Talk:Binary prefix/Sandboxes/Archive1

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This page is an archive of work on the article Binary prefixes. It is preserved here to preserve the edit history. Please do not edit it. The contents of this page replaced the previous contents of Binary prefixes as shown in this diff.

For the actual article, see Binary prefixes. For the actual article's main talk page, where discussion of this sandbox occurred, see Talk:Binary prefix.
Prefixes for multiples of
bits (b) or bytes (B)
Decimal
Value Metric
1000 k kilo
10002 M mega
10003 G giga
10004 T tera
10005 P peta
10006 E exa
10007 Z zetta
10008 Y yotta
Binary
Value JEDEC IEC
1024 K kilo Ki kibi
10242 M mega Mi mebi
10243 G giga Gi gibi
10244 - - Ti tebi
10245 - - Pi pebi
10246 - - Ei exbi
10247 - - Zi zebi
10248 - - Yi yobi

In computing, a binary prefix is a specifier or mnemonic that is prepended to the units of digital information, the bit and the byte, to indicate multiplication by a power of 2. In practice the powers used are mostly multiples of 10, so the prefixes denote powers of 1024 = 210.

The computer industry uses terms such as "kilobyte," "megabyte," and "gigabyte," and corresponding abbreviations "KB", "MB", and "GB", in two different ways. For example, in citations of main memory or RAM capacity, "gigabyte" customarily means 1073741824 bytes. This is a power of 2, specifically 230, so this usage is referred to as a "binary unit" or "binary prefix." However, in other contexts, the industry uses "kilo", "mega", "giga", etc., in a manner consistent with their meaning in the International System of Units (SI): as powers of 1000. For example, a "500 gigabyte" hard drive is 500000000000 bytes, and a "100 megabit" Ethernet connection is running at 100000000 bits per second.

Starting in about 2000, a number of standards and trade organizations approved standards and recommendations for a new set of binary prefixes, proposed earlier by the International Electrotechnical Commission (IEC), that would refer unambiguously to powers of 1024. According to these, the SI prefixes would only be used in the decimal sense, even when referring to data storage capacities: kilobyte and megabyte would denote one thousand bytes and one million bytes respectively (consistent with SI), while new terms such as kibibyte, mebibyte and gibibyte, abbreviated KiB, MiB, and GiB, would denote 1024 bytes, 1048576 bytes, and 1073741824 bytes respectively.[1]

In practice, the IEC binary prefixes have seen little use by the computing industry, marketplace, or press.

History[edit]

Main memory[edit]

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 (1952) used binary and could address 2048 36-bit words, while the IBM 702 (1953) used decimal and could address 10000 7-bit words.

By the mid 1960s, binary addressing had become the standard architecture in computer design. 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 2, 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 adapted from the International System of Units (SI). These are known as the the SI prefixes.[defn. 1] They are defined as indicating multipliers that are powers of 1000: A kilogram is 1000 grams, one Megahertz is 1000000 Hertz, and so on.

The International System of Units defines no units such as "bytes" 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 naturally came in sizes that were easily expressed as multiples of 1024, "kilobyte" when applied to computer memory was commonly used to mean 1024 bytes instead of 1000.

The use of K in the binary sense as in a "32K core" meaning 32×1024, or 32768, can be found as early as 1959[2][3] Gene Amdahl's seminal 1964 article on IBM System/360 used 1K to mean 1024.[4] This style was used by other computer vendors, the CDC 7600 System Description (1968) made extensive use of K as 1024.[5] Thus the first binary prefix was born.[defn. 2]

Another style was to truncate the last 3 digits and append K, essentially using K as a decimal prefix[defn. 3] in accordance with SI. The exact values 32768, 65536 and 131072 would then become 32K, 65K and 131K.[6] (If 32768 were instead rounded up, it would be 33K; if K = 1024 were used, 65536 would become 64K.) This style was used from about 1965 to 1975.

These two styles (K = 1024 and truncation) were used loosely around the same time, sometimes by the same company. In discussions of binary-addressed memories, the exact size was evident from context. The HP 21MX real-time computer (1974) denoted 196608 (which is 192×1024) as 196K and 1048576 as 1M,[7] while the HP 3000 business computer (1973) could have 64K, 96K, or 128K bytes of memory.[8]

The "truncation" method gradually waned, while the practice of using the SI-inspired "kilo" to indicate 1024 was later extended to higher powers of 1024: "megabyte" meaning 10242 (1048576) bytes, and later "gigabyte" for 10243 (1073741824) bytes. For example, a "512 megabyte" RAM module is 512×10242 bytes (512×1048576, or 536870912), rather than 512000000.

