Binary prefix

A binary prefix is a prefix attached
before a unit symbol to multiply it by a power of 2. In computing, such a prefix
is seen in combination with a unit of information, to indicate a power of
1024. The computer industry has historically
used the units kilobyte, megabyte, and gigabyte, and the corresponding symbols
KB, MB, and GB, in at least two slightly different measurement systems. In
citations of main memory capacity, gigabyte customarily means
7009107374182400000♠1073741824 bytes. As this is the third power of 1024, and
1024 is a power of two, this usage is referred to as a binary prefix.
In most other contexts, the industry uses the multipliers kilo, mega, giga,
etc., in a manner consistent with their meaning in the International System of
Units, namely as powers of 1000. For example, a 500 gigabyte hard disk holds
7011500000000000000♠500000000000 bytes, and a 100-megabit-per-second Ethernet
connection transfers data at 7008100000000000000♠100000000 bit/s. In
contrast with the binary prefix usage, this use is described as a decimal
prefix, as 1000 is a power of 10. The use of the same unit prefixes with
two different meanings has caused confusion. Starting around 1998, the
International Electrotechnical Commission and several other standards
and trade organizations addressed the ambiguity by publishing standards and
recommendations for a set of binary prefixes that refer exclusively to
powers of 1024. Accordingly, the US National Institute of Standards and
Technology requires that SI prefixes only be used in the decimal sense:
kilobyte and megabyte denote one thousand bytes and one million bytes
respectively, while new terms such as kibibyte, mebibyte and gibibyte, having
the symbols KiB, MiB, and GiB, denote 1024 bytes, 7006104857600000000♠1048576
bytes, and 7009107374182400000♠1073741824 bytes,
respectively. In 2008, the IEC prefixes were incorporated into the IEC 80000-13
standard. History
=Main memory=Early computers used one of two
addressing methods to access the system memory; binary or decimal. For example,
the IBM 701 used binary and could address 2048 words of 36 bits each,
while the IBM 702 used decimal 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 their
address lines map to a valid address, allowing easy aggregation into a larger
block of memory with contiguous addresses.
Early computer system documentation would specify the memory size with an
exact number such as 4096, 8192, or 16384 words of storage. These are all
powers of two, and furthermore are small multiples of 210, or 1024. As storage
capacities increased, several different methods were developed to abbreviate
these quantities. The method most commonly used today uses
prefixes such as kilo, mega, giga, and corresponding symbols K, M, and G, which
the computer industry originally adopted from the metric system. The prefixes
kilo- and mega-, meaning 1000 and 7006100000000000000♠1000000
respectively, were commonly used in the electronics industry before World War
II. Along with giga- or G-, meaning 7009100000000000000♠1000000000, they are
now known as SI prefixes after the International System of Units,
introduced in 1960 to formalize aspects of the metric system. and should not be
confused with k, the SI prefix for kilo.)
The International System of Units does not define units for digital information
but notes that the SI prefixes may be applied outside the contexts where base
units or derived units would be used. But as computer main memory in a
binary-addressed system is manufactured in sizes that were easily expressed as
multiples of 1024, kilobyte, when applied to computer memory, came to be
used to mean 1024 bytes instead of 1000. The use of K in the binary sense as in a
“32K core” meaning 32 × 1024 words, i.e., 7004327680000000000♠32768 words,
can be found as early as 1959. Gene Amdahl’s seminal 1964 article on IBM
System/360 used “1K” to mean 1024. This style was used by other computer
vendors, the CDC 7600 System Description made extensive use of K as 1024. Thus
the first binary prefix was born. Another style was to truncate the last
three digits and append K, essentially using K as a decimal prefix similar to
SI, but always truncating to the next lower whole number instead of rounding
to the nearest. The exact values 7004327680000000000♠32768 words,
7004655360000000000♠65536 words and 7005131072000000000♠131072 words would
then be described as “32K”, “65K” and “131K”. This style was used from about
1965 to 1975. These two styles were used loosely
around the same time, sometimes by the same company. In discussions of
binary-addressed memories, the exact size was evident from context. The HP
21MX real-time computer denoted 7005196608000000000♠196608 as “196K” and
7006104857600000000♠1048576 as “1M”, while the HP 3000 business computer
could have “64K”, “96K”, or “128K” bytes of memory.
