Binary prefix

A binary prefix is a unit prefix that indicates a multiple of a unit of measurement by an integer power of two. The most commonly used binary prefixes are kibi, mebi, and gibi. They are most often used in information technology as multipliers of bit and byte, when expressing the capacity of storage devices or the size of computer files.
The binary prefixes "kibi", "mebi", etc. were defined in 1999 by the International Electrotechnical Commission, in the IEC 60027-2 standard. They were meant to replace the metric decimal power prefixes, such as "kilo", "mega" and "giga", that were commonly used in the computer industry to indicate the nearest powers of two. For example, a memory module whose capacity was specified by the manufacturer as "2 megabytes" or "2 MB" would hold =, instead of =.
On the other hand, a hard disk whose capacity is specified by the manufacturer as "10 gigabytes" or "10 GB", holds = bytes, or a little more than that, but less than = and a file whose size is listed as "2.3 GB" may have a size closer to ≈ or to =, depending on the program or operating system providing that measurement. This kind of ambiguity is often confusing to computer system users and has resulted in lawsuits. The IEC 60027-2 binary prefixes have been incorporated in the ISO/IEC 80000 standard and are supported by other standards bodies, including the BIPM, which defines the SI system, the US NIST, and the European Union.
Prior to the 1999 IEC standard, some industry organizations, such as the Joint Electron Device Engineering Council, noted the common use of the terms kilobyte, megabyte, and gigabyte, and the corresponding symbols KB, MB, and GB in the binary sense, for use in storage capacity measurements. However, other computer industry sectors continued using those same terms and symbols with the decimal meaning. Since then, the major standards organizations have expressly disapproved the use of SI prefixes to denote binary multiples, and recommended or mandated the use of the IEC prefixes for that purpose, but the use of SI prefixes in this sense has persisted in some fields.

Definitions

In 2022, the International Bureau of Weights and Measures adopted the decimal prefixes ronna for 1000⁹ and quetta for 1000¹⁰. In 2025, the prefixes robi and quebi were adopted by the IEC.

Comparison of binary and decimal prefixes

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 kibi vs. kilo to nearly 27% for the quebi vs. quetta.

History

Early prefixes

There are several numeral prefixes in the English language that are binary prefixes, such as bi-, semi-, hemi-, di-, tetra- and octo-.
The original metric system adopted by France in 1795 included two binary prefixes named double- and demi-. However, these were not retained when the SI prefixes were internationally adopted by the 11th CGPM conference in 1960.

Storage capacity

Main memory

Early computers used one of two addressing methods to access the system memory; binary or decimal. For example, the IBM 701 used a binary methods and could address 2048 words of 36 bits each, while the IBM 702 used a decimal system, and could address ten thousand 7-bit words.
By the mid-1960s, binary addressing had become the standard architecture in most computer designs, and main memory sizes were most commonly powers of two. This is the most natural configuration for memory, as all combinations of states of their address lines map to a valid address, allowing easy aggregation into a larger block of memory with contiguous addresses.
While early documentation specified those memory sizes as exact numbers such as 4096, 8192, or units, computer professionals also started using the long-established metric system prefixes "kilo", "mega", "giga", etc., defined to be powers of 10, to mean instead the nearest powers of two; namely, 2¹⁰ = 1024, 2²⁰ = 1024², 2³⁰ = 1024³, etc. The corresponding metric prefix symbols were used with the same binary meanings. The symbol for 2¹⁰ = 1024 could be written either in lower case or in uppercase. The latter was often used intentionally to indicate the binary rather than decimal meaning. This convention, which could not be extended to higher powers, was widely used in the documentation of the IBM 360 and of the IBM System/370, of the CDC 7600, of the DEC PDP-11/70 and of the DEC VAX-11/780.
In other documents, however, the metric prefixes and their symbols were used to denote powers of 10, but usually with the understanding that the values given were approximate, often truncated down. Thus, for example, a 1967 document by Control Data Corporation abbreviated "2¹⁶ = = words" as "65K words", while the documentation of the HP 21MX real-time computer denoted = = as "196K" and 2²⁰ = as "1M".
These three possible meanings of "k" and "K" were used loosely around the same time, sometimes by the same company. The HP 3000 business computer could have "64K", "96K", or "128K" bytes of memory. The use of SI prefixes, and the use of "K" instead of "k" remained popular in computer-related publications well into the 21st century, although the ambiguity persisted. The correct meaning was often clear from the context; for instance, in a binary-addressed computer, the true memory size had to be either a power of 2, or a small integer multiple thereof. Thus a "512 megabyte" RAM module was generally understood to have = bytes, rather than.

