The Kbyte and Similar Units

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The Kbyte

Memory modules can be constructed by integration two smaller modules. Repeating this construction, one module contains two other modules, then four other modules, then eight, then sixteen and so on. One gets powers of two. After ten duplication 1024 units are integrated.

A Kbyte (pronounce „kay-bite“) has 1024 bytes.

In everyday life, often powers of ten are used, for example a “kilogram” contains 1000 grams. Because memory modules are built in multiples of powers of two, such as 1024 bytes and not in multiples of 1000 bytes, digital engineers have traditionally been using the Kbyte with 1024 bytes.

For this reason, the unit “Kbyte” is not pronounced “kilo-bite”: The prefix “kilo” would mean “thousand”. The unit “Kbyte” also is not written with a lowercase “k”, because a lowercase “k” would denote the factor thousand.

The kbyte (kilobyte)

A unit “kilobyte” with the token “kbyte” with a lowercase “k”, however, might also be constructed. It stands for 1000 bytes and thus is pronunced “kilo-bite ”. In digital engineering such a unit is unhandily and unusual, because memory sizes can rarely by expressed in integral multiples of this unit.

A kbyte (prounce „kilo-byte“) has 1000 bytes.

Because the unit “kbyte” is slightly smaller than the unit “Kbyte”, the numerical value of a specific memory amount given in the unit “kbyte” is a little bit larger than in the unit “Kbyte”. For this reason, manufacturers of memory and storage units, especially of harddisks, have often been using the unit “kbyte” (while Microsoft is using the KByte). A storage medium with 1024 KBytes for example has 1048.576 kbytes. Because one does not always distinguished carefully between “Kbytes” and “kbyte”, some people might get the impression as if a Kbyte would have only 1000 bytes. So this assertion now can be found in several resources and a certain confusion has arisen. Specifying the capacity of a MS-DOS formatted 90-mm-Disk as “1.44 MB” is particularly irregular because in this case both the factor 1000 and the factor 1024 are used since the real capacity of 1440 Kbytes or 1474560 bytes is factored as 1.44 · 1000 · 1024 in this case.

In the seventies of the twentieth century, computer scientist have been using the unit “Kbyte” in the sense of 1024 bytes to all intents and purposes, so this is the actual and original meaning of this unit. By the large proliferation of information technology in the following years, parts of the population have been facing the unit “Kbyte”, who where not familiar with its meaning, but were aware of the “kilogram” as 1000 grams. Together with the concerns of the manufactures of storage media, this was a reason for the following ambiguities regarding the usage of this unit.

But also in the domain of engineering powers of ten are not that uncommon in connection with units of information technology: They are used in fact for rates, which are measured in the unit baud. So a kilobaud has 1000 bauds indeed.

The Kibibyte (Kibyte)

To make it clear that the prefix “kilo” for “thousand” is not intended, in the meantime, special new prefixes have been conceived. The “kilobinary” is written with the prefix “ki”, for “kibi” (“kilobinary ”, where “kibi” is pronounced like “keebee”). The kilobinary is defined to be 1024 and differs clearly in notation and pronunciation from the prefix “kilo”. Using the “kilobinary”, the unit “kibibyte” (“kilobinarybyte ” analogous to „kilogramm“) is formed, having the symbol “KiB” (analogous to „kg“).

A kibibyte (kibyte ) has 1024 bytes.

Using this notation a “kbyte” unambiguously has 1000 byte, and no assertion is made about the meaning of “KByte”.

According to a decision of the International Electrotechnical Commission as of 1998, the kibibyte should be used instead of the Kbyte, but this does not seem to have happened yet in significant extend.

The Mebibyte (Mibyte) and Larger Units

1024 Kibytes are a Mibyte. 1024 Mibyte are a Gibyte. Other units according to this specification and two other units are listed in the table “multiples of a byte”.

multiples of a byte (table)

"name",     "symbol", "meaning",                        "in bytes":

"Kibibyte", "KiB", "1024 byte",                        "1024 byte".
"Mebibyte", "MiB", "1024 kibyte",                   "1048576 byte".
"Gibibyte", "GiB", "1024 mibyte",                "1073741824 byte".
"Tebibyte", "TiB", "1024 gibyte",             "1099511627776 byte".
"Pebibyte", "PiB", "1024 tibyte",          "1125899906842624 byte".
"Exbibyte", "EiB", "1024 pibyte",       "1152921504606846976 byte".
"Zebibyte", "ZiB", "1024 eibyte",    "1180591620717411303424 byte".
"Yobibyte", "YiB", "1024 zibyte", "1208925819614629174706176 byte".

