote decimal prefixes when displaying disk drive capacities and file sizes. Some manufacturers, such as Seagate Technology, have released recommendations stating that properly-written software and documentation should specify clearly whether prefixes such as "K", "M", or "G" mean binary or decimal multipliers. [36] [37]

Floppy disks

Floppy disks used a variety of formats, and their capacities was usually specified with SI-like prefixes "K" and "M" with either decimal or binary meaning. The capacity of the disks was often specified without accounting for the internal formatting overhead, leading to more irregularities.

The early 8-inch diskette formats could contain less than a megabyte with the capacities of those devices specified in kilobytes, kilobits or megabits. [38] [39]

The 5.25-inch diskette sold with the IBM PC AT could hold 1200 × 1024 = 1228800 bytes, and thus was marketed as "1200 KB" with the binary sense of "KB". [40] However, the capacity was also quoted "1.2 MB", [41] which was a hybrid decimal and binary notation, since the "M" meant 1000 × 1024. The precise value was 1.2288 MB (decimal) or 1.171875 MiB (binary).

The 5.25-inch Apple Disk II had 256 bytes per sector, 13 sectors per track, 35 tracks per side, or a total capacity of 116480 bytes. It was later upgraded to 16 sectors per track, giving a total of 140 × 210 = 143360 bytes, which was described as "140KB" using the binary sense of "K".

The most recent version of the physical hardware, the "3.5-inch diskette" cartridge, had 720 512-byte blocks (single-sided). Since two blocks comprised 1024 bytes, the capacity was quoted "360 KB", with the binary sense of "K". On the other hand, the quoted capacity of "1.44 MB" of the High Density ("HD") version was again a hybrid decimal and binary notation, since it meant 1440 pairs of 512-byte sectors, or 1440 × 210 = 1474560 bytes. Some operating systems displayed the capacity of those disks using the binary sense of "MB", as "1.4 MB" (which would be 1.4 × 220 ≈ 1468000 bytes). User complaints forced both Apple[ citation needed ] and Microsoft [42] to issue support bulletins explaining the discrepancy.

Optical disks

When specifying the capacities of optical compact discs, "megabyte" and "MB" usually meant 10242 bytes. Thus a "700-MB" (or "80-minute") CD has a nominal capacity of about 700 MiB, which is approximately 730 MB (decimal). [43]

On the other hand, capacities of other optical disc storage media like DVD, Blu-ray Disc, HD DVD and magneto-optical (MO) have been generally specified in decimal gigabytes ("GB"), that is, 10003 bytes. In particular, a typical "4.7 GB" DVD has a nominal capacity of about 4.7×109 bytes, which is about 4.38 GiB. [44]

Tape drives and media

Tape drive and media manufacturers have generally used SI decimal prefixes to specify the maximum capacity, [45] [46] although the actual capacity would depend on the block size used when recording.

Data 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 4770000 Hz.

Similarly, digital information transfer rates are quoted using decimal prefixe. The Parallel ATA "100 MB/s" disk interface can transfer 100000000 bytes per second, and a "56 Kb/s" modem transmits 56000 bits per second. Seagate specified the sustained transfer rate of some hard disk drive models with both decimal and IEC binary prefixes. [36] The standard sampling rate of music compact disks, quoted as 44.1 kHz, is indeed 44100 samples per second.[ citation needed ] A "1 Gb/s" Ethernet interface can receive or transmit up to 109 bits per second, or 125000000 bytes per second within each packet. A "56k" modem can encode or decode up to 56000 bits per second.

Decimal SI prefixes are also generally used for processor-memory data transfer speeds. A PCI-X bus with 66 MHz clock and 64 bits wide can transfer 66000000 64-bit words per second, or 4224000000 bit/s = 528000000 B/s, which is usually quoted as 528 MB/s. A PC3200 memory on a double data rate bus, transferring 8 bytes per cycle with a clock speed of 200 MHz has a bandwidth of 200000000 × 8 × 2 = 3200000000 B/s, which would be quoted as 3.2 GB/s.