Hard disks

In specifying disk drive capacities, manufacturers have always used conventional decimal SI prefixes representing powers of 10. Storage in a rotating disk drive is organized in platters and tracks whose sizes and counts are determined by mechanical engineering constraints so that the capacity of a disk drive has hardly ever been a simple multiple of a power of 2. For example, the first commercially sold disk drive, the IBM 350, had 50 physical disk platters containing a total of sectors of 100 characters each, for a total quoted capacity of 5 million characters.
Moreover, since the 1960s, many disk drives used IBM's disk format, where each track was divided into blocks of user-specified size; and the block sizes were recorded on the disk, subtracting from the usable capacity. For example, the IBM 3336 disk pack was quoted to have a 200-megabyte capacity, achieved only with a single -byte block in each of its 808 × 19 tracks.
Decimal megabytes were used for disk capacity by the CDC in 1974. The Seagate ST-412, one of several types installed in the IBM PC/XT, had a capacity of when formatted as 306 × 4 tracks and 32 256-byte sectors per track, which was quoted as "10 MB". Similarly, a "300 GB" hard drive can be expected to offer only slightly more than =, bytes, not . The first terabyte hard disk drive was introduced in 2007. Decimal prefixes were generally used by information processing publications when comparing hard disk capacities.
Some programs and operating systems, such as Microsoft Windows, still use "MB" and "GB" to denote binary prefixes even when displaying disk drive capacities and file sizes, as did Classic Mac OS. Thus, for example, the capacity of a "10 MB" disk drive could be reported as "", and that of a "300 GB" drive as "279.4 GB". Some operating systems, such as Mac OS X, Ubuntu, and Debian, have been updated to use "MB" and "GB" to denote decimal prefixes when displaying disk drive capacities and file sizes. Some manufacturers, such as Seagate Technology, have released recommendations stating that properly-written software and documentation should specify clearly whether prefixes such as "K", "M", or "G" mean binary or decimal multipliers.

Floppy disks

used a variety of formats, and their capacities were usually specified with SI-like prefixes "K" and "M" with either decimal or binary meaning. The capacity of the disks was often specified without accounting for the internal formatting overhead, leading to more irregularities.
The early 8-inch diskette formats could contain less than a megabyte with the capacities of those devices specified in kilobytes, kilobits or megabits.
The 5.25-inch diskette sold with the IBM PC AT could hold = bytes, and thus was marketed as "1200 KB" with the binary sense of "KB". However, the capacity was also quoted "1.2 MB", which was a hybrid decimal and binary notation, since the "M" meant 1000 × 1024. The precise value was or .
The 5.25-inch Apple Disk II had 256 bytes per sector, 13 sectors per track, 35 tracks per side, or a total capacity of bytes. It was later upgraded to 16 sectors per track, giving a total of = bytes, which was described as "140KB" using the binary sense of "K".
The most recent version of the physical hardware, the "3.5-inch diskette" cartridge, had 720 512-byte blocks. Since two blocks comprised 1024 bytes, the capacity was quoted "360 KB", with the binary sense of "K". On the other hand, the quoted capacity of "1.44 MB" of the High Density version was again a hybrid decimal and binary notation, since it meant 1440 pairs of 512-byte sectors, or =. Some operating systems displayed the capacity of those disks using the binary sense of "MB", as "1.4 MB". User complaints forced both Apple and Microsoft to issue support bulletins explaining the discrepancy.

Optical disks

When specifying the capacities of optical compact discs, "megabyte" and "MB" usually meant 1024² bytes. Thus a "700-MB" CD has a nominal capacity of about, which is approximately .
On the other hand, capacities of other optical disc storage media like DVD, Blu-ray Disc, HD DVD and magneto-optical have been generally specified in decimal gigabytes, that is, 1000³ bytes. In particular, a typical "" DVD has a nominal capacity of about, which is about.