The “truncation” method gradually waned. Capitalization of the letter K became
the de facto standard for binary notation, although this could not be
extended to higher powers, and use of the lowercase k did persist.
Nevertheless, the practice of using the SI-inspired “kilo” to indicate 1024 was
later extended to “megabyte” meaning 10242 bytes, and later “gigabyte” for
10243 bytes. For example, a “512 megabyte” RAM module is 512×10242 bytes,
rather than 7008512000000000000♠512000000.
The symbols Kbit, Kbyte, Mbit and Mbyte started to be used as “binary
units”—”bit” or “byte” with a multiplier that is a power of 1024—in the early
1970s. For a time, memory capacities were often expressed in K, even when M
could have been used: The IBM System/370 Model 158 brochure had the following:
“Real storage capacity is available in 512K increments ranging from 512K to
2,048K bytes.” Megabyte was used to describe the 22-bit
addressing of DEC PDP-11/70 and gigabyte the 30-bit addressing DEC VAX-11/780.
In 1998, the International Electrotechnical Commission IEC
introduced the binary prefixes kibi, mebi, gibi … to mean 1024, 10242,
10243 etc., so that 1048576 bytes could be referred to unambiguously as 1
mebibyte. The IEC prefixes were defined for use alongside the International
System of Quantities in 2009.=Disk drives=
The disk drive industry followed a different pattern. Industry practice,
more thoroughly documented at Timeline of binary prefixes and continuing today,
is to specify hard drives using SI prefixes and symbols in their SI or
“decimal” interpretation. Unlike binary-addressed computer main memory,
there is nothing in a disk drive that influences it to have a total capacity
easily expressed using a power of 1024. The first commercially sold disk drive,
the IBM 350, had 50 physical disk “platters” containing a total of 50,000
sectors of 100 characters each, for a total quoted capacity of “5 million
characters.” It was introduced in September 1956.
In the 1960s most disk drives used IBM’s variable block length format. Any block
size could be specified up to the maximum track length. Since the block
headers occupied space, the usable capacity of the drive was dependent on
the block size. Blocks of 88, 96, 880 and 960 were often used because they
related to the fixed block size of punch cards. The drive capacity was usually
stated under conditions of full track record blocking. For example, the
100-megabyte 3336 disk pack only achieved that capacity with a full track
block size of 13,030 bytes. Hard disk drive manufacturers used
“megabytes” or “MB”, meaning 106 bytes, to characterize their products as early
as 1974. By 1977, in its first edition, Disk/Trend, a leading hard disk drive
industry marketing consultancy segmented the industry according to MBs of
capacity. One of the earliest hard disk drives in
personal computing history, the Seagate ST-412, was specified as “Formatted:
10.0 Megabytes”. The specification of 4 heads or active surfaces, 306 cylinders
and when formatted with a sector size of 256 bytes and 32 sectors/track results
in a capacity of 7007100270080000000♠10027008 bytes. This
drive was one of several types installed into the IBM PC/XT and extensively
advertised and reported as a “10 MB” hard disk drive. Operating systems and
programs using the customary binary prefixes show this as “9.5625 MB”.
The hard drive industry continues to use decimal prefixes for drive capacity.
Today, for example, a “300 GB” hard drive offers slightly more than 300×109,
or 7011300000000000000♠300000000000, bytes, not 300 × 230. Operating systems
such as Microsoft Windows that display hard drive sizes using the customary
binary prefix “GB” would display this as “279.4 GB”. On the other hand, Mac OS X
has since version 10.6 shown hard drive size using decimal prefixes.
However, other usages still occur. For example, in one document, Seagate
specifies data transfer rates of some of its hard drives in both IEC and decimal
units. “Advanced Format” drives using 4096-byte sectors are described as
having “4K sectors.”=Information transfer and clock rates=
Like the hard drive, there is nothing in a computer clock circuit or data
transfer path that demands or even encourages that things happen at rates
easily expressed using powers of 1024, or even using powers of 2.