Ambiguous standards

The ambiguous usage of the prefixes "kilo ("K" or "k"), "mega" ("M"), and "giga" ("G"), as meaning both powers of 1000 or (in computer contexts) of 1024, has been recorded in popular dictionaries, [47] [48] [49] and even in some obsolete standards, such as ANSI/IEEE 1084-1986 [50] and ANSI/IEEE 1212-1991, [51] IEEE 610.10-1994, [52] and IEEE 100-2000. [53] Some of these standards specifically limited the binary meaning to multiples of "byte" ("B") or "bit" ("b").

Early binary prefix proposals

Before the IEC standard, several alternative proposals existed for unique binary prefixes, starting in the late 1960s. In 1996, Markus Kuhn proposed the extra prefix "di" and the symbol suffix or subscript "2" to mean "binary"; so that, for example, "one dikilobyte" would mean "1024 bytes", denoted "K2B" or "K2B". [54]

In 1968, Donald Morrison proposed to use the Greek letter kappa (κ) to denote 1024, κ2 to denote 10242, and so on. [55] (At the time, memory size was small, and only K was in widespread use.) In the same year, Wallace Givens responded with a suggestion 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. [56] Bruce Alan Martin of Brookhaven National Laboratory proposed that, instead of prefixes, binary powers of two were indicated by the letter B followed by the exponent, similar to E in decimal scientific notation. Thus one would write 3B20 for 3 × 220. [57] This convention is still used on some calculators to present binary floating point-numbers today. [58]

In 1969, Donald Knuth, who uses decimal notation like 1 MB = 1000 kB, [59] proposed that the powers of 1024 be designated as "large kilobytes" and "large megabytes", with abbreviations KKB and MMB. [60]

Consumer confusion

The ambiguous meanings of "kilo", "mega", "giga", etc., has caused significant consumer confusion, especially in the personal computer era. A common source of confusion was the discrepancy between the capacities of hard drives specified by manufacturers, using those prefixes in the decimal sense, and the numbers reported by operating systems and other software, that used them in the binary sense, such as the Apple Macintosh in 1984. For example, a hard drive marketed as "1 TB" could be reported as having only "931 GB". The confusion was compounded by fact that RAM manufacturers used the binary sense too.

The different interpretations of disk size prefixes 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. [61] [62] [63] [64]

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 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. [65]

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. [66] The consumers could apply for "a discount of ten percent off a future online purchase from Defendants' Online Stores Flash Memory Device". [67]

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. [68]

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. [69]

Western Digital offered to compensate customers with a free download of backup and recovery software valued at US$30. They also paid $500000 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. [70] [71] [72] Western Digital had this footnote in their settlement. "Apparently, Plaintiff believes that he could sue an egg company for fraud for labeling a carton of 12 eggs a 'dozen', because some bakers would view a 'dozen' as including 13 items." [73]

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, 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. [74]

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 1000000000 bytes. [75]

IEC 1999 Standard

In 1995, the International Union of Pure and Applied Chemistry's (IUPAC) Interdivisional Committee on Nomenclature and Symbols (IDCNS) proposed the prefixes "kibi" (short for "kilobinary"), "mebi" ("megabinary"), "gibi" ("gigabinary") and "tebi" ("terabinary"), with respective symbols "kb", "Mb", "Gb" and "Tb", [76] for binary multipliers. The proposal suggested that the SI prefixes should be used only for powers of 10; so that a disk drive capacity of "500 gigabytes", "0.5 terabytes", "500 GB", or "0.5 TB" should all mean 500×109 bytes, exactly or approximately, rather than 500 × 230 (= 536870912000) or 0.5 × 240 (= 549755813888).