The abbreviated terms 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.[9] 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."[10]

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

Disk drives and other devices[edit]

The disk drive industry followed a different pattern. Industry practice, more thoroughly documented at Timeline of binary prefixes and continuing today, is to specify hard drives using SI prefixes and symbols in their SI or "decimal" interpretation. Unlike binary-addressed computer main memory, there is nothing in a disk drive that influences it to have a total capacity easily expressed using a power of 1024. The first commercially sold disk drive, the IBM 350, had 50 (not 32 or 64) physical disk "platters" containing a total of 50,000 sectors of 100 characters each, for a total quoted capacity of "5 million characters."[12]

In the 1960s most disk drives used IBM's variable block length format (called Count Key Data or "CKD").[13] Any block size could be specified up to the maximum track length. Blocks ("records" in IBM's terminology) of 88, 96, 880 and 960 were often used because they related to the fixed block size of punch cards. The drive capacity was usually stated in full track record blocking, for example, the 100 megabyte 3336 disk pack only achieved that capacity with a full track block size of 13,030 bytes.

Hard disk drive manufacturers used "megabytes" or "MB", meaning 106 bytes, to characterize their products as early as 1974.[14] 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.[15]

An early hard drive in personal computing history, the Seagate ST251, had 6 heads or active surfaces (tracks per cylinder), 17 sectors per track, and 820 cylinders; with a sector size of 512 bytes, this gives a capacity of 42823680 bytes.[16] Seagate like other hard drive manufacturers before and since used the SI prefixes in their marketing, and labeled this as a "42 MB" drive, meaning 42000000 bytes. With the customary binary prefixes[defn. 4] used for RAM, this would have been described as 40.84 megabytes.

The hard drive industry continues to use SI prefixes. Today, for example, a "300 GB" hard drive offers slightly more than 300×109, or 300000000000, bytes, not 300×230 (which would be about 322×109). Operating systems such as Microsoft Windows that display hard drive sizes using the customary binary prefix "GB" (as it is used for RAM) would display this as 279.4 GB (meaning 279.4×10243, or 279.4×1073741824).

Information transfer and clock rates[edit]

Like the hard drive, there is nothing in a computer clock circuit or data transfer path that demands or even encourages that things happen at rates easily expressed using powers of 1024, or even using powers of 2.

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 MHz.

Similarly, digital information transfer rates are quoted using SI prefixes:

  • The ATA-100 disk interface refers to 100000000bytes/s.
  • 1x CD-ROM speed is 150K or 150000bytes/s
  • A "56K" modem refers to 56000bits/s
  • SATA-2 has a raw bit rate of 3Gb/s = 3000000000bits/s
  • PC-6400 ram transfers 6400000000bytes/s
  • Firewire 800 has a raw rate of 800000000bits/s

Standardization of dual definitions[edit]

By the mid 1970s it was common to see K meaning 1024 and the occasional M meaning 1048576 for words or bytes of main memory (RAM) while K and M were commonly used with their decimal meaning for disk storage. In the 1980s, as capacities of both types of devices increased, the SI prefix G, with SI meaning, was commonly applied to disk storage, while M in its binary meaning, became common for computer memory. In the 1990s, the prefix G, in its binary meaning, became commonly used for computer memory capacity. The first terabyte (SI prefix, 1000000000000 bytes) hard disk drive was introduced in 2007.[17]

The dual usage of the kilo, mega, and giga prefixes and their corresponding symbols K, M, and G as both powers of 1000 and powers of 1024 was recorded in standards and dictionaries. For example, the 1986 ANSI/IEEE Std 1084-1986[18] defined dual uses for kilo and mega.

kilo (K). (1) A prefix indicating 1000. (2) In statements involving size of computer storage, a prefix indicating 210, or 1024.

mega (M). (1) A prefix indicating one million. (2) In statements involving size of computer storage, a prefix indicating 220, or 1048576.

The binary units Kbyte and Mbyte were formally defined in ANSI/IEEE Std 1212-1991.[19]

Many dictionaries have noted, often incorrectly stated, the practice of using prefixes borrowed from SI to indicate binary multiples.[20][21] Oxford online dictionary defines, for example, megabyte as: "Computing: a unit of information equal to one million or (strictly) 1048576bytes."[22]

The units Kbyte, Mbyte, and Gbyte are found in the trade press and in IEEE journals. Gigabyte was formally defined in IEEE Std 610.10-1994 as either 1000000000 or 230 bytes.[23] Kilobyte, Kbyte, and KB are equivalent units and all are defined in the current standard, IEEE 100-2000.[24] Byte multiples using powers of 1024 up to yottabyte are given by the on-line computing dictionary FOLDOC (Free On-Line Dictionary Of Computing).[25]

The hardware industry has coped with the dual definitions because of relative consistency: system memory (RAM) typically uses the binary meaning while magnetic disk storage uses the SI meaning. There are, however, exceptions and special cases. Diskettes use yet another "megabyte" equal to 1024×1000 bytes.[26] In optical disks, Compact Disks use MB to mean 10242 bytes while DVDs use GB to mean 10003 bytes.[27][28]

Inconsistent use of units[edit]

Deviation between powers of 1024 and powers of 1000[edit]

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 over 20% for the yotta prefix.

