Editing Binary prefix (section)

=== Storage capacity ===
==== Main memory ====
Early computers used one of two addressing methods to access the system memory; binary (base 2) or decimal (base 10).<ref name="weik1961" /> For example, the [[IBM 701]] (1952) used a binary methods and could address 2048 [[Word (computer architecture)|word]]s of 36 [[bit]]s each, while the [[IBM 702]] (1953) 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 line]]s 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 {{val|16384}} units (usually [[word (computer architecture)|word]]s, bytes, or bits), computer professionals also started using the long-established metric system prefixes "kilo", "mega", "giga", etc., defined to be powers of 10,<ref name="BIPM8" /> to mean instead the nearest powers of two; namely, 2<sup>10</sup> = 1024, 2<sup>20</sup> = 1024<sup>2</sup>, 2<sup>30</sup> = 1024<sup>3</sup>, etc.<ref name="blais1930" /><ref name="liny1972" /> The corresponding metric prefix symbols ("k", "M", "G", etc.) were used with the same binary meanings.<ref name="real1959" /><ref name="gruen1960" /> The symbol for 2<sup>10</sup> = 1024 could be written either in lower case ("k")<ref name="horak2008" /><ref name="dodd1997" /><ref name="laver1989" /> or in uppercase ("K"). The latter was often used intentionally to indicate the binary rather than decimal meaning.<ref name="amda1964" /> This convention, which could not be extended to higher powers, was widely used in the documentation of the [[IBM&nbsp;360]] (1964)<ref name="amda1964" /> and of the [[IBM System/370]] (1972),<ref name="IBM1972" /> of the [[CDC&nbsp;7600]],<ref name="CDC7600" /> of the DEC [[PDP-11]]/70 (1975)<ref name="bell1975" /> and of the DEC [[VAX-11/780]] (1977).{{citation needed|date=August 2023}}

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]] (CDC) abbreviated "2<sup>16</sup> = {{nowrap|64 × 1024}} = {{val|65536}} words" as "65K words" (rather than "64K" or "66K"),<ref name="CDC1967" /> while the documentation of the [[HP 2100|HP 21MX]] real-time computer (1974) denoted {{nowrap|3 × 2<sup>16</sup>}} = {{nowrap|192 × 1024}} = {{val|196608}} as "196K" and 2<sup>20</sup> = {{val|1048576}} as "1M".<ref name="frank1974" />

These three possible meanings of "k" and "K" ("1024", "1000", or "approximately 1000") were used loosely around the same time, sometimes by the same company. The [[HP 3000]] business computer (1973) could have "64K", "96K", or "128K" bytes of memory.<ref name="HP1973" /> 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 {{nowrap|512 × 1024<sup>2</sup>}} = {{val|536870912}} bytes, rather than {{val|512000000}}.

==== 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]] (1956), had 50 physical disk platters containing a total of {{val|50000}} sectors of 100 characters each, for a total quoted capacity of 5 million characters.<ref name="IBM1956" />

Moreover, since the 1960s, many disk drives used IBM's [[Count Key Data|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 {{val|13030}}-byte block in each of its 808 × 19 tracks.

Decimal megabytes were used for disk capacity by the CDC in 1974.<ref name="CDC1974" /> The Seagate [[ST-412]],<ref name="seag1982" /> one of several types installed in the [[IBM PC/XT]],<ref name="CSN1984" /> had a capacity of {{val|10027008|u=bytes}} when formatted as 306 × 4 tracks and 32 256-byte sectors per track, which was quoted as "10&nbsp;MB".<ref name="mall2011" /> Similarly, a "300&nbsp;GB" hard drive can be expected to offer only slightly more than {{val|300|e=9}} = {{val|300000000000}}, bytes, not {{nowrap|300 × 2<sup>30</sup>}} (which would be about {{val|322|e=9}} bytes or "322&nbsp;GB"). The first terabyte (SI prefix, {{val|1000000000000}} bytes) hard disk drive was introduced in 2007.<ref name="hita2007" /> Decimal prefixes were generally used by information processing publications when comparing hard disk capacities.<ref name="RDD1977" />