The proposal was not accepted by IUPAC at the time, but was taken up in 1996 by the Institute of Electrical and Electronics Engineers (IEEE) in collaboration with the International Organization for Standardization (ISO) and International Electrotechnical Commission (IEC). The prefixes "kibi", "mebi", "gibi" and "tebi" were retained, but with the symbols "Ki" (with capital "K"), "Mi", "Gi" and "Ti" respectively. [77]

In January 1999, the IEC published this proposal, with additional prefixes "pebi" ("Pi") and "exbi" ("Ei"), as an international standard (IEC 60027-2 Amendment 2) [78] [79] [80] The standard reaffirmed the BIPM's position that the SI prefixes should always denote powers of 10. The third edition of the standard, published in 2005, added prefixes "zebi" and "yobi", thus matching all then-defined SI prefixes with binary counterparts. [81]

The harmonized ISO/IEC IEC 80000-13:2008 standard cancels and replaces subclauses 3.8 and 3.9 of IEC 60027-2:2005 (those defining prefixes for binary multiples). The only significant change is the addition of explicit definitions for some quantities. [82] In 2009, the prefixes kibi-, mebi-, etc. were defined by ISO 80000-1 in their own right, independently of the kibibyte, mebibyte, and so on.

The BIPM standard JCGM 200:2012 "International vocabulary of metrology – Basic and general concepts and associated terms (VIM), 3rd edition" lists the IEC binary prefixes and states "SI prefixes refer strictly to powers of 10, and should not be used for powers of 2. For example, 1 kilobit should not be used to represent 1024 bits (210 bits), which is 1 kibibit." [83]

The IEC 60027-2 standard recommended operating systems and other software were updated to use binary or decimal prefixes consistently, but incorrect usage of SI prefixes for binary multiples is still common. At the time, 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. [84]

Other standards bodies and organizations

The IEC standard binary prefixes are supported by other standardization bodies and technical organizations.

The United States National Institute of Standards and Technology (NIST) supports the ISO/IEC standards for "Prefixes for binary multiples" and has a web page [85] 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. [5] NIST has stated the SI prefixes "refer strictly to powers of 10" and that the binary definitions "should not be used" for them. [86]

As of 2014, the microelectronics industry standards body JEDEC describes the IEC prefixes in its online dictionary, but acknowledges that the SI prefixes and the symbols "K", "M" and "G" are still commonly used with the binary sense for memory sizes. [87] [88]

On 19 March 2005, the IEEE standard IEEE 1541-2002 ("Prefixes for Binary Multiples") was elevated to a full-use standard by the IEEE Standards Association after a two-year trial period. [89] [90] as of April 2008, the IEEE Publications division does not require the use of IEC prefixes in its major magazines such as Spectrum [91] or Computer. [92]

The International Bureau of Weights and Measures (BIPM), which maintains the International System of Units (SI), expressly prohibits the use of SI prefixes to denote binary multiples, and recommends the use of the IEC prefixes as an alternative since units of information are not included in the SI. [93] [1]

The Society of Automotive Engineers (SAE) prohibits the use of SI prefixes with anything but a power-of-1000 meaning, but does not cite the IEC binary prefixes. [94]

The European Committee for Electrotechnical Standardization (CENELEC) adopted the IEC-recommended binary prefixes via the harmonization document HD 60027-2:2003-03. [95] The European Union (EU) has required the use of the IEC binary prefixes since 2007. [96]

Current practice

The 536870912-byte capacity of these RAM modules is stated as "512 MB" on the label. Elixir M2U51264DS8HC3G-5T 20060320.jpg
The 536870912-byte capacity of these RAM modules is stated as "512 MB" on the label.
Linux GNOME's partition editor uses IEC prefixes to display partition sizes. The total capacity of the 120 x 10 -byte disk is displayed as "111.79 GiB". GParted 0.3.5 -- 2008, 06.png
Linux GNOME's partition editor uses IEC prefixes to display partition sizes. The total capacity of the 120 × 10 -byte disk is displayed as "111.79 GiB".
GNOME's system monitor uses IEC prefixes to show memory size and networking data rate. GNOME System Monitor memory size and network rate.png
GNOME's system monitor uses IEC prefixes to show memory size and networking data rate.

Some computer industry participants, such as Hewlett-Packard (HP), [97] and IBM [98] [99] have adopted or recommended IEC binary prefixes as part of their general documentation policies.