Linear-log graph of percentage of the difference between decimal and binary interpretations of the unit prefixes versus the storage size.
Prefix Bin ÷ Dec Dec ÷ Bin Percentage difference
kilo 1.024 0.9766 +2.4% or −2.3%
mega 1.049 0.9537 +4.9% or −4.6%
giga 1.074 0.9313 +7.4% or −6.9%
tera 1.100 0.9095 +10.0% or −9.1%
peta 1.126 0.8882 +12.6% or −11.2%
exa 1.153 0.8674 +15.3% or −13.3%
zetta 1.181 0.8470 +18.1% or −15.3%
yotta 1.209 0.8272 +20.9% or −17.3%

Consumer confusion[edit]

Proponents of new prefixes for binary multiples claim that to use, for example, "GB" to mean 1073741824 bytes in some contexts (for example in computer RAM capacity, and in hard drive capacities and file sizes as displayed by many operating systems) and to mean 1000000000 bytes in others (for example, in communications speeds, and in hard drive capacities as quoted by manufacturers) is confusing and that a given prefix should always mean the same thing.[citation needed] Opponents counter that introducing new, unfamiliar prefixes will introduce confusion of its own.[citation needed]

In the early days of computers there was little or no consumer confusion because of the sophisticated nature of the consumers and the practice of computer manufacturers to specify their products with capacities in full precision. For example, in 1968 IBM stated "System/360 Model 91s can accommodate up to 6291496bytes of main storage."[29]

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. As noted previously, hard drives are described and sold using "GB" or "TB" in their SI meaning: one billion and one trillion bytes. Many current operating systems and other software however display hard drive and file sizes using "MB", "GB" or other SI-looking prefixes in their "binary" meaning, just as they do for displays of RAM capacity. (This is fairly recent. The presentation of hard disk drive capacity by an operating system using "MB" in a binary sense appears no earlier than Macintosh Finder after 1984. Prior to that, on the systems that had a hard disk drive, capacity was presented in decimal digits with no prefix of any sort (e.g., MS/PC DOS CHKDSK command).)

The following three images show the discrepancy of reporting the identical disk capacity on the manufacturer's packaging (160 GB = 160×10003), the Windows XP disk manager (149.05 GB = 149.05×10243), and the drive properties display (152625MB = 152625×10242). (These are all the same number to within less than 0.03%.)

todo: Uncomment the following images when this page goes live.  ---jeh

Legal disputes[edit]

The different interpretations of disk size prefixes has led to two significant class action lawsuits against digital storage manufacturers. One case involved flash memory and the other involved hard disk drives. Both were settled with the manufactures admitting no wrongdoing but agreeing to clarify the storage capacity of their products on the consumer packaging. Flash memory and hard disk manufacturers now have disclaimers on their packaging and web sites clarifying the formatted capacity of the devices[30] or defining MB as 1 million bytes and 1 GB as 1 billion bytes.[31]

Willem Vroegh v. Eastman Kodak Company[edit]

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.[32]

The manufacturers agreed to clarify the flash memory card capacity on the packaging and web sites.[33] The consumers could apply for "a discount of ten percent off a future online purchase from Defendants' Online Stores Flash Memory Device".[34]

Orin Safier v. Western Digital Corporation[edit]

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.[35]

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.[36]

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.[37][38][39]


Unique binary prefixes[edit]

Early suggestions[edit]

While early computer scientists typically used k to mean 1000, some recognized the convenience that would result from working with multiples of 1024 and the confusion that resulted from using the same prefixes for two different meanings.

