Mebibyte

The mebibyte is a multiple of the unit byte for digital information. The binary prefix mebi means 2²⁰; therefore 1 mebibyte is 1048576 bytes. The unit symbol for the mebibyte is MiB.^[1] The unit was established by the International Electrotechnical Commission (IEC) in 1998^[2] It was designed to replace the megabyte used in some computer science contexts to mean 2²⁰ bytes, which is similar to the SI definition of the prefix mega (10⁶) but conflicts with it.

The unit has been accepted for use by all major standards organizations, and appears increasingly in scientific literature. It has seen little usage in non-scientific literature or by the computer industry.^[3][4][5][6] The unit megabyte (symbol MB), formally meaning 1000000bytes, is still commonly used in place of this unit.

Definition

1 MiB = 2²⁰ bytes = 1024 kibibytes = 1048576bytes

The prefix mebi is a binary prefix derived from the words mega and binary, indicating its origin in the closeness in value to the SI prefix mega. One mebibyte (MiB) is 2²⁰ (i.e., 1024 x 1024) bytes,^[7] or 1048576bytes. One MiB differs from one megabyte (MB), which means 10⁶ (i.e. 1000 x 1000 = 1000000) bytes.

The term mebibyte is not commonly used even when reporting numbers calculated as mebibytes. Instead, megabyte is often used to mean 1000 x 1000 (correctly used), 1024 x 1024 (properly mebibytes) or even 1024 x 1000 (a hybrid not recognised by any standards body) by operating system and utility software. Disk drive manufacturers generally use megabyte correctly to mean 1,000,000 bytes. The inconsistency can be confusing, since operating systems using the nonstandards-based method report lower numbers for hard disks than advertised by manufacturers. Many operating systems compute file size in mebibytes, but report the number as MB. For example, all versions of Microsoft Windows operating system shows a file of 2²⁰ bytes as "1.00 MB" or "1,024 KB" in its file properties dialog, while showing a file of 10⁶ (1000000) bytes as 976 KB.

All versions of Apple's operating systems had the same behavior, until Mac OS X version 10.6, which now uses megabytes for all file and disk sizes, so it reports a 10⁶ byte file as 1 MB.^[8][9]

Ubuntu developer Canonical implemented an updated Units Policy in 2010 and as of Ubuntu 10.10 all versions now adhere to the IEC binary prefix for base-2 units and the SI prefix for base-10 units. ^[10]

History

The "Mi" (mebi-) binary prefix (which equals 2²⁰) was created to counter casual misuse of the "M" (mega-) decimal prefix (which equals 10⁶). An example of such casual misuse is the marking of 3½-inch HD floppy disks. While they have an actual capacity of 1474560bytes, they have usually been marked "1.44 MB" in error. The error is this: Though 1474560bytes does equal 1440 KiB, 1440 KiB cannot be designated "1.44 MB" because doing so mixes binary and decimal prefixes. The resulting mixed prefix-base creates a quantity that is not only confusing, it is non-calculable. To maintain consistent prefix-base, 1440 KiB must be designated either "1.40625 MiB" (possibly rounded to "1.41 MiB") or 1.47456 MB (possibly rounded to "1.47 MB"). Lower capacity predecessors of this disquette include versions able to store 720 KiB (designated "720 KB") and 360 KiB (designated "360 KB").

The mebi- prefix was defined by the International Electrotechnical Commission (IEC) in December 1998. Its use (and related units) is presently endorsed by the Institute of Electrical and Electronics Engineers (IEEE) and the International Committee for Weights and Measures (CIPM) in contexts where use of a binary prefix makes sense.

In The Art of Computer Programming, Donald Knuth proposed that the mebibyte be called a large megabyte (abbreviated MMB).

Binary prefixes are increasingly used in scientific literature and open source software. In product advertising and other non-scientific publications, the kilobyte sometimes refers to a power of ten and sometimes a power of two.^{[11][12] [13]}

See also

• SI prefix
• IEEE 1541
• Orders of magnitude (data)

References