As of 2023, the use of SI prefixes with the binary meanings is still prevalent for specifying the capacity of the main memory of computers, of RAM, ROM, EPROM, and EEPROM chips and memory modules, and of the cache of computer processors. For example, a "512-megabyte" or "512 MB" memory module holds 512 MiB; that is, 512 × 220 bytes, not 512 × 106 bytes. [100] [101] [102] [103]

JEDEC continues to include the customary binary definitions of "kilo", "mega", and "giga" in the document Terms, Definitions, and Letter Symbols, [104] and, as of 2010, still used those definitions in their memory standards. [105] [106] [107] [108] [109]

On the other hand, the SI prefixes with powers of ten meanings are generally used for the capacity of external storage units, such as disk drives, [110] [111] [112] [113] [114] solid state drives, and USB flash drives, [64] except for some flash memory chips intended to be used as EEPROMs. However, some disk manufacturers have used the IEC prefixes to avoid confusion. [115] The decimal meaning of SI prefixes is usually also intended in measurements of data transfer rates, and clock speeds.[ citation needed ]

Some operating systems and other software use either the IEC binary multiplier symbols ("Ki", "Mi", etc.) [116] [117] [118] [119] [120] [121] or the SI multiplier symbols ("k", "M", "G", etc.) with decimal meaning. Some programs, such as the Linux/GNU ls command, let the user choose between binary or decimal multipliers. However, some continue to use the SI symbols with the binary meanings, even when reporting disk or file sizes. Some programs may also use "K" instead of "k", with either meaning. [122]

Other uses

While the binary prefixes are almost always used with the units of information, bits and bytes, they may be used with any other unit of measure, when convenient. For example, in signal processing one may need binary multiples of the frequency unit hertz (Hz), for example the kibihertz (KiHz), equal to 1024 Hz. [123] [124]

See also

Related Research Articles

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An order of magnitude is usually a factor of ten. Thus, four orders of magnitude is a factor of 10,000 or 104.

<span class="mw-page-title-main">Cylinder-head-sector</span> Historical method for giving addresses to physical data blocks on hard disk drives

Cylinder-head-sector (CHS) is an early method for giving addresses to each physical block of data on a hard disk drive.

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 sizes are commonly formed by the use of such prefixes. The prefixes of the metric system, such as kilo and milli, represent multiplication by positive or negative powers of ten. In information technology it is common to use binary prefixes, which are based on powers of two. Historically, many prefixes have been used or proposed by various sources, but only a narrow set has been recognised by standards organisations.

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. IEEE 1541-2021 revises and supersedes IEEE 1541–2002, which is 'inactive'.

The octet is a unit of digital information in computing and telecommunications that consists of eight bits. The term is often used when the term byte might be ambiguous, as the byte has historically been used for storage units of a variety of sizes.

<span class="mw-page-title-main">History of hard disk drives</span>

In 1953, IBM recognized the immediate application for what it termed a "Random Access File" having high capacity and rapid random access at a relatively low cost. After considering technologies such as wire matrices, rod arrays, drums, drum arrays, etc., the engineers at IBM's San Jose California laboratory invented the hard disk drive. The disk drive created a new level in the computer data hierarchy, then termed Random Access Storage but today known as secondary storage, less expensive and slower than main memory but faster and more expensive than tape drives.

<span class="mw-page-title-main">Power Macintosh 5500</span> Personal computer by Apple Computer

The Power Macintosh 5500 is a personal computer designed, manufactured, and sold by Apple Computer from February 1997 to March 1998. Like the Power Macintosh 5260 and 5400 that preceded it, the 5500 is an all-in-one design, built around a PowerPC 603ev processor operating at 225, 250 or 275 megahertz (MHz).

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 engineering standardization organization.

In telecommunications, data transfer rate is the average number of bits (bitrate), characters or symbols (baudrate), or data blocks per unit time passing through a communication link in a data-transmission system. Common data rate units are multiples of bits per second (bit/s) and bytes per second (B/s). For example, the data rates of modern residential high-speed Internet connections are commonly expressed in megabits per second (Mbit/s).

