In computing, binary prefixes are names or associated symbols that can precede a unit of measure (such as a byte) to designate multiplication by a power of two. In certain contexts in computing (such as computer memory sizes), it is convenient and useful to express large multiples of units using powers of two. As the binary multipliers 1024 (210), 1048576 (220) (etc.) are close to certain SI prefixes such as kilo- (1000 = 103) and mega- (1000000 = 106) respectively, it has been traditional in some settings to use these SI prefixes with the binary meanings, that is, to use "mega" (or the symbol, M) to mean 1048576 instead of 1000000 and so on. However, as SI prefixes have the decimal meanings in every other context, this usage leads to ambiguity. Furthermore, even in computing, certain areas have always used the SI prefixes to mean decimal multipliers, and not the binary sense. To resolve this confusion, standards organisations deprecate the use of SI prefixes in the binary sense, and instead propose a new set of binary prefixes to designate binary multipliers. Each successive prefix is 1024 (210) times the previous one, instead of the 1000 (103) used by the SI prefix system. Adoption of these prefixes has been slow, but is growing.

History

Early computers used one of two addressing methods to access the system memory; binary (base-2) or decimal (base-10). For instance, the IBM 701 (1952) used binary and could address 2,048 36-bit words, while the IBM 702 (1953) used decimal and could address 10,000 7-bit words.

One of the most successful early computers was the IBM 1401. It was introduced in 1959 and by 1961 one out of every four electronic stored-program computers was an IBM 1401. It used decimal addressing and could have 1400, 2000, 4000, 8000, 12000 or 16000 characters of 8-bit core storage. In the 1950s, computer engineers were familiar with the terms kilo (k) and mega (M). It was common to see 4.7k for a 4700 ohm resistor or 10Mc for a 10 megacycle (megahertz) frequency. It was natural to borrow the term k to express large quantities of storage. A reference to a "4k IBM 1401" meant 4,000 characters of storage (memory).

By the mid 1960s, binary addressing had become the standard architecture in computer design. The computer system documentation would specify the memory size with an exact number such as 32,768, 65,536 or 131,072 words of storage (all powers of 2). There were several methods used to abbreviate these quantities. The use of K in the binary sense as in a "32K store" can be found as early as 1960. 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 (1968) made extensive use of K as 1024. A further style was to truncate the last 3 digits and append K. The exact values 32,768, 65,536 and 131,072 would then become 32K, 65K and 131K. (If 32,768 were instead rounded off, it would be 33K; if K = 1024 were used, 65,536 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 196,608 as 196K and 1,048,576 as 1 M, while the HP 3000 business computer (1973) could have 64K, 96K, or 128K bytes of memory.

The terms Kbit, Kbyte, Mbit and Mbyte started to be used as binary units in the early 1970s. Most memory capacities were expressed in K, even when M could have been used: The IBM System/370 Model 158 brochure (1972) had the following: "Real storage capacity is available in 512K increments ranging from 512K to 2,048K bytes." Megabyte was used to describe the 22-bit addressing of DEC PDP-11/70 (1975) and gigabyte the 30-bit addressing DEC VAX11/780 (1977).

By the mid 1970s it was common to see K (or Kbyte) as 1,024 and the occasional M (or Mbyte) as 1,048,576 for words or bytes of memory (RAM). K and M were also used with their decimal meaning for disk storage. In the 1980s the terms kilobyte, megabyte, and gigabyte became popular along with the abbreviations KB, MB, and GB.

The dual use of these prefixes as both decimal and binary quantities was defined in early standards and dictionaries. The ANSI/IEEE Std 1084-1986 is still available for reference and defined kilo and mega. (The term "computer storage" means system memory.)

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

mega (M). (1) A prefix signifying one million. (2) In statements involving size of computer storage, a prefix signifying 220, or 1,048,576.

The binary units Kbyte and Mbyte were formally defined in ANSI/IEEE Std 1212-1991. The terms 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 1,000,000,000 or 230 bytes. Kilobyte, Kbyte, and KB are equivalent units and all are defined in the current standard, IEEE 100-2000.

The industry has coped with the dual definitions because system memory (RAM) typically uses the binary meaning while disk storage uses the decimal meaning. There are exceptions like diskettes and CDs. There are no SI units for computer storage capacity but the decimal prefix meanings of KB, MB, and GB are often referred to as SI prefixes.