Computer clock frequencies are always quoted using SI prefixes in their
decimal sense. For example, the internal clock frequency of the original IBM PC
was 4.77 MHz, that is, 7006477000000000000♠4770000 Hz.
Similarly, digital information transfer rates are mostly quoted using decimal
prefixes: The ATA-100 disk interface refers to
7008100000000000000♠100000000 bytes per second
A “56K” modem refers to 7004560000000000000♠56000 bits per
second SATA-2 has a raw bit rate of 3 Gbit/s=
7009300000000000000♠3000000000 bits per second
PC2-6400 RAM transfers 7009640000000000000♠6400000000 bytes per
second Firewire 800 has a raw rate of
7008800000000000000♠800000000 bits per second
As of 2011, Seagate specifies the transfer speed of some hard disk drives
with IEC binary prefixes as well as decimal.
=Standardization of dual definitions=By the mid-1970s it was common to see K
meaning 1024 and the occasional M meaning 7006104857600000000♠1048576 for
words or bytes of main memory while K and M were commonly used with their
decimal meaning for disk storage. In the 1980s, as capacities of both types of
devices increased, the SI prefix G, with SI meaning, was commonly applied to disk
storage, while M in its binary meaning, became common for computer memory. In
the 1990s, the prefix G, in its binary meaning, became commonly used for
computer memory capacity. The first terabyte hard disk drive was introduced
in 2007. The dual usage of the kilo, mega, and
giga prefixes and their corresponding symbols K, M, and G as both powers of
1000 and powers of 1024 was recorded in standards and dictionaries. For example,
the 1986 ANSI/IEEE Std 1084-1986 defined dual uses for kilo and mega.
kilo. A prefix indicating 1000. In statements involving size of computer
storage, a prefix indicating 210, or 1024.
mega. A prefix indicating one million. In statements involving size of computer
storage, a prefix indicating 220, or 1048576.
The binary units Kbyte and Mbyte were formally defined in ANSI/IEEE Std
1212-1991. Many dictionaries have noted the
practice of using traditional prefixes to indicate binary multiples. Oxford
online dictionary defines, for example, megabyte as: “Computing: a unit of
information equal to one million or 7006104857600000000♠1048576 bytes.”
The units Kbyte, Mbyte, and Gbyte are found in the trade press and in IEEE
journals. Gigabyte was formally defined in IEEE Std 610.10-1994 as either
7009100000000000000♠1000000000 or 230 bytes. Kilobyte, Kbyte, and KB are
equivalent units and all are defined in the obsolete standard, IEEE 100-2000.
Byte multiples using powers of 1024 up to yottabyte are given by the on-line
computing dictionary FOLDOC. The hardware industry has coped with the
dual definitions because of relative consistency: system memory typically
uses the binary meaning while magnetic disk storage uses the SI meaning. There
are, however, exceptions and special cases. Diskettes use yet another
“megabyte” equal to 1024×1000 bytes. In optical disks, Compact Disks use MB to
mean 10242 bytes while DVDs use GB to mean 10003 bytes.
Inconsistent use of units=Deviation between powers of 1024 and
powers of 1000=Computer storage has become cheaper per
unit and thereby larger, by many orders of magnitude since “K” was first used to
mean 1024. Because both the SI and “binary” meanings of kilo, mega, etc.,
are based on powers of 1000 or 1024 rather than simple multiples, the
difference between 1M “binary” and 1M “decimal” is proportionally larger than
that between 1K “binary” and 1k “decimal,” and so on up the scale. 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 kilo to nearly 21% for the yotta prefix.
