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In computing, binary prefixes can be used to quantify large numbers where powers of two are more useful than powers of ten. Each successive prefix is multiplied by 1024 (210) rather than the 1000 (103) used by the SI prefix system. Despite the ambiguity, binary prefixes are often written and pronounced identically to the SI prefixes, rather than using the IEC system described below.

History

Using the prefixes kilo-, mega-, giga-, etc., and their symbols K, M, G, etc. (see below for the peculiarities of "K"), in the binary sense can cause serious confusion.

In January 1999, the International Electrotechnical Commission introduced the prefixes kibi-, mebi-, gibi-, etc., and the symbols Ki, Mi, Gi, etc. to specify binary multiples of a quantity. Amendment 2 to IEC International Standard IEC 60027-2: Letter symbols to be used in electrical technology — Part 2: Telecommunications and electronics * They have since been officially adopted by many other organizations, most notably the Institute of Electrical and Electronics Engineers; see standard IEEE 1541. However, they have not been widely adopted and many people continue to use the SI prefixes in a binary sense, despite the lack of support from official bodies. As a result, there is no unambiguous notation for decimal multiples of bits and bytes.

The names and values of the SI prefixes were defined in the 1960 SI standard, with powers-of-1000 values. As of 2005, standard dictionaries do not recognize the binary meanings for these prefixes.

Binary prefixes using SI symbols (non-standard, but common)

Name Symbol Value Base 16 Base 10
kilo k/K 210 = 1,024 = 162.5 > 103
mega M 220 = 1,048,576 = 165 > 106
giga G 230 = 1,073,741,824 = 167.5 > 109
tera T 240 = 1,099,511,627,776 = 1610 > 1012
peta P 250 = 1,125,899,906,842,624 = 1612.5 > 1015
exa E 260 = 1,152,921,504,606,846,976 = 1615 > 1018
zetta Z 270 = 1,180,591,620,717,411,303,424 = 1617.5 > 1021
yotta Y 280 = 1,208,925,819,614,629,174,706,176  = 1620 > 1024

The one-letter abbreviations are identical to SI prefixes, except for "K", which is used interchangeably with "k" (in SI, "K" stands for the kelvin, and only "k" stands for 1,000). Some have suggested that "k" be used for 1,000, and "K" for 1,024, but this cannot be extended to the higher order prefixes and has never been widely recognised.

Although the 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. Thus one might hear about "a 40K file" (40 binary kilobytes) 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 exactly what is being measured.

IEC standard prefixes

In 1999, the International Electrotechnical Commission (IEC) published Amendment 2 to "IEC 60027-2: Letter symbols to be used in electrical technology — Part 2: Telecommunications and electronics". This standard, which was approved in 1998, introduced the prefixes kibi-, mebi-, gibi-, tebi-, pebi-, exbi-, to be used in specifying binary multiples of a quantity. The names come from the first two letters of the original SI prefixes followed by bi which is short for "binary". It also clarifies that, from the point of view of the IEC, the SI prefixes only have their base-10 meaning and never have a base-2 meaning.

This amendment was included in the next edition of the standard: "IEC 60027-2 (2000-11) Ed. 2.0"

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

As of 2005 this naming convention has not gained widespread use, but its use is growing. It is strongly supported by many standardization bodies and technical organizations, such as IEEE, CIPM, NIST, and SAE.Prefixes for Binary Multiples — The NIST Reference on Constants, Units, and UncertaintyRules for SAE Use of SI (Metric) Units — Section C.1.12 — SI prefixes BIPM (which maintains SI) expressly prohibits the binary prefix usage, and recommends the use of the IEC prefixes as an alternative (computing units are not included in SI).The International System of Units, 8th edition, 2006 — Side note in section 3.1 — SI prefixes In particular, on March 19, 2005 the IEEE standard IEEE 1541-2002 (Prefixes for Binary Multiples) has been elevated to a full-use standard by the IEEE Standards Association after a two-year trial period.

Name Symbol Base 2 Base 16 Base 10
kibi Ki 210 162.5 0x400 = 1,024 > 103
mebi Mi 220 165 0x10 0000 = 1,048,576 > 106
gibi Gi 230 167.5 0x4000 0000 = 1,073,741,824 > 109
tebi Ti 240 1610 0x100 0000 0000 = 1,099,511,627,776 > 1012
pebi Pi 250 1612.5 0x4 0000 0000 0000 = 1,125,899,906,842,624 > 1015
exbi Ei 260 1615 0x1000 0000 0000 0000 = 1,152,921,504,606,846,976 > 1018
zebi Zi 270 1617.5 0x40 0000 0000 0000 0000 = 1,180,591,620,717,411,303,424 > 1021
yobi Yi 280 1620 0x1 0000 0000 0000 0000 0000 = 1,208,925,819,614,629,174,706,176 > 1024

Example: 300 GB ~ 279.5 GiB (= 0x117.6592E GiB = 0x45D96.4B8 MiB = 0x1176592E KiB = 0x45D964B800 bytes).