In January 1999, the International Electrotechnical Commission introduced the prefixes kibi-(Kibibyte), mebi-, gibi-, etc., and the symbols Ki, Mi, Gi, etc. to specify binary multiples of a quantity and eliminate this ambiguity. The names for the new standard are derived from the first two letters of the original SI prefixes proceeded by bi, short for "binary". The new standard also clarifies that, from the point of view of the IEC, the SI prefixes will henceforth only have their base-10 meaning and never have a base-2 meaning.

The second edition of the standard defined them only up to exbi-, but in 2005, the third edition added prefixes zebi- and yobi-,thereforematching all standard SI prefixes with their binary counterparts.

On March 19, 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.

Consumer confusion

In the early days of computers there was little or no consumer perplexity because of the sophisticated nature of the consumers and the practice of the computer manufacturers to specify (as opposed to advertise) their products with decimal digits of sufficient places, e.g., the 1968 IBM stated System 360 "Model 91s can accommodate up to 6,291,496 bytes of main storage."

Hard disk drive manufacturers used MB, i.e. 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 (decimal sense) of capacity.

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).

See, for example, the following two images; consumers may be confused by the difference between the 160 GB on the disk drive package and the 149.05 GB reported by the operating system.

SI prefixes used in the binary sense

The one-letter symbols are indistinguishable to SI prefixes, except for "K", which is used interchangeably with "k" (in SI, the upper-case or capital "K" stands for kelvin, and only the lower-case "k" represents 1,000).

These prefixes are in common use in contexts such as file and memory sizes. The names and values of the SI prefixes were defined in the 1960 SI standard, with powers-of-1000 values. Standard dictionaries do recognize the binary meanings for these prefixes. Oxford online dictionary define, for example, megabyte as: "Computing a unit of information equal to one million or (strictly) 1,048,576 bytes."

BIPM (the International Bureau of Weights and Measures which maintains SI) expressly prohibits the binary prefix usage, and recommends the use of the IEC prefixes as an alternative since computing units are not included in SI.

Some have suggested that "k" be used for 1,000, and "K" for 1,024, but this can't be extended to the higher order prefixes and has never been widely recognised.

Although the SI prefixes denoting fractions of a bit or byte might theoretically find application in areas such as cryptography, data compression, and data transfer rates, they are not used in practice.

Informally, the prefixes are often used on their own.Thereforeone might hear about a "256K DRAM" (256 binary kilobytes), "a 160 MB HDD" (160 decimal megabytes) or "a 2M Internet connection" (2 decimal megabits per second). What units are being used, and whether the multipliers are decimal or binary, depends on context and can't be determined by the units alone.

IEC standard prefixes

Example: 300 GB ≅ 279.5 GiB.

Approximate ratios between binary & decimal prefixes

As the order of magnitude increases, the percentage difference between the binary and decimal values of a prefix increases, from 2.4% (with the kilo prefix) to over 20% (with the yotta prefix). This makes differentiating between the two increasingly important as larger and larger data storage and transmission technologies are developed.

Adoption

As of 2007, the IEC binary naming convention has been adopted by some, but is not used universally. Most[specify] publications, computer manufacturers and software companies are still using the traditional binary units defined in IEEE 100, The Authoritative Dictionary of IEEE Standards Terms, Seventh Edition, 2000.[dubious – discuss]

The binary convention is strongly supported by many standardization bodies and technical organizations, such as IEEE, CIPM, NIST, and SAE. The new binary prefixes have also been adopted by the European Committee for Electrotechnical Standardization (CENELEC) as the harmonization document HD 60027-2:2003-03. This document will be adopted as a European standard.

The prefixes are beginning to be used in technical articles and software where it is vital to avoid ambiguity. Instances of software that use IEC standard prefixes (along with standard SI prefixes) include:

the Linux kernel

GNU Core Utilities

Launchpad

GParted

ifconfig

Deluge (BitTorrent client)

Azureus

Pidgin (IM client)

BitTornado

Other programs, such as fdisk and apt-get, use SI prefixes with their decimal meaning.

It can be argued that the main purpose of the binary prefixes is to clarify that, according to national and international standards, the traditional SI prefixes always refer to powers of ten, even in the context of information technology. Therefore, instead of measuring the success of the binary prefixes based on how frequently they appear in technical and marketing literature, it may be more appropriate to judge them by their success in restoring the original power-of-ten meaning of the standard SI prefixes in information technology. Binary prefixes are only convenient for a small number of information-technology quantities, most notably the size of address spaces (e.g., of RAM chips). They provide no practical advantage for quantities where powers-of-two times a small integer are not preferred numbers, such as file sizes, download speeds, line rates, symbol rates, clock frequencies, and tape or disk capacities. There, decimal prefixes are far more convenient for mental arithmetic.