=Consumer confusion=In the early days of computers there was
little or no consumer confusion because of the technical sophistication of the
buyers and their familiarity with the products. In addition, it was common for
computer manufacturers to specify their products with capacities in full
precision. In the personal computing era, one
source of consumer confusion is the difference in the way many operating
systems display hard drive sizes, compared to the way hard drive
manufacturers describe them. Hard drives are specified and sold using “GB” and
“TB” in their decimal meaning: one billion and one trillion bytes. Many
operating systems and other software, however, display hard drive and file
sizes using “MB”, “GB” or other SI-looking prefixes in their binary
sense, just as they do for displays of RAM capacity. For example, many such
systems display a hard drive marketed as “160 GB” as “149.05 GB”. The earliest
known presentation of hard disk drive capacity by an operating system using
“KB” or “MB” in a binary sense is 1984; earlier operating systems generally
presented the hard disk drive capacity as an exact number of bytes, with no
prefix of any sort, for example, in the output of the MS-DOS or PC DOS CHKDSK
command.=Legal disputes=
The different interpretations of disk size prefixes has led to three
significant class action lawsuits against digital storage manufacturers.
One case involved flash memory and the other two involved hard disk drives. Two
of these were settled with the manufacturers admitting no wrongdoing
but agreeing to clarify the storage capacity of their products on the
consumer packaging. Flash memory and hard disk manufacturers now have
disclaimers on their packaging and web sites clarifying the formatted capacity
of the devices or defining MB as 1 million bytes and 1 GB as 1 billion
bytes. Willem Vroegh v. Eastman Kodak Company
On 20 February 2004, Willem Vroegh filed a lawsuit against Lexar Media, Dane–Elec
Memory, Fuji Photo Film USA, Eastman Kodak Company, Kingston Technology
Company, Inc., Memorex Products, Inc.; PNY Technologies Inc., SanDisk
Corporation, Verbatim Corporation, and Viking Interworks alleging that their
descriptions of the capacity of their flash memory cards were false and
misleading. Vroegh claimed that a 256 MB Flash
Memory Device had only 244 MB of accessible memory. “Plaintiffs allege
that Defendants marketed the memory capacity of their products by assuming
that one megabyte equals one million bytes and one gigabyte equals one
billion bytes.” The plaintiffs wanted the defendants to use the traditional
values of 10242 for megabyte and 10243 for gigabyte. The plaintiffs
acknowledged that the IEC and IEEE standards define a MB as one million
bytes but stated that the industry has largely ignored the IEC standards.
The manufacturers agreed to clarify the flash memory card capacity on the
packaging and web sites. The consumers could apply for “a discount of ten
percent off a future online purchase from Defendants’ Online Stores Flash
Memory Device”. Orin Safier v. Western Digital
Corporation On 7 July 2005, an action entitled Orin
Safier v. Western Digital Corporation, et al. was filed in the Superior Court
for the City and County of San Francisco, Case No. CGC-05-442812. The
case was subsequently moved to the Northern District of California, Case
No. 05-03353 BZ. Although Western Digital maintained that
their usage of units is consistent with “the indisputably correct industry
standard for measuring and describing storage capacity”, and that they “cannot
be expected to reform the software industry”, they agreed to settle in
March 2006 with 14 June 2006 as the Final Approval hearing date.
Western Digital offered to compensate customers with a free download of backup
and recovery software valued at US$30. They also paid $500,000 in fees and
expenses to San Francisco lawyers Adam Gutride and Seth Safier, who filed the
suit. The settlement called for Western Digital to add a disclaimer to their
later packaging and advertising. Cho v. Seagate Technology Holdings, Inc.
A lawsuit Holdings, Inc., San Francisco Superior Court, Case No. CGC-06-453195)
was filed against Seagate Technology, alleging that Seagate overrepresented
the amount of usable storage by 7% on hard drives sold between March 22, 2001
and September 26, 2007. The case was settled without Seagate admitting
wrongdoing, but agreeing to supply those purchasers with free backup software or
a 5% refund on the cost of the drives. Unique binary prefixes
=Early suggestions=While early computer scientists
typically used k to mean 1000, some recognized the convenience that would
result from working with multiples of 1024 and the confusion that resulted
from using the same prefixes for two different meanings.