Several proposals for unique binary prefixes[defn. 2] were made in 1968. Donald Morrison proposed to use the Greek letter kappa (κ) to denote 1024, κ² to denote 1024×1024, and so on.[40] (At the time, memory size was small, and only K was in widespread use.) Wallace Givens responded with a proposal to use bK as an abbreviation for 1024 and bK2 or bK² for 1024×1024, though he noted that neither the Greek letter nor lowercase letter b would be easy to reproduce on computer printers of the day.[41] Bruce A. Martin further proposed that the prefixes be abandoned altogether, and the letter B be used as a binary exponent, similar to E notation, to create shorthands like 3B20 for 3×220[42]

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).[43]

IEC prefixes[edit]

The set of binary prefixes that were eventually adopted, eventually referred to as the "IEC prefixes,"[defn. 5] were first proposed by the International Union of Pure and Applied Chemistry's (IUPAC) Interdivisional Committee on Nomenclature and Symbols (IDCNS) in 1995. At that time, it was proposed that the terms kilobyte and megabyte be used only for 103 bytes and 106 bytes, respectively. The new prefixes kibi (kilobinary), mebi (megabinary) and gibi (gigabinary) were also proposed at the time, and the proposed symbols for the prefixes were kb, Mb and Gb respectively, rather than Ki, Mi and Gi.[44] The proposal was not accepted at the time.

The Institute of Electrical and Electronic Engineers (IEEE) began to collaborate with the International Organization for Standards (ISO) and International Electrotechnical Commission (IEC) to find acceptable names for binary prefixes. The IEC proposed kibi, mebi, gibi and tebi, with the symbols Ki, Mi, Gi and Ti respectively, in 1996.[45]

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.[46]

Adoption by IEC and NIST[edit]

In January 1999, the IEC published the first international standard (IEC 60027-2 Amendment 2) with the new prefixes, extended up to pebi (Pi) and exbi (Ei).[47][48]

The IEC 60027-2 Amendment 2 also states that the IEC position is the same as that of BIPM (the body who regulate the SI system); the SI prefixes retain their definitions in powers of 1000 and are never used to mean a power of 1024.[citation needed]

In usage, products and concepts typically described using powers of 1024 would continue to be, but with the new IEC prefixes. For example, a memory module of 536870912 bytes (512×1048576) would be referred to as 512 MiB or 512 mebibytes instead of 512 MB or 512 megabytes. Conversely, since hard drives have historically been marketed using the SI convention that "giga" means 1000000000, a "500 GB" hard drive would still be labeled as such. According to these recommendations, operating systems and other software would also use binary and SI prefixes in the same way, so the purchaser of a "500 GB" hard drive would find the operating system showing it as that and not "477 GB", while 536870912 bytes of RAM would be displayed as "512 MiB".

The second edition of the standard, published in 2000,[49] defined them only up to exbi,[50] but in 2005, the third edition added prefixes zebi and yobi, thus matching all SI prefixes with binary counterparts.[51]

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.[52]

Specific units of IEC 60027-2 A.2 and ISO/IEC 80000[edit]

IEC prefix Representations Customary prefix
Name Symbol Base 2 Base 1024 Value Base 10 Name Symbol
kibi Ki 210 10241 1024 ~1.02×10^3 kilo k, K
mebi Mi 220 10242 1048576 ~1.05×10^6 mega M
gibi Gi 230 10243 1073741824 ~1.07×10^9 giga G
tebi Ti 240 10244 1099511627776 ~1.10×10^12 tera T
pebi Pi 250 10245 1125899906842624 ~1.13×10^15 peta P
exbi Ei 260 10246 1152921504606846976 ~1.15×10^18 exa E
zebi Zi 270 10247 1180591620717411303424 ~1.18×10^21 zetta Z
yobi Yi 280 10248 1208925819614629174706176 ~1.21×10^24 yotta Y

Other standards bodies and organizations[edit]

The IEC-proposed binary prefixes are now supported by other standardization bodies and technical organizations.

The United States National Institute of Standards and Technology (NIST) supports the ISO/IEC standards for "Prefixes for binary multiples" and has a web site documenting them, describing and justifying their use. NIST suggests that in English, the first syllable of the name of the binary-multiple prefix should be pronounced in the same way as the first syllable of the name of the corresponding SI prefix, and that the second syllable should be pronounced as bee.[1] The binary definition of the SI prefix names is not permitted by NIST.[53]

In December 2002 JEDEC, a leading standards organization in the microelectronics industry, mentioned the IEC prefixes in their Terms, Definitions, and Letter Symbols for Microcomputers, Microprocessors, and Memory Integrated Circuits document. This document defines "kilo," "mega," and "giga" with binary multipliers. A "Note" to this definition then states that that definition is only presented "to reflect common usage", and quotes the IEC in describing the binary prefixes as "an alternative system".[54]

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.[60][61]

  • Nevertheless, as of April 2008, the IEEE Publications division does not require the use of IEC prefixes in its major magazines such as Spectrum[62] or Computer.[63]