Usage notes

In this section, the phrase "decimal unit" will be used to denote "SI designation understood in its standard, decimal, power-of-1000 sense" and "binary unit" will mean "SI designation understood in its binary, power-of-1024 sense." B will be used as the symbol for byte as per computer-industry standard (IEEE 1541 and IEC 60027).

Certain units are always understood as decimal even in computing contexts. For example, hertz (Hz), which is used to measure clock rates of electronic components, and bit/s, used to measure bit rate. So a 1 GHz processor performs 1,000,000,000 clock ticks per second, a 128 kbit/s MP3 stream consumes 128,000 bits (16 kB, 15.625 KiB) per second, and a 1 Mbit/s Internet connection can transfer 1,000,000 bits (125 kB, approx 122 KiB) per second, assuming an 8-bit byte, and no overhead.

Pronunciation

It is suggested 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."

Computer memory

Main article: JEDEC memory standards
The 536,870,912 byte (512x220) capacity of these RAM modules is stated as "512 MB" on the label.

Measurements of most types of electronic memory such as RAM and ROM and Flash (large scale disk-like flash is sometimes an exception) are given in binary units, as they are made in power-of-two sizes. 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 contiguous block of memory.

JEDEC Solid State Technology Association, the semiconductor engineering standardization body of the Electronic Industries Alliance (EIA) in Standard 100B.01 defines in the binary sense K, M and G as prefixes to units of semiconductor memory, noting that these definitions are “only included to reflect common usage” and noting that ‘IEEE/ASTM SI 10-1997 state “This practice frequently leads to perplexity and is deprecated.” '. All standards published by JEDEC are still using the common usage, including end-user packaging recommendations for memory chips.

Many computer programming tasks naturally reference memory in terms of powers of two. For example, a 16-bit pointer can reference at most 65,536 items (bytes, words, or other objects), or an operating system might map memory in terms of 4,096-byte pages, in which case exactly 8,192 pages could be allocated within 33,554,432 bytes of hardware memory. It is convenient to informally express these numbers, respectively, as 64K items, or as 8K pages of 4 Kbytes (KiB) each within 32 MBytes (MiB) of memory. A programmer can easily mentally calculate that "8K x 4K is 32 meg" and get it exactly right, within this powers-of-two context. This convenience is likely one source of originally adapting "kilo" and "mega" from SI as shorthand for 1,024 and 1,048,576, as specialized jargon within a segment of the industry.

Almost all computer user tasks (and many high-level programming tasks) have no natural affinity or need for explicit powers of two. The consumer perplexity between powers of 1000 and powers of 1024 may derive largely from some operating systems and applications that were originally written by and for programmers, and whichthereforereported quantities such as file sizes in familiar (to programmers) powers of 1024 while using SI (powers of 1000) abbreviations. Without such reporting, most users might not have been substantially exposed to powers of 1024, as the net memory available to users after various overheads is rarely a power of two. This legacy behavior of operating systems reporting sizes in powers of 1024 has continued to this day (in 2007) even in many GUI oriented operating systems intended mainly for non-programmers.

Hard disk drives

HDD manufacturers state capacity in decimal units. This usage has a long tradition, even predating the SI system of decimal prefixes adopted in 1960, as follows:

The first disk drive the IBM 350 (1950s) had 5,000,000 6 bit characters organized in 100 character sectors (i.e., blocks). This predates the SI system.

In the 1960s most disk drives used IBM's variable block length format (called, Count Key Data or "CKD"). 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 typically 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.

CKD continued into the 1990s and perhaps into this day. In the 1970s and 1980s most drives were specified with unformatted tracks (the unformatted capacity) with the specific block size and formatted capacity a function of the controller design. For example, the ST412 of IBM PC/XT fame had an unformatted capacity of 12.75 MB (not MiB) and with the Xebec controller and 512 byte blocks it formatted to and was advertised as a 10.0 MB (not MiB) HDD. Other controllers supported other block sizes resulting in other formatted capacities.

The advent of intelligent interfaces (SCSI and IDE) in the early 1990s took the block size decision into the drive and virtually all chose 512 bytes, for no reason other than that was what IBM had chosen when they picked the Xebec controller for the PC/XT. Capacity continued to be specified by the HDD manufacturers with SI prefix definitions.