Several proposals for unique binary prefixes were made in 1968. Donald
Morrison proposed to use the Greek letter kappa to denote 1024, κ2 to
denote 1024×1024, and so on. Wallace Givens responded with a proposal to use
bK as an abbreviation for 1024 and bK2 or bK2 for 1024×1024, though he noted
that neither the Greek letter nor lowercase letter b would be easy to
reproduce on computer printers of the day. Bruce Alan Martin of Brookhaven
National Laboratory further proposed that the prefixes be abandoned
altogether, and the letter B be used for base-2 exponents, similar to E in
decimal scientific notation, to create shorthands like 3B20 for 3×220, a
convention still used on some calculators to present binary floating
point-numbers today. None of these gained much acceptance,
and capitalization of the letter K became the de facto standard for
indicating a factor of 1024 instead of 1000, although this could not be
extended to higher powers. As the discrepancy between the two
systems increased in the higher-order powers, more proposals for unique
prefixes were made. In 1996, Markus Kuhn proposed a system with di prefixes, like
the “dikilobyte”. Donald Knuth, who uses decimal notation like 1 MB=1000 kB,
expressed “astonishment” that the IEC proposal was adopted, calling them
“funny-sounding” and opining that proponents were assuming “that standards
are automatically adopted just because they are there.” Knuth proposed that the
powers of 1024 be designated as “large kilobytes” and “large megabytes”. Double
prefixes were already abolished from SI, however, having a multiplicative
meaning, and this proposed usage never gained any traction.
=IEC prefixes=The set of binary prefixes that were
eventually adopted, now referred to as the “IEC prefixes”, were first proposed
by the International Union of Pure and Applied Chemistry’s Interdivisional
Committee on Nomenclature and Symbols in 1995. At that time, it was proposed that
the terms kilobyte and megabyte be used only for 103 bytes and 106 bytes,
respectively. The new prefixes kibi, mebi, gibi and tebi were also proposed
at the time, and the proposed symbols for the prefixes were kb, Mb, Gb and Tb
respectively, rather than Ki, Mi, Gi and Ti. The proposal was not accepted at the
time. The Institute of Electrical and
Electronic Engineers began to collaborate with the International
Organization for Standardization and International Electrotechnical
Commission to find acceptable names for binary prefixes. IEC proposed kibi,
mebi, gibi and tebi, with the symbols Ki, Mi, Gi and Ti respectively, in 1996.
The names for the new prefixes are derived from the original SI prefixes
combined with the term binary, but contracted, by taking the first two
letters of the SI prefix and “bi” from binary. The first letter of each such
prefix is therefore identical to the corresponding SI prefixes, except for
“K”, which is used interchangeably with “k”, whereas in SI, only the lower-case
k represents 1000. The IEEE decided that their standards
would use the prefixes kilo, etc. with their metric definitions, but allowed
the binary definitions to be used in an interim period as long as such usage was
explicitly pointed out on a case-by-case basis.
=Adoption by IEC, NIST and ISO=In January 1999, the IEC published the
first international standard with the new prefixes, extended up to pebi and
exbi. The IEC 60027-2 Amendment 2 also states
that the IEC position is the same as that of BIPM; the SI prefixes retain
their definitions in powers of 1000 and are never used to mean a power of 1024.
In usage, products and concepts typically described using powers of 1024
would continue to be, but with the new IEC prefixes. For example, a memory
module of 7008536870912000000♠536870912 bytes would be referred to as 512 MiB or
512 mebibytes instead of 512 MB or 512 megabytes. Conversely, since hard drives
have historically been marketed using the SI convention that “giga” means
7009100000000000000♠1000000000, a “500 GB” hard drive would still be labeled as
such. According to these recommendations, operating systems and
other software would also use binary and SI prefixes in the same way, so the
purchaser of a “500 GB” hard drive would find the operating system reporting
either “500 GB” or “466 GiB”, while 7008536870912000000♠536870912 bytes of
RAM would be displayed as “512 MiB”. The second edition of the standard,
published in 2000, defined them only up to exbi, but in 2005, the third edition
added prefixes zebi and yobi, thus matching all SI prefixes with binary
counterparts. The harmonized ISO/IEC IEC 80000-13:2008
standard cancels and replaces subclauses 3.8 and 3.9 of IEC 60027-2:2005. The
only significant change is the addition of explicit definitions for some
quantities. In 2009, the prefixes kibi-, mebi-, etc. were defined by ISO 80000-1
in their own right, independently of the kibibyte, mebibyte, and so on.