The International Bureau of Weights and Measures (BIPM), which maintains the International System of Units (SI), expressly prohibits the use of SI prefixes to denote binary multiples, and recommends the use of the IEC prefixes as an alternative since units of information are not included in SI.[64][65]

The European Committee for Electrotechnical Standardization (CENELEC) has adopted the IEC-recommended binary prefixes via the harmonization document HD 60027-2:2003-03.[66] This document will be adopted as a European standard.[67]

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. [68]

Dissent[edit]

Even among proponents of unique prefixes for binary multiples, proposals for alternative sets of prefixes have continued following the introduction of Ki, Mi, etc., by the IEC. For example, Donald Knuth, who uses decimal notation like 1 MB = 1000 kB,[69] 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" (abbreviated KKB and MMB, as "doubling the letter connotes both binary-ness and large-ness").[70]

Current practice[edit]

The IEC binary prefixes have seen little adoption by the computing industry, marketplace, or press.

The use of the customary binary prefixes[defn. 4] kilo, mega, giga and their corresponding symbols K (or k), M and G when denoting the capacity of solid‑state memory remains virtually universal.[71][72][73][74][75].

With a few exceptions, most operating systems and other software continue to use the customary binary prefixes in displays of memory, disk storage capacity, and file size, but SI prefixes[defn. 6] in other areas such as network communication speeds and processor speeds.

Nearly all articles, papers, and marketing materials in the industry continue to use the customary binary prefixes when referring to computer memory, even those published under the aegis of organizations that have shown support for the IEC prefixes.

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.

Software[edit]

As of February 2010, most software does not distinguish symbols for binary and decimal prefixes.[defn. 3] The IEC binary naming convention has been adopted by a few, but this is not used universally.

Examples of software that use IEC binary prefixes for powers of 1024 (along with standard SI prefixes for powers of 1000) include:

One of the stated goals of the introduction of the IEC prefixes was "to preserve the SI prefixes as unambiguous decimal multipliers."[60] 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 (KiB) and mebibytes (MiB), 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 (17.7 MiB)  TX bytes:45708 (44.6 KiB)

Files[edit]

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

  • Most Unix-like systems, which use the ls command to display file sizes, use powers of 1024 indicated as KB/MB (customary binary prefixes).
  • In Linux, the directory listing tool (ls) has options for file size listings using SI decimal prefixes.
  • Microsoft Windows reports file sizes and disk device capacities using the customary binary prefixes or, in a "Properties" dialog, using the exact value in bytes.

Computer hardware[edit]

As of February 2010, no examples of hardware marketed using IEC binary prefixes have been found. Even hardware types that use powers-of-1024 multipliers, such as memory, continue to be marketed with customary binary prefixes.

Computer memory[edit]

The 536,870,912 byte (512×220) capacity of these RAM modules is stated as "512 MB" on the label.

Measurements of most types of electronic memory such as RAM, ROM and Flash (large scale disk-like flash is sometimes an exception) are given using customary binary prefixes (kilo, mega, and giga). For example, a "512 megabyte" memory module is 512×220 bytes (512×1048576, or 536870912.

JEDEC Solid State Technology Association, the semiconductor engineering standardization body of the Electronic Industries Alliance (EIA), continues to include the customary binary definitions of kilo, mega and giga in their Terms, Definitions, and Letter Symbols document[54], and uses those definitions in later memory standards[55][56][57][58][59] (See also JEDEC memory standards.)

Many computer programming tasks reference memory in terms of powers of two because of the inherent binary design of current hardware addressing systems. For example, a 16-bit processor register can reference at most 65,536 items (bytes, words, or other objects); this is conveniently expressed as "64K" items. An operating system might map memory as 4096-byte pages, in which case exactly 8192 pages could be allocated within 33554432bytes of memory: 8K (8192) pages of 4 kilobytes (4096) each within 32 megabytes (32 MiB) of memory.

Hard disk drives[edit]

Hard disk drive manufacturers state capacity using SI decimal prefixes. As of January 2007, most, if not all, HDD manufacturers continue to use SI decimal prefixes to identify capacity.[100]

Flash drives[edit]

USB Flash Drive and Flash-based memory cards like CompactFlash and Secure Digital are typically sized as a small "power of two" (1, 2, 4, 8, 16, etc.) multiple of decimal megabytes; for example, a "256 MB" flash card provides at least 256 million bytes (256000000), not 256×1024×1024 (268435456).[30] Although the devices usually have at least the expected byte capacity, each manufacturer allocates different portions of the device's ultimate capacity for such things as wear levelling.