As of January 2007, most, if not all, HDD manufacturers continue to use decimal prefixes to identify capacity.

Flash drives

USB Flash Drive and Flash-based memory cards like CompactFlash and Secure Digital are typically classified in "powers of two" multiples of decimal megabytes; for example, a "256 MB" card would hold 256 million bytes. Although the devices typically 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

Floppy disk drive and media manufacturers use decimal units for unformatted recording capacity while most computer operating systems use binary units to measure the formatted capacity. The original IBM Personal Computer (1981) used a Tandon TM100 5¼ inch floppy disk drive. The single sided drive was rated at 250 kilobytes (unformatted) and the double sided version was rated at 500 kilobytes.

A 5¼ inch diskette recorded at double density (MFM) will hold 6,250 bytes per track and has 40 tracks per side, yielding 250,000 bytes per side. To make it practical to record smaller blocks of data, the tracks are formatted into sectors with gaps between them. The gaps allow individual sectors to be recorded without overwriting adjacent sectors. Each sector also has extra header bytes to identify the sector.

With IBM PC-DOS 1.0 and 1.1, each track has 8 sectors of 512 bytes and this provides 163,840 bytes per side (8 x 512 x 40). The IBM user documentation referred to this as "160KB" for single sided diskette and "320KB" for double sided diskette. Starting with PC-DOS 2.0 (1983), each track had 9 sectors of 512 bytes. The formatted capacity was increased to 184,320 bytes per side or 368,640 bytes per diskette. The IBM documentation referred to these as "180KB" and "360KB" diskettes. The same drives and media can have different capacities depending on format.

On all diskettes the capacity available to the user will be smaller that the total number of sectors because some are reserved by the operating system for boot records or directory tables.

The IBM Personal Computer/AT (1984) had a new 5¼ inch disk drive that had 80 tracks per side, rotated at 360 rpm (versus 300 rpm) and had a new diskette media. The formatted capacity was 1,228,800 bytes or 1200 KB. (80 tracks x 15 sectors x 512 bytes x 2 sides)

The IBM PC Convertible (1986) used the 3½ inch diskettes. These were similar in recording technology to the original 5¼ inch drives except they had 80 tracks per side. The formatted capacity was 737,280 bytes or 720 KB. Apple used the same disk with a different recording technology, GRC, that gave a formatted capacity of 819,200 bytes or 800 KB. Apple referred to this as an "800K" disk.

The last widely adopted diskette was the 3½ inch high density. This has twice the capacity as the 720 KB diskettes, 1,474,560 bytes or 1440 KB. The drive was marketed as 1.44 MB when a more accurate value would have been 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. The 1200 KB 5¼ inch diskette was marketed as 1.2 MB (1.171875 MiB) without any controversy.

Optical discs

CD capacities are always given in binary units. A "700 MB" (or "80 minute") CD has a nominal capacity of about 700 MiB (approx 730 MB). However, the capacities of other optical disc storage media like DVD, Blu-ray Disc, HD DVD are given in decimal units. A "4.7 GB" DVD has a nominal capacity of about 4.38 GiB.

Buses

Bus bandwidth is given in decimal units. This is not because hard drive capacities use the decimal versions, nor because bit rates do, but because clock speeds do. For example, "PC3200" memory runs on a double pumped 200 MHz bus, transferring 8 bytes per cycle, and hence has a bandwidth of 200,000,000x2x8 = 3,200,000,000 byte/s.

Legal disputes

There have been two significant class action lawsuits against digital storage manufactures. One case involved flash memory and the other involved hard disk drives. Both were settled with the manufactures agreeing to clarify the storage capacity of their products on the consumer packaging.

On February 20, 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 to use the binary values 220 for megabyte and 230 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 manufacturers agreed to clarify the flash memory card capacity on 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". The law firms Gutride Safier, LLP and Milberg Weiss received $2.4 million.

On July 7, 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 "can't be expected to reform the software industry", they agreed to settle in March 2006 with June 14, 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.

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."

The flash memory and hard disk manufacturers now have disclaimers on their packaging and web sites clarifying the formatted capacity of the flash memory or defining MB as 1 million bytes and 1 GB as 1 billion bytes.

Also, the Class Action Fairness Act of 2005 requires greater scrutiny on coupon settlements. One of the plaintiff law firms in the Vroegh case, Milberg Weiss & Bershad, was indicted for fraud in unrelated class action cases.