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" (decimal "M") disk drive could be reported as "{{nowrap|9.56 MB}}", and that of a "300&nbsp;GB" drive as "279.4&nbsp;GB". Some operating systems, such as [[Mac OS X]],<ref>{{cite web |title=How iOS and macOS report storage capacity |url=https://support.apple.com/en-us/HT201402 |website=Apple Support |access-date=9 January 2022 |language=en |date=27 February 2018 |archive-date=9 April 2020 |archive-url=https://web.archive.org/web/20200409170256/https://support.apple.com/en-us/HT201402 |url-status=live }}</ref> [[Ubuntu]],<ref>{{cite web |title=UnitsPolicy |url=https://wiki.ubuntu.com/UnitsPolicy |website=Ubuntu Wiki |publisher=Ubuntu |access-date=9 January 2022 |archive-date=18 November 2021 |archive-url=https://web.archive.org/web/20211118114902/https://wiki.ubuntu.com/UnitsPolicy |url-status=live }}</ref> and [[Debian]],<ref>{{cite web |title=ConsistentUnitPrefixes |url=https://wiki.debian.org/ConsistentUnitPrefixes |website=Debian Wiki |access-date=9 January 2022 |archive-date=3 December 2021 |archive-url=https://web.archive.org/web/20211203075715/https://wiki.debian.org/ConsistentUnitPrefixes |url-status=live }}</ref> 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.<ref name="seaga2011" /><ref name="seag2010" />

==== Floppy disks ====
[[Floppy disks]] used [[List of floppy disk formats|a variety of formats]], and their capacities was 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 [[disk formatting|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.<ref>{{Cite web |date=2012-03-07 |title=IBM100 – The Floppy Disk |url=http://www-03.ibm.com/ibm/history/ibm100/us/en/icons/floppy/breakthroughs/ |archive-url=https://web.archive.org/web/20120403025215/http://www-03.ibm.com/ibm/history/ibm100/us/en/icons/floppy/breakthroughs/ |url-status=dead |archive-date=3 April 2012 |access-date=2023-10-17 |website=www-03.ibm.com |language=en-US}}</ref><ref>{{cite magazine|magazine=Datamation |title=Disc Storage |date= May 1972 |pages=154, 162, 164 |quote= CDS 100 ... stores over 600 kilobits, Model 650 ... store 1.5 megabits ... }}</ref>

The 5.25-inch diskette sold with the [[PC AT|IBM PC AT]] could hold {{nowrap|1200 × 1024}} = {{val|1228800}} bytes, and thus was marketed as "1200&nbsp;KB" with the binary sense of "KB".<ref>{{Cite web |last=Brutman |first=Michael B. |date=July 8, 2001 |title=Working with Disks: An intro to floppy disks and floppy drives |url=http://brutmanlabs.org/Diskettes/Diskette_handling.html |website=Brutmanlabs |access-date=2024-02-19  |archive-date=2024-02-19  |archive-url=https://web.archive.org/web/20240219085221/http://brutmanlabs.org/Diskettes/Diskette_handling.html |url-status=dead }}</ref> However, the capacity was also quoted "1.2&nbsp;MB",<ref>{{Cite web |title=Floppy disk storage {{!}} IBM |url=https://www.ibm.com/history/floppy-disk#1970s+high-density+storage |access-date=2024-12-14 |website=www.ibm.com |language=en}}</ref> which was a hybrid decimal and binary notation, since the "M" meant 1000 × 1024. The precise value was {{val|1.2288|u=MB}} (decimal) or {{val|1.171875|u=MiB}} (binary).