Floppy drives[edit]

The last widely adopted diskette was the 3½ inch high density. This has a formatted capacity of 1474560 bytes or 1440 KB (1440×1024, using "KB" in the customary binary sense). These are marketed as 1.44 MB. This usage defines a "third megabyte" of 1000×1024.

Most operating systems display the capacity using "MB" in the customary binary sense, resulting in a display of "1.4 MB" (1.40625 MB). Some users have noticed the missing 0.04 MB and both Apple and Microsoft have support bulletins referring to them as 1.4 MB.[26]

The earlier 1200 KB (1200×1024) 5¼ inch diskette was marketed as 1.2 MB (1.171875 MiB) without any controversy.

Optical discs[edit]

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 (approx 730 MB).[27]

However, the capacities of other optical disc storage media like DVD, Blu-ray Disc, HD DVD are given using SI decimal prefixes. A "4.7 GB" DVD has a nominal capacity of about 4.38 GiB.[28]


Data transmission and clock rates[edit]

Certain units are always used with SI decimal prefixes even in computing contexts. Two examples are hertz (Hz), which is used to measure the clock rates of electronic components, and bit/s, used to measure data transmission speed.

  • A 1 GHz processor receives 1000000000 clock ticks per second
  • A sound file sampled at 44.1 kHz has 44100 samples per second
  • A 128 kbit/s MP3 stream consumes 128000bits (16 kilobytes, 15.625 KiB) per second
  • A 1 Mbit/s Internet connection can transfer 1000000bits per second (125000 bytes per second, assuming an 8-bit byte and no overhead)
  • A 1 Gbit/s Etherrnet connection can transfer 1000000000bits per second (125000000 bytes per second, assuming an 8-bit byte and no overhead)

Bus clock speeds and therefore bandwidths are both quoted using SI decimal prefixes.

  • PC3200 memory on a double pumped bus, transferring 8 bytes per cycle with a clock speed of 200 MHz (200000000cycles per second) has a bandwidth of 200000000×8×2 = 3200000000bytes/second = 3.2 GB/s (about 2.98 GiB/s).
  • A PCI-X bus at 66 MHz (66000000cycles per second), 64 bits per transfer, has a bandwidth of 66000000transfers/second×64bits/transfer = 4224000000bits/second, or 528000000bytes/second, usually quoted as 528 MB/s.

See also[edit]

Definitions[edit]

  1. ^ Cite error: The named reference d.SIp was invoked but never defined (see the help page).
  2. ^ a b A binary prefix is a prefix that denotes a power of 1024. For example, in the computer industry's customary practice, one "megabyte" of RAM is 10242 bytes of RAM, one "gigabyte" of RAM is 10243 bytes of RAM, and so on. In the IEC binary of prefixes, these would be expressed as one "mebibyte" and one "gibibyte," respectively. Both are "binary prefixes" in these usages.
  3. ^ a b A decimal prefix is a prefix that denotes a power of 1000. For example, "kilo" denotes 1000, "mega" denotes 10002 or one million, "giga" denotes 10003 or one billion, and so on. SI prefixes are decimal prefixes.
  4. ^ a b As used in this article, the term customary binary prefix or similar refers to prefixes such as kilo, mega, giga, etc., borrowed from the similarly named SI prefixes but commonly used to denote a power of 1024.
  5. ^ The term IEC binary prefix or IEC prefix refers to the prefixes such as kibi, mebi, gibi, etc., or their corresponding symbols Ki, Mi, Gi, etc., first adopted by the International Electrotechnical Commission (IEC). Such prefixes are only used with the units bits or bytes (or compound units derived from them such as bytes/second) and always denote powers of 1024; that is, they are always used as binary prefixes. Thus 1 mebibyte of RAM is 10242 bytes of RAM, 1 gibibyte or 1 GiB of RAM is 10243 bytes, and so on.
  6. ^ The term SI prefix or similar refers to prefixes such as kilo, mega, giga, etc., defined by the SI system of units and always used to denote a power of 1000; in other words, always as decimal prefixes.