The BIPM standard JCGM 200:2012 “International vocabulary of metrology –
Basic and general concepts and associated terms, 3rd edition” lists the
IEC binary prefixes and states “SI prefixes refer strictly to powers of 10,
and should not be used for powers of 2. For example, 1 kilobit should not be
used to represent 7003102400000000000♠1024 bits, which is
1 kibibit.” =Other standards bodies and
organizations=The IEC standard binary prefixes are now
supported by other standardization bodies and technical organizations.
The United States National Institute of Standards and Technology supports the
ISO/IEC standards for “Prefixes for binary multiples” and has a web site
documenting them, describing and justifying their use. NIST suggests 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. NIST has stated the SI prefixes “refer strictly to powers of 10” and
that the binary definitions “should not be used” for them.
The microelectronics industry standards body JEDEC describes the IEC prefixes in
its online dictionary. The JEDEC standards for semiconductor memory use
the customary prefix symbols K, M, G and T in the binary sense.
On 19 March 2005, the IEEE standard IEEE 1541-2002 was elevated to a full-use
standard by the IEEE Standards Association after a two-year trial
period. However, as of April 2008, the IEEE Publications division does not
require the use of IEC prefixes in its major magazines such as Spectrum or
Computer. The International Bureau of Weights and
Measures, which maintains the International System of Units, expressly
prohibits the use of SI prefixes to denote binary multiples, and recommends
the use of the IEC prefixes as an alternative since units of information
are not included in SI. The Society of Automotive Engineers
prohibits the use of SI prefixes with anything but a power-of-1000 meaning,
but does not recommend or otherwise cite the IEC binary prefixes.
The European Committee for Electrotechnical Standardization adopted
the IEC-recommended binary prefixes via the harmonization document HD
60027-2:2003-03. The European Union has required the use of the IEC binary
prefixes since 2007. Current practice
Most computer hardware uses SI prefixes to state capacity and define other
performance parameters such as data rate. Main and cache memories are
notable exceptions. Capacities of main memory and cache
memory are usually expressed with customary binary prefixes On the other
hand, flash memory, like that found in solid state drives, mostly uses SI
prefixes to state capacity. Some operating systems and other
software continue to use the customary binary prefixes in displays of memory,
disk storage capacity, and file size, but SI prefixes in other areas such as
network communication speeds and processor speeds.
In the following subsections, unless otherwise noted, examples are first
given using the common prefixes used in each case, and then followed by
interpretation using other notation where appropriate.
=Operating systems=Prior to the release of Macintosh System
Software, file sizes were typically reported by the operating system without
any prefixes. Today, most operating systems report file sizes with prefixes.
The Linux kernel uses binary prefixes when booting up. However, many Unix-like
system utilities like the ls command, use powers of 1024 indicated as KB/MB.
The Ubuntu GNU/Linux distribution uses the IEC prefixes for base-2 numbers as
of the 10.10 release. Microsoft Windows reports file sizes and
disk device capacities using the customary binary prefixes or, in a
“Properties” dialog, using the exact value in bytes.
Since Mac OS X Snow Leopard,, Apple’s Mac OS X reports sizes using SI decimal
As of February 2010, most software does not distinguish symbols for binary and
decimal prefixes. The IEC binary naming convention has been adopted by a few,
but this is not used universally. One of the stated goals of the
introduction of the IEC prefixes was “to preserve the SI prefixes as unambiguous
decimal multipliers.” Programs such as fdisk/cfdisk, parted, and apt-get use SI
prefixes with their decimal meaning. Example of the use of IEC binary
prefixes in the Linux operating system displaying traffic volume on a network
interface in kibibytes and mebibytes, as obtained with the ifconfig utility:
eth0 Link encap:Ethernet HWaddr 00:14:A0:B0:7A:42
inet6 addr: 2001:491:890a:1:214:a5ff:febe:7a42/64
Scope:Global inet6 addr: fe80::214:a5ff:febe:7a42/64
Metric:1 RX packets:254804 errors:0 dropped:0
overruns:0 frame:0 TX packets:756 errors:0 dropped:0
overruns:0 carrier:0 collisions:0 txqueuelen:1000
RX bytes:18613795 TX bytes:45708 Software that uses standard SI prefixes
for powers of 1000, but not IEC binary prefixes for powers of 1024, includes:
Mac OS X v10.6 and later for hard drive and file sizes
Software that uses IEC binary prefixes for powers of 1024 and uses standard SI
prefixes for powers of 1000 includes:=Computer hardware=
Hardware types that use powers-of-1024 multipliers, such as memory, continue to
be marketed with customary binary prefixes.
