Mebibyte

The mebibyte is a multiple of the unit byte for digital information.[1] The binary prefix mebi means 2²⁰; therefore one mebibyte is equal to 1048576bytes, i.e., 1024 kibibytes. The unit symbol for the mebibyte is MiB.

The unit was established by the International Electrotechnical Commission (IEC) in 1998.[2] It was designed to replace the megabyte when used in the binary sense to mean 2²⁰ bytes, which conflicts with the definition of the prefix mega in the International System of Units (SI) as a multiplier of 10⁶. The binary prefixes have been accepted by all major standards organizations and are part of the International System of Quantities.[3] Many Linux distributions use the unit, but it is not widely acknowledged within the industry or media.[4][5][6][7]

Definition

1 MiB = 2²⁰ bytes = 1048576bytes = 1024 kibibytes

1024 MiB = 1 gibibyte (GiB)

The prefix mebi is a binary prefix and multiplier derived from the SI prefix mega and the word binary. Its value is 1024², having the same power of 1024 as the power of 1000 of its decimal counterpart, the prefix mega (1000²).

Despite its official status, the unit mebibyte is not commonly used even when reporting byte counts calculated in binary multiples, but is often represented as a megabyte. The discrepancy may cause confusion, since operating systems using the binary method report lower numerical values for storage size than advertised by manufacturers, such as disk drive manufacturers, who strictly use decimal units.

History and usage

The binary prefixes, including mebi, were defined by the International Electrotechnical Commission (IEC) in December 1998. All major standards bodies have endorsed the use of them for binary multiples.

Prior to this official definition, the unit megabyte was originally used in computer science to mean one million bytes (for example for 35 MB hard drive would be capable of storing 35 million bytes). Later the same term 'megabyte' was used to mean 1048576 bytes in the context of computer memory, although it continued to mean exactly one million (1000000) bytes in the context of computer storage.[8] The error associated with this ambiguity is relatively small for the megabyte.

In 1995, the International Union of Pure and Applied Chemistry's Interdivisional Committee on Nomenclature and Symbols decided to attempt to resolve this ambiguity by proposing new prefixes for powers of 1024.[9][10] Accepted by the International Electrotechnical Commission (IEC), the IEC published the standard in January 1999.[11][12][13][14]

Some operating systems still compute file size in mebibytes, but report the number as MB (megabytes). For example, all versions of the Microsoft Windows operating system show a file of 2²⁰ bytes as "1.00 MB" or "1,024 KB" in its file properties dialog and show a file of 10⁶ (1000000) bytes as 976 KB.

All versions of Apple's operating systems had the same behavior until 2009 with Mac OS X version 10.6, which instead uses megabytes for all file and disk sizes, so it reports a 10⁶ byte file as 1 MB.[15][16]

The Ubuntu developer Canonical implemented an updated units policy in 2010 and as of Ubuntu 10.10 all versions use IEC binary prefixes for base-2 quantities and SI prefixes for base-10 quantities.[17]

See also

• IEEE 1541
• Orders of magnitude (data)

References

1. International Electrotechnical Commission (January 2010). "IEC 60050 - International Electrotechnical Vocabulary - Details for IEV number 112-01-27". Retrieved 2011-06-19.
2. International Electrotechnical Commission (January 1999), IEC 60027-2 Amendment 2: Letter symbols to be used in electrical technology - Part 2: Telecommunications and electronics.
3. "IEC 80000-13:2008". International Organization for Standardization. Retrieved 21 July 2013.
4. Upgrading and Repairing PCs, Scott Mueller, Pg. 596, ISBN 0-7897-2974-1
5. The silicon web: physics for the Internet age, Michael G. Raymer, Pg. 40, ISBN 978-1-4398-0311-0
6. Knuth: Recent News. Cs-staff.stanford.edu. Retrieved on 2011-01-07.
7. Atwood, Jeff. (2007-09-10) Gigabyte: Decimal vs. Binary. Coding Horror. Retrieved on 2011-01-07.
8. NIST "Prefixes for binary multiples" https://physics.nist.gov/cuu/Units/binary.html
9. IUCr 1995 Report - IUPAC Interdivisional Committee on Nomenclature and Symbols (IDCNS) http://ww1.iucr.org/iucr-top/cexec/rep95/idcns.htm
10. "Binary Prefix" University of Aukland Department of Computer Science https://wiki.cs.auckland.ac.nz/stageonewiki/index.php/Binary_prefix
11. NIST "Prefixes for binary multiples" https://physics.nist.gov/cuu/Units/binary.html
12. Amendment 2 to IEC International Standard IEC 60027-2: Letter symbols to be used in electrical technology - Part 2: Telecommunications and electronics.
13. HDD Turns 50 Years Today - The Chronicles
14. Backman, R. B. (2004). The Description, Evolution, and Applications of Binary Prefixes.
15. "How Mac OS X reports drive capacity". Apple Inc. 2009-08-27. Retrieved 2009-10-16.
16. David Pogue (2011), Mac OS X Lion: The Missing Manual Missing Manual, Oreilly Series, O'Reilly Media, pp. 473–474, ISBN 978-1-4493-9749-4
17. "Ubuntu UnitsPolicy". Ubuntu. 2010. Retrieved 2013-09-26.