References[edit]

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  2. ^ Real, P. (September 1959). "A generalized analysis of variance program utilizing binary logic.". ACM '59: Preprints of papers presented at the 14th national meeting of the Association for Computing Machinery (ACM Press): 78–1–78–5. doi:10.1145/612201.612294. "On a 32K core size 704 computer, approximately 28000 data may be analyzed, ... without resorting to auxiliary tape storage."  Note: the IBM 704 core memory units had 4096 36-bit words. Up to 32768 words could be installed
  3. ^ Gruenberger, Fred; Burgess, C. R.; Gruenberger, Fred (October 1960). "Letters to the Editor". Communications of the ACM 3 (10). doi:10.1145/367415.367419.  "The 8K core stores were getting fairly common in this country in 1954. The 32K store started mass production in 1956; it is the standard now for large machines and at least 200 machines of the size (or its equivalent in the character addressable machines) are in existence today (and at least 100 were in existence in mid-1959)." Note: The IBM 1401 was a character addressable computer.
  4. ^ Amdahl, Gene M. (1964). "Architecture of the IBM System/360" (PDF). IBM Journal of Research and Development (IBM) 8 (2).  Figure 1 gives storage (memory) capacity ranges of the various models in "Capacity 8 bit bytes, 1 K = 1024"
  5. ^ Control Data Corporation (November 1968). Control Data 7600 Computer System: Preliminary System Description (PDF). "One type, designated as the small core memory (SCM) is a many bank coincident current type memory with a total of 64K words of 60 bit length (K=1024)." 
  6. ^ Control Data Corporation (1965-1967). Control Data 6400/6500/6600 Computer Systems Reference Manual (Pub No. 60100000 ed.). pp. pg 2–1. "Central Memory is organized into 32K, 65K, or 131K words (60-bit) in 8, 16, or 32 banks of 4096 words each." 
  7. ^ Frankenberg, Robert (October 1974). "All Semiconductor Memory Selected for New Minicomputer Series" (PDF). Hewlett-Packard Journal (Hewlett-Packard) 26 (2): pg 15–20. Retrieved 2007-06-18. "196K-word memory size" 
  8. ^ Hewlett-Packard (November 1973). "HP 3000 Configuration Guide" (PDF). HP 3000 Computer System and Subsystem Data: pg 59. Retrieved 2010-01-22. 
  9. ^ Lin, Yeong; Mattson, R. (September 1972). "Cost-performance evaluation of memory hierarchies". Magnetics, IEEE Transactions on (IEEE) 8 (3): pg 390–392. doi:10.1109/TMAG.1972.1067329. "Also, random access devices are advantageous over serial access devices for backing store applications only when the memory capacity is less than 1 Mbyte. For capacities of 4 Mbyte and 16 Mbyte serial access stores with shift register lengths of 256 bit and 1024 bit, respectively, look favorable." 
  10. ^ IBM (1972). System/370 Model 158 brochure (PDF). IBM. "All-monolithic storage ... (1024-bit NMOS) This new improvement of processor storage makes system expansion more economical. Real storage capacity is available in 512K increments ranging from 512K to 2,048K bytes." 
  11. ^ Bell, Gordon (November 1975). "Computer structures: What have we learned from the PDP-11?" (PDF). ISCA '76: Proceedings of the 3rd annual symposium on Computer architecture (ACM Press): pg 1–14. "memory size (8k bytes to 4 megabytes)." 
  12. ^ IBM Corporation. "IBM 350 disk storage unit". IBM Archives. 
  13. ^ IBM invented the disk drive in 1956 and until the late 1960s its drives and their clones were dominant. See, e.g. US vs. IBM antitrust litigation (Jan 1969), especially IBM analyses of Memorex and other disk drive companies.
  14. ^ The Product Line Card unambiguously uses MB to characterize HDD capacity in millions of bytes
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  18. ^ ANSI/IEEE Std 1084-1986 IEEE Standard Glossary of Mathematics of Computing Terminology. 30 October 1986. "kilo (K). (1) A prefix indicating 1000. (2) In statements involving size of computer storage, a prefix indicating 210, or 1024. mega (M). (1) A prefix indicating one million. (2) In statements involving size of computer storage, a prefix indicating 220, or 1048576." 
  19. ^ ANSI/IEEE Std 1212-1991 IEEE Standard Control and Status Register (CSR) Architecture for Microcomputer Buses. 22 July 1992. "Kbyte. Kilobyte. Indicates 210 bytes. Mbyte. Megabyte. Indicates 220bytes. Gbyte is used in the Foreword." 
  20. ^ "Definition of megabyte". 
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  23. ^ IEEE Std 610.10-1994 IEEE Standard Glossary of Computer Hardware Terminology. 24 June 1994. "gigabyte (gig, GB). This term may mean either a) 1000000000 bytes or b) 230 bytes. ... As used in this document, the terms kilobyte (kB) means 210 or 1024 bytes, megabyte (MB) means 1024 kilobytes, and gigabyte (GB) means 1024 megabytes." 