Computer memory Measurements of most types of electronic
memory such as RAM and ROM are given using customary binary prefixes. This
includes some flash memory, like EEPROMs. For example, a “512-megabyte”
memory module is 512×220 bytes. JEDEC Solid State Technology
Association, the semiconductor engineering standardization body of the
Electronic Industries Alliance, continues to include the customary
binary definitions of kilo, mega and giga in their Terms, Definitions, and
Letter Symbols document, and uses those definitions in later memory standards
Many computer programming tasks reference memory in terms of powers of
two because of the inherent binary design of current hardware addressing
systems. For example, a 16-bit processor register can reference at most 65,536
items; this is conveniently expressed as “64K” items. An operating system might
map memory as 4096-byte pages, in which case exactly 8192 pages could be
allocated within 7007335544320000000♠33554432 bytes of
memory: “8K” pages of “4 kilobytes” each within “32 megabytes” of memory.
Hard disk drives All hard disk drive manufacturers state
capacity using SI prefixes. Flash drives
USB flash drives, flash-based memory cards like CompactFlash or Secure
Digital, and flash-based SSDs use SI prefixes; for example, a “256 MB” flash
card provides at least 256 million bytes, not 256×1024×1024. The flash
memory chips inside these devices contain considerably more than the
quoted capacities, but much like a traditional hard drive, some space is
reserved for internal functions of the flash drive. These include wear
leveling, error correction, sparing, and metadata needed by the device’s internal
firmware. Floppy drives
Floppy disks have existed in numerous physical and logical formats, and have
been sized inconsistently. In part, this is because the end user capacity of a
particular disk is a function of the controller hardware, so that the same
disk could be formatted to a variety of capacities. In many cases, the media are
marketed without any indication of the end user capacity, as for example, DSDD,
meaning double-sided double-density. The last widely adopted diskette was the
3½-inch high density. This has a formatted capacity of
7006147456000000000♠1474560 bytes or 1440 KB. These are marketed as “HD”, or
“1.44 MB” or both. This usage creates a third definition of “megabyte” as
1000×1024 bytes. Most operating systems display the
capacity using “MB” in the customary binary sense, resulting in a display of
“1.4 MB”. Some users have noticed the missing 0.04 MB and both Apple and
Microsoft have support bulletins referring to them as 1.4 MB.
The earlier “1200 KB” 5¼-inch diskette sold with the IBM PC AT was marketed as
“1.2 MB”. The largest 8-inch diskette formats could contain more than a
megabyte, and the capacities of those devices were often irregularly specified
in megabytes, also without controversy. Older and smaller diskette formats were
usually identified as an accurate number of KB, for example the Apple Disk II
described as “140KB” had a 140×1024-byte capacity, and the original “360KB”
double sided, double density disk drive used on the IBM PC had a 360×1024-byte
capacity. In many cases diskette hardware was
marketed based on unformatted capacity, and the overhead required to format
sectors on the media would reduce the nominal capacity as well, leading to
more irregularities. Optical discs
The capacities of most optical disc storage media like DVD, Blu-ray Disc, HD
DVD and magneto-optical are given using SI decimal prefixes. A “4.7 GB” DVD has
a nominal capacity of about 4.38 GiB. However, CD capacities are always given
using customary binary prefixes. Thus a “700-MB” CD has a nominal capacity of
about 700 MiB. Tape drives and media
Tape drive and media manufacturers use SI decimal prefixes to identify
capacity. Data transmission and clock rates
Certain units are always used with SI decimal prefixes even in computing
contexts. Two examples are hertz, which is used to measure the clock rates of
electronic components, and bit/s, used to measure data transmission speed.