Approximate ratios between binary and decimal prefixes

Notice that 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).

Name Bin ÷ Dec Dec ÷ Bin Example Percentage difference
kilobyte : kibibyte 1.024 0.976 100 KB ≅ 97.6 KiB +2.4 % or −2.3 %
megabyte : mebibyte 1.049 0.954 100 MB ≅ 95.4 MiB +4.9 % or −4.6 %
gigabyte : gibibyte 1.074 0.931 100 GB ≅ 93.1 GiB +7.4 % or −6.9 %
terabyte : tebibyte 1.100 0.909 100 TB ≅ 90.9 TiB +10 % or −9.1 %
petabyte : pebibyte 1.126 0.888 100 PB ≅ 88.8 PiB +12.6 % or −11.2 %
exabyte : exbibyte 1.153 0.867 100 EB ≅ 86.7 EiB +15.3 % or −13.3 %
zettabyte : zebibyte 1.181 0.847 100 ZB ≅ 84.7 ZiB +18.1 % or −15.3 %
yottabyte : yobibyte 1.209 0.827 100 YB ≅ 82.7 YiB +20.9 % or −17.3 %

Usage notes

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 traditional computer-industry, binary, power-of-1024 sense." B will be used as the symbol for byte as per computer-industry standard (IEEE 1541 and IEC 60027; despite B being also the symbol for bel).

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).Binary vs. Decimal Measurements

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.

Hard disk drives: Most manufacturers state capacity in decimal units. This usage has a long tradition, even predating the SI system of decimal prefixes adopted in 1960. The decimal-based capacity in hard disk drives follows the method used for serially accessed storage media which predated direct access storage media like hard disk drives. When a stream of data is stored, it's more logical to indicate how many thousands, millions, or billions of bytes have been stored versus how many multiples of 1024, 1,048,576, or 1,073,741,824 bytes have been. When the first hard disk drives were developed, the decimal measurement continued the tradition of punch cards and tapes. Thus, today, most devices that are addressed or seen as "storage" use the decimal system to identify capacity.

Flash Drives: Some manufacturers of disk-like flash memory seem to have adopted the practice of selling drives measured in power of two multiples of decimal megabytes, purportedly using the roughly 5 percent difference between, say, 256 MB and 256 MiB for wear levelling.

Floppy Drives: The confused usage of decimal prefixes may have started in floppy drives where the drive and media manufacturers stated their unformatted capacity while various systems houses published differing formatted capacities as a consequence of their varying controller designs. It appears that some system manufactures and OS vendors began reporting in what we now know as Ki bytes. A very confusing hybrid system developed with the double sided high density 3½" floppy disk, in which a "megabyte" means a thousand 1024-byte "kilobytes". Thus, as of 2005, manufacturers universally use the designation "1.44 MB diskette" for a product which holds neither 1.44×220 bytes nor 1.44×106 bytes, but rather 1.44×1000×1024 bytes (approximately 1.406 MiB, or 1.475 MB). This is probably because some marketing person decided that this was best advertised as a double capacity version of the prior generation 720 KB product (of course, it was 720 KiB).

Some modern-day PC users regard both RAM and disk as similar kinds of storage and expect their capacities to be measured in the same way. Operating systems usually report disk space using the binary version. To the purchaser of a "30 GB" hard drive, rather than reporting "30 GB", Microsoft Windows, for example, reports HDD capcity in two forms, "30,064,771,072" and "28 GB". This creates confusion and has led to legal disputes, sometimes made worse by other technical issues such as failure to distinguish between unformatted and formatted capacities and to account for the overhead inherent in disk file systems.

CD capacities are always given in binary units. A "700 MB" (or "80 minute") CD has a nominal capacity of about 700 MiB.Data capacity of CDs But DVD capacities are given in decimal units. A "4.7 GB" DVD has a nominal capacity of about 4.38 GiB.Understanding Recordable and Rewritable DVD

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 200,000,000×2×8 = 3,200,000,000 byte/s.

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."

Legal disputes

The implicit use of decimal units to describe the capacity of storage devices has become a source of confusion as these devices are increasingly marketed to non-technical consumers. When a user buys a device advertised using decimal units, and installs it in a system that shows the available space in binary units, a misinformed user may be disturbed by the apparent discrepancy. As a result, there have been several lawsuits against companies who sell hard drives, flash memory devices, and computer systems that list drive capacities.

At least 3 significant lawsuits have been filed:

References

See also

Specific units of IEC 60027-2 A.2

External links

Measurement | Naming conventions | Prefixes | Units of information | Numeration

Двоична представка | Binární předpona | Binært præfiks | Binärpräfixe | Prefijo binario | Préfixe binaire | Prefissi per multipli binari | Bináris prefixum | Veelvouden van bytes | 2進接頭辞 | Binærprefiks | Przedrostek dwójkowy | Prefixo binário | Prefixe binare | Двоичные приставки | Binárny prefix | Јобибит | 二进制前缀

 

This article is licensed under the GNU Free Documentation License. It uses material from the "Binary prefix".

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