Binary prefix
Binärpräfixe ( also IEC prefixes or IEC prefixes ) are resolutions for units of measurement ( unit attachments), denote the multiples of certain powers of two. They are used primarily with units such as bit (symbol " bit " rare " b") or byte (symbol " B") used to measure amounts of data because of frequently occurring powers of two for technical reasons. In contrast to this are Dezimalpräfixe unit prefixes denoting multiples of certain powers of ten. SI prefixes are Dezimalpräfixe for use in the SI unit system, IEC Binärpräfixe are Binärpräfixe, intended for use in data volumes. As a unit intent of both the name and the icon is called.
Only the SI prefixes were historically set of data initially used as Binärpräfixe while serving the SI prefixes (as Dezimalpräfixe ) for physical SI units. Later, the SI prefixes were used as Binärpräfix times and times as Dezimalpräfix for datasets depending on the context. In order to have an alternative to the ambiguous use of the SI prefixes, the IEC put up specific prefixes that are now used exclusively as Binärpräfixe.
IEC prefixes to the base 2
The Binärpräfixe are defined in the following table according to IEC 60027-2:
Example: 512 MiB ( mebibyte ) = 512 x 220 bytes = 536 870 912 bytes ≈ 537 MB ( megabytes).
Standardize
To avoid ambiguity, the International Electrotechnical Commission (IEC ) proposed in June 1996 before a new draft standard for Binärpräfixe that should be used only in the binary sense. This design was adopted as a standard in December 1998 and published in January 1999 as a supplement to IEC 60027-2. He led the prefixes kibi, mebi, gibi, Tebi, Pebi and exbi for binary multiples of units a. In these terms, the first two letters of the already standardized SI prefixes to "bi" were for " binary" supplemented. For the symbols of Binärpräfixe the symbols of the SI prefixes were used and appended to these lower-case letter "i", which was used for the kibi in contrast to the kilo, the capital letter "K". The standard has also been noted that the SI prefixes should only be used for based on powers of ten multiples. These supplements were incorporated into the published in November 2000 second edition of the standard IEC 60027-2. In the published in the August 2005 edition of the standard IEC 60027-2 third the Binärpräfixe taken Zebi and yobi.
Many standards organizations joined in this recommendation. Among them may be mentioned the BIPM / CIPM (1998), the IEEE 1541 ( 2002) and especially in Germany, the Physikalisch- Technische Bundesanstalt (2007 ) (further: NIST, CENELEC, DIN / EN).
Also responsible for the SI prefixes International Bureau of Weights and Measures ( BIPM) does not recommend the use of the binary SI prefixes expressly and recommends the designation of powers of the Binärpräfixe according to the IEC 60027-2 so far by the global ISO standard IEC 80000-13:2008 was ( or DIN EN 80000-13:2009-01 ) identical replacement.
SI prefixes for binary multiples to the base 10
Since there was no special unit Resolutions for powers of two up to 1996, it has become common to use the SI prefixes in connection with storage for designation of powers of two ( by a factor of 210 = 1024 instead of 1000 ), who came to the desired powers of the next. It should be apparent from the combination with the bit or byte units or another context that a power of two meant. This binary using SI prefixes in 1986 was documented by the IEEE in a glossary.
While this is not very problematic in memory modules that are usually only produced in sizes of powers of two, this led, for example, when referring to hard disk capacity in GB or data transfer rates in MB / s or Mbit / s to doubts as to the exact meaning. In addition, the difference in value-added prefixes is getting bigger, so that it no longer is often negligible. Also come sporadically mixed forms before, such as the storage capacity of a 3.5 -inch floppy disk: 1.44 MB = 1440 kB = 1440 × 1024 bytes.
The body responsible for the SI prefixes International Bureau of Weights and Measures ( BIPM) therefore advises of this non-standard proper usage of the SI prefixes and expressly recommends the designation of powers of the IEC 60027-2 Binärpräfixe.
Nevertheless, this notation recommended in 2009 was not widely used (see also Section acceptance and dissemination ).
The values of the SI prefixes and the nearest power of two, and the percentage ( rounded ) differences are shown in the following table:
One other occasionally used approach to draw attention to the proposed deviation from the power of ten, is to use the powers of the capital letter "K" (often spoken as " Ka " ) instead of the lowercase letter "k". Thus, "k " are used for 1000 units and "K" for 1024. This convention is neither standardized nor is it applied consistently. Also, this approach can not be transferred to the larger prefixes, as the symbols for the SI prefixes are written from mega in uppercase ( "M" for mega, "G" for giga and so on ).