A 1-GHz processor receives 7009100000000000000♠1000000000 clock
ticks per second. A sound file sampled at
7004441000000000000♠44.1 kHz has 7004441000000000000♠44100 samples per
second. A 7005128000000000000♠128 kbit/s MP3
stream consumes 7005128000000000000♠128000 bits per
second. A 7006100000000000000♠1 Mbit/s Internet
connection can transfer 7006100000000000000♠1000000 bits per
second A 7009100000000000000♠1 Gbit/s Ethernet
connection can transfer 7009100000000000000♠1000000000 bits per
second A 56k modem transfers
7004560000000000000♠56000 bits per second ≈ 7000680000000000000♠6.8 KiB/s.
Bus clock speeds and therefore bandwidths are both quoted using SI
decimal prefixes. PC3200 memory on a double data rate bus,
transferring 8 bytes per cycle with a clock speed of 7008200000000000000♠200
MHz has a bandwidth of 7008200000000000000♠200000000 × 8 × 2=
7009320000000000000♠3200000000 bytes/second=7010256000000000000♠3.2
GB/s. A PCI-X bus at 7007660000000000000♠66
MHz, 64 bits per transfer, has a bandwidth of
7007660000000000000♠66000000 transfers/second × 64 bits/transfer=
7009422400000000000♠4224000000 bits/second, or
7008528000000000000♠528000000 bytes/second, usually quoted as
7009422400000000000♠528 MB/s.=Use by industry=
IEC prefixes are used by Toshiba, IBM, HP to advertise or describe some of
their products. According to one HP brochure, [4] “[t]o reduce confusion,
vendors are pursuing one of two remedies: they are changing SI prefixes
to the new binary prefixes, or they are recalculating the numbers as powers of
ten.” The IBM Data Center also uses IEC prefixes to reduce confusion. The IBM
Style Guide reads “To help avoid inaccuracy and potential
ambiguity, the International Electrotechnical Commission in 2000
adopted a set of prefixes specifically for binary multipliers. Their use is now
supported by the United States National Institute of Standards and Technology
and incorporated into ISO 80000. They are also required by EU law and in
certain contexts in the US. However, most documentation and products in the
industry continue to use SI prefixes when referring to binary multipliers. In
product documentation, follow the same standard that is used in the product
itself. Whether you choose to use IEC prefixes for powers of 2 and SI prefixes
for powers of 10, or use SI prefixes for a dual purpose … be consistent in your
usage and explain to the user your adopted system.”
=Websites and government agencies=The UK government
Ars Technica Anandtech
See also Integer
Bit Nibble
Byte Octet
Orders of magnitude Timeline of binary prefixes
IEC 60027-2 ISO/IEC 80000
IEEE 1541-2002 Definitions
References Further reading
“When is a kilobyte a kibibyte? And an MB an MiB?”. International
Electrotechnical Commission. 2007-02-12. Archived from the original on
2009-04-03. – An introduction to binary prefixes
“Prefixes for binary multiples”. NIST. “Get Ready for the mebi, gibi and tebi”.
NIST. 1999-03-02. Markus Kuhn. “What is a Megabyte …?”.
—a 1996–1999 paper on bits, bytes, prefixes and symbols
Jonathan de Boyne Pollard. “There is no such thing as a 1.44 MB standard format
floppy disc”. Frequently Given Answers. Michael Quinion. “Kibibyte”. World Wide
Words. —Another description of binary prefixes
James Wiebe. “When One Billion does not equal One Billion, or: Why your
computer’s disk drive capacity doesn’t appear to match the stated capacity”.
Retrieved 2010-01-22. —White-paper on the controversy over drive capacities
External links A plea for sanity
A summary of the organizations, software, and so on that have
implemented the new binary prefixes KiloBytes vs. kilobits vs. Kibibytes
SI/Binary Prefix Converter Storage Capacity Measurement Standards

Leave a Reply

Your email address will not be published. Required fields are marked *