  24. ^ Institute of Electrical and Electronics Engineers (2000). The Authoritative Dictionary of IEEE Standards Terms. IEEE Computer Society Press. ISBN 0-7381-2601-2.  "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.
  25. ^ "yottabyte". Free on-line Dictionary of Computing. Retrieved 2010-02-04. 
  26. ^ a b Microsoft (2003-05-06). "Determining Actual Disk Size: Why 1.44 MB Should Be 1.40 MB". Article ID: 121839. Microsoft. Retrieved 2007-07-07.  "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."
  27. ^ a b Data capacity of CDs
  28. ^ a b Understanding Recordable and Rewritable DVD
  29. ^ System/360 Model 91
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  43. ^ Markus Kuhn (December 29, 1996). "Standardized units for use in information technology". 
  44. ^ http://ww1.iucr.org/cexec/rep95/idcns.htm
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  46. ^ Bruce Barrow, "A Lesson in Megabytes," IEEE Standards Bearer, January 1997, page 5
  47. ^ "These prefixes for binary multiples, which were developed by IEC Technical Committee (TC) 25, Quantities and units, and their letter symbols, with the strong support of the International Committee for Weights and Measures (CIPM) and the IEEE, were adopted by the IEC as Amendment 2 to IEC International Standard IEC 60027-2: Letter symbols to be used in electrical technology - Part 2: Telecommunications and electronics."
  48. ^ IUCR 1999 report on IUPAC Interdivisional Committee on Nomenclature and Symbols
  49. ^ IEC 60027-2 (2000-11) Ed. 2.0
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  51. ^ "HERE COME ZEBI AND YOBI" (Press release). International Electrotechnical Commission. 2005-08-15. 
  52. ^ niso, New Specs and Standards
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  55. ^ a b JEDEC (September 2009). "DDR3 SDRAM Standard". Retrieved 2010-02-04. 
  56. ^ a b JEDEC (November 2009). "DDR2 SDRAM Standard". Retrieved 2010-02-04. 
  57. ^ a b JEDEC. "Memory Configurations". Retrieved 2010-02-04. 
  58. ^ a b JEDEC. "Memory Configurations Table of Contents". Retrieved 2010-02-04. 
  59. ^ a b JEDEC. "Terms and Definitions". Retrieved 2010-02-04. 
  60. ^ a b IEEE Std 1541-2002: IEEE Trial-Use Standard for Prefixes for Binary Multiples (PDF). Reaffirmed 27 March 2008. 12 February 2003. doi:10.1109/IEEESTD.2003.94236. Retrieved 2007-07-29. "This standard is prepared with two goals in mind: (1) to preserve the SI prefixes as unambiguous decimal multipliers and (2) to provide alternative prefixes for those cases where binary multipliers are needed. The first goal affects the general public, the wide audience of technical and nontechnical persons who use computers without much concern for their construction or inner working. These persons will normally interpret kilo, mega, etc., in their proper decimal sense. The second goal speaks to specialists—the prefixes for binary multiples make it possible for persons who work in the information sciences to communicate with precision." 
  61. ^ "IEEE-SA STANDARDS BOARD STANDARDS REVIEW COMMITTEE (RevCom) MEETING AGENDA". 2005-03-19. 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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  66. ^ HD 60027-2:2003 Information about the harmonization document (obtainable on order)
  67. ^ prEN 60027-2:2006 Information about the EN standardization process
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  74. ^ Gateway
    Sun Microsystems
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  79. ^ Flyspray
  80. ^ bugs.mysql.com
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  82. ^ DFSee
  83. ^ disktype
  84. ^ Mac OS X Manual Page For raidutil(8)
  85. ^ FreeDOS-32 - Standards Compliance
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  87. ^ GNOME Network
  88. ^ SLIB
  89. ^ Cygwin/XFree86
  90. ^ Re: minor typo - HTTrack Website Copier Forum
  91. ^ http://developer.pidgin.im/ticket/1684 Developer discussion
  92. ^ "Deluge changeset". Retrieved 2007-06-13. "proper prefix for size" 
  93. ^ What's New in zFTPServer Suite
  94. ^ SourceForge.net: Files
  95. ^ archive.netbsd.se
  96. ^ WinSCP :: Recent Version History
  97. ^ "MediaInfo". MediaInfo main site. Retrieved 01 March 2010. 
  98. ^ "News - Snow Leopard: 1 GB = 1000 MB". macprime.ch. 2009-06-19. Retrieved 2009-08-29. 
  99. ^ "How Mac OS X reports drive capacity". Apple Inc. 2009-08-27. Retrieved 2009-10-16. 
  100. ^ On 6 January 2007, a check of the websites of Fujitsu, HGST, Samsung, Seagate, Toshiba and Western Digital showed these companies (representing virtually all of the HDD industry by unit volume) specify capacity with the SI prefix definitions.

Further reading[edit]

External links[edit]