Ratio of binary and decimal prefixes
The values of the SI prefixes increase in orders of magnitude, and therefore the SI prefixes are also referred to as a decimal prefixes, while the values of Binärpräfixe increase in powers of two. Specifically, increase the values of the decimal prefixes - starting from kilo - by a factor and the values of the binary prefixes to the factor. That is equivalent to kilo, mega, giga and so on, and kibi corresponds mebi, gibi and so on. Describes the prefixes such that for kilo and kibi stands for mega and mebi, for giga and gibi and so on, so the values of the decimal prefixes to and the values of the binary prefixes to arise. From this fact, it is easy to create a formula that indicates the ratio of the prefix values to each other.
The following table gives an overview of the resulting ratios:
Motivation and History
An important component of a computer is the memory that is now commonly implemented as semiconductor memories. The individual memory cells are addressed with the help of parallel binary working lines which together are referred to as the address bus. With an address bus having lines, memory cells can be addressed. Therefore, semiconductor memory are usually manufactured in sizes of powers of two. With increasing size of the memory, it has become common due to lack of standardized alternatives to use SI prefixes to the memory units and byte bits to quantify power of two, although the SI prefixes based on powers of ten. For data storage with sequential addressing or in the sequential transmission of data, however, there is no reason to work with powers of two, so here the SI prefixes are usually used according to standard. This has led to some confusion, partly because is no longer clearly visible, even for experts, whether the respective SI prefix to standards as a power or to be deviant interpreted as a power of two. Hard disk manufacturers use both systems, orders of magnitude in memory sizes, powers of two in the cache sizes.
For example, three different interpretations have for the term " 1 MB " naturalized in practice:
- " 1 MB " = 1,000,000 B = 106 B = 1000 kB - eg hard disks, DVD - media and duration of storage media flash memory, such as USB sticks or SD memory cards;
- " 1 MB " = 1048576 B = 220 B = 1 MiB - for example, in memory ( RAM, ROM, ..., and cache), flash memory chips, CD- media;
- " 1 MB " = 1,024,000 B = 1000 x 1024 B = 1024 kB = 1000 KiB - the capacity specified in the classical 3 ½ "floppy disk.
In addition, there is still the designation " 1 Mb " (with a small "b" for " bit" ):
- " 1 Mb " = 1,000,000 b - in data transmission, such as telecommunication lines and Ethernet;
This inconsistent approach can lead to hard to understand errors, as will be shown in the following simple example in arithmetic with units: A computer user wants to download a file of the specified size of " 40 MB " from the Internet and has to a data line with a data transfer rate of 8 Mbit / s. The time required to complete transmission of this file can be combined with the conversion 1 B = 8 bits ( Simplified) calculated as follows:
It comes to mind that to cut "MB" in the numerator against the "MB" in the denominator, resulting in a profit of results. However, when using the "MB" in the numerator a power of two is meant, while in the denominator is a power of ten is meant can these units do not cut against each other, although this is practically not visible.
For a clean solution to this problem, there are several options:
The introduction of Binärpräfixe does not mean that they are to replace the SI prefixes for use with bits and bytes. For example, one the size of a 536 870 912 byte memory with 536 870 912 B, 229 B, 537 approx specify MB, or just conveniently than 512 MiB. Thus, the SI prefixes can be used always clear in their standard meaning.
Which statement is more appropriate depends on the application, in particular whether the background of a binary addressing and whether this is of concern (such as in the size of a semiconductor memory or partition a hard drive), or whether this background no longer is relevant ( eg, in the later work with files on the same media ). However, the work by powers of two can be more complicated than with the use of the cut to the decimal SI prefixes ( such as 537 MB) when adding or subtracting amounts of data with various Binärpräfixen and the transition to larger or smaller Binärpräfixe.
Acceptance and dissemination
The acceptance of these IEC Binärpräfixe stayed until at least January 2002, industrial and scientific literature as well as in software limits and was therefore rarely used. Even today, only a very slowly growing acceptance and diffusion is observed. In the Information for Authors, IEEE explicitly requires that SI prefixes are used only for powers of ten, the Binärpräfixe not mentioned. The computer magazine PC Games Hardware used them for issue 11 /2007 ( Release date October 2, 2007). That being said, there are now several programs that support the Binärpräfixe, such as the Linux kernel, all Linux distributions that are structured tools such as partitioner ( GParted ), the GNU core utilities, KDE 4, phpMyAdmin, WinSCP and some BitTorrent programs. For Linux, the IEC standard is now completely implemented and allowed the user to select the output or displayed both sizes. Mac OS X version 10.6 comes from the opposite approach and uses SI prefixes as they are normalized for SI units, also IEC -compliant only in their decimal meaning.