This timeline of binary prefixes lists events in the history of the evolution, development, and use of units of measure that are germane to the definition of the binary prefixes by the International Electrotechnical Commission (IEC) in 1998, used primarily with units of information such as the bit and the byte.

In digital computing and telecommunications, a unit of information is the capacity of some standard data storage system or communication channel, used to measure the capacities of other systems and channels. In information theory, units of information are also used to measure information contained in messages and the entropy of random variables.

The maximum random access memory (RAM) installed in any computer system is limited by hardware, software and economic factors. The hardware may have a limited number of address bus bits, limited by the processor package or design of the system. Some of the address space may be shared between RAM, peripherals, and read-only memory. In the case of a microcontroller with no external RAM, the size of the RAM array is limited by the size of the integrated circuit die. In a packaged system, only enough RAM may be provided for the system's required functions, with no provision for addition of memory after manufacture.

References

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  2. ↑ "Order Granting Motion to Dismiss" (PDF). United States District Court for the Northern District of California . Retrieved 2020-01-24.
  3. ↑ See also Dinan v. SanDisk LLC, No. 20-15287 (9th Cir. Feb. 11, 2021) https://scholar.google.com/scholar_case?case=16989791406584358656
  4. ↑ "SI prefixes". The NIST Reference on Constants, Units, and Uncertainty: International System of Units (SI). National Institute of Standards and Technology. 2010-01-13. Retrieved 2017-04-03.
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  6. ↑ "List of Resolutions for the 27th meeting of the General Conference on Weights and Measures" (PDF). 2022-11-18. Archived (PDF) from the original on 2022-11-18. Retrieved 2022-11-18.
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  10. ↑ "La Loi Du 18 Germinal An 3: Décision de tracer le mètre, unité fondamentale, sur une règle de platine. Nomenclature des " mesures républicaines ". Reprise de la triangulation" [The Law of 18 Germinal, Year 3: Decision to draw the fundamental unit metre on a platinum ruler. Nomenclature of "Republican measures". Resumption of the triangulation.]. L'Histoire Du Mètre [The history of the metre] (in French). histoire.du.metre.free.fr. Archived from the original on 2022-11-26. Retrieved 2015-10-12. Art. 8. Dans les poids et mesures de capacité, chacune des mesures décimales de ces deux genres aura son double et sa moitié, afin de donner à la vente des divers objets toute la commodité que l'on peut désirer. Il y aura donc le double-litre et le demi-litre, le double-hectogramme et le demi-hectogramme, et ainsi des autres.[Art. 8. In the weights and measures of capacity, each of the decimal measures of these two kinds will have its double and its half, in order to give to the sale of the various articles all the convenience that one can desire. There will therefore be the double-litre and the half-litre, the double-hectogram and the half-hectogram, and so on.]
  11. ↑ Weik, Martin H. (March 1961). "A Third Survey of Domestic Electronic Digital Computing Systems: Chapter III Analysis and Trends". Ballistic Research Laboratories Report No. 1115: 1027. Of 187 different relevant systems, 131 utilize a straight binary system internally, whereas 53 utilize the decimal system (primarily binary coded decimal) and 3 systems utilize a binary coded alphanumeric system of notation. This lengthy report describes many of the early computers.
  12. ↑ Hunting Trouble on 28 Megacycles, A. L. Blais, QST, January 1930.
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  90. ↑ "IEEE-SA Standards Board Standards Review Committee (RevCom) Meeting Agenda". 2005-03-19. Archived from the original on 2007-09-22. Retrieved 2007-02-25. 1541-2002 (SCC14) IEEE Trial-Use Standard for Prefixes for Binary Multiples [No negative comments received during trial-use period, which is now complete; Sponsor requests elevation of status to full-use.]Recommendation: Elevate status of standard from trial-use to full-use. Editorial staff will be notified to implement the necessary changes. The standard will be due for a maintenance action in 2007.
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  98. ↑ DeRespinis, F., Hayward, P., Jenkins, J., Laird, A., McDonald, L., and Radzinski, E. (2011): The IBM style guide: conventions for writers and editors. IBM Press. quote: "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."
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