The 5.25-inch [[Disk II|Apple Disk II]] had 256 bytes per sector, 13 sectors per track, 35 tracks per side, or a total capacity of {{val|116480}} bytes. It was later upgraded to 16 sectors per track, giving a total of {{nowrap|140 × 2<sup>10</sup>}} = {{val|143360}} 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 (single-sided). Since two blocks comprised 1024 bytes, the capacity was quoted "360&nbsp;KB", with the binary sense of "K". On the other hand, the quoted capacity of "1.44&nbsp;MB" of the High Density ("HD") version was again a hybrid decimal and binary notation, since it meant 1440 pairs of 512-byte sectors, or {{nowrap|1440 × 2<sup>10</sup>}} = {{val|1474560|u=bytes}}. Some operating systems displayed the capacity of those disks using the binary sense of "MB", as "1.4&nbsp;MB" (which would be {{nowrap|1.4 × 2<sup>20</sup>}} ≈ {{val|1468000|u=bytes}}). User complaints forced both Apple{{citation needed|date=August 2023}} and Microsoft<ref name="msoftxxxx" /> to issue support bulletins explaining the discrepancy.

==== Optical disks ====
When specifying the capacities of optical [[compact disc]]s, "megabyte" and "MB" usually meant 1024<sup>2</sup>&nbsp;bytes. Thus a "700-MB" (or "80-minute") CD has a nominal capacity of about {{val|700|u=MiB}}, which is approximately {{val|730|u=MB}} (decimal).<ref name="cdromcap" />

On the other hand, capacities of other [[optical disc]] storage media like [[DVD]], [[Blu-ray Disc]], [[HD DVD]] and [[Magneto-optical drive|magneto-optical (MO)]] have been generally specified in decimal gigabytes ("GB"), that is, 1000<sup>3</sup> bytes. In particular, a typical "{{val|4.7|u=GB}}" DVD has a nominal capacity of about {{val|4.7|e=9|u=bytes}}, which is about {{val|4.38|u=GiB}}.<ref name="dvdcap" />

==== Tape drives and media ====
Tape drive and media manufacturers have generally used SI decimal prefixes to specify the maximum capacity,<ref name="IBMt2016" /><ref name="ECMA2013" /> although the actual capacity would depend on the [[block (data storage)|block size]] used when recording.

==== Data and clock rates ====
Computer [[Clock signal|clock]] frequencies are always quoted using SI prefixes in their decimal sense. For example, the internal clock frequency of the original [[IBM PC]] was {{val|4.77|u=MHz}}, that is {{val|4770000|u=Hz}}.

Similarly, digital information transfer rates are quoted using decimal prefixe. The [[Parallel ATA]] "{{val|100|u=MB/s}}" disk interface can transfer {{val|100000000}} bytes per second, and a "{{val|56|u=Kb/s}}" modem transmits {{val|56000}} bits per second. Seagate specified the sustained transfer rate of some hard disk drive models with both decimal and IEC binary prefixes.<ref name="seaga2011" /> 
The standard sampling rate of music [[compact disk]]s, quoted as {{val|44.1|u=kHz}}, is indeed {{val|44100}} samples per second.{{citation needed|date=August 2023}} A "{{val|1|u=Gb/s}}" [[Ethernet]] interface can receive or transmit up to 10<sup>9</sup> bits per second, or {{val|125000000}} bytes per second within each packet. A "[[56k]]" modem can encode or decode up to {{val|56000}} bits per second.

Decimal SI prefixes are also generally used for [[computer bus|processor-memory data transfer]] speeds. A [[PCI-X]] bus with {{val|66|u=MHz}} clock and 64 bits wide can transfer {{val|66000000}} 64-bit words per second, or {{val|4224000000|u=bit/s}} = {{val|528000000|u=B/s}}, which is usually quoted as {{val|528|u=MB/s}}. A [[DDR SDRAM|PC3200]] memory on a [[double data rate]] bus, transferring 8 bytes per cycle with a clock speed of {{val|200|u=MHz}} has a bandwidth of {{nowrap|{{val|200000000}} × 8 × 2}} = {{val|3200000000|u=B/s}}, which would be quoted as {{val|3.2|u=GB/s}}.