The following table prefixes and symbols contains the prefixes according to the Amendment 2 to IEC International Standard IEC 60027-2 [0] and two other prefixes: Even though they are not part of the specification, the next prefixes after the “exbi” should be the “zebi” (“Zi”, similar to “Zetta”) and the “yobi” (“Yi”, according to “Yotta”).

Prefixes and Symbols (table)

"name", "symbol",                       "factor", "power", "approx.", "magnitude":

"kibi", "Ki",                             "1.024", "2^10",   "10^3",  "thousand".
"mebi", "Mi",                         "1.048.576", "2^20",   "10^6",  "million".
"gibi", "Gi",                     "1.073.741.824", "2^30",   "10^9",  "billion".
"tebi", "Ti",                 "1.099.511.627.776", "2^40",   "10^12", "trillion".
"pebi", "Pi",             "1.125.899.906.842.624", "2^50",   "10^15", "quadrillion".
"exbi", "Ei",         "1.152.921.504.606.846.976", "2^60",   "10^18", "quintillion".
"zebi", "Zi",     "1.180.591.620.717.411.303.424", "2^70",   "10^21", "sextillion".
"yobi", "Yi", "1.208.925.819.614.629.174.706.176", "2^80",   "10^24", "septillion".

The prefixes listed here could be used for other units as well, especially the bit or the octet.

The MByte and similar units

Traditionally the unit “MByte” was used instead of “Mebibyte”. To a computer technician, an “Mbyte” contains 1024 Kbyte and is pronounced “em byte”. The layman might pronounce it as “mega byte”. To some laymen, producers, or dealers an MBytes has 1000 Kbytes or 1000000 bytes, the problem here is similar to the one described for the KByte with the additional complication in this case that the “Mbyte” with 1024 Kbytes can not be differentiated from the „Mbyte“ with 1000000 byte in writing, because in this case the SI is using an uppercase “ M”, too. (The SI is using a lowercase “k” for “kilo”, so that an uppercase “K” for 1024 can be differentiated from that.)

Corresponding to what was being said about the “ Kbyte” and the “ Mbyte”, the units “Gbyte”, “Tbyte”, “Pbyte”, “Ebyte”, “Zbyte” and “ Ybyte” are used. The connoisseur pronounces these as “gee-byte”, “tee-byte”, “pee-byte” and “ee-byte”. The pronunciation „zee-byte“ and „wye-byte“ is suggested here for the „Zbyte“ and the „Ybyte“ , however, these units are so rare, that no perceptions has been collected about their pronunciation.

To the technician, the units mentioned are equal to the corresponding units that result if an “ i” would be inserted as a second character. Thus, the “Kbyte” has as many bytes as a “Kibyte”, the “Mbyte” has as many bytes as an “Mibyte” and so on. Differing from this, sometimes a convention with the factor 1000 is used, as it was being described regarding the “KByte”, where prefixes beginning at “M” have meanings according to the SI.

Information measures (Memory measures)

The “Kibyte” is not a good measure for information, because the relevant ISO standard does not fix the number of bits within a byte. So a “Kibyte” is in fact a certain amount of bytes, but not a certain amount of information (bits) or memory.

A tuple with 8 bits is, for example, called an octet (not a “byte”). Thus, the octet is a good measure for memory organized in octets or information, occurring in integral multiples of octets. With this fixing, the information of larger binary-units can be expressed in SI -units. (The conversion is not completely precise in this case, because the Boltzmann-constant used is only known approximately.)

Multiples of an octet (table)

"Name",      "symbol",   "meaning",                        "in octet", "in the SI":

    "octet", "O",      "8     bit",                         "1 octet",  "0,000000000000000000000076559509 J/K".
"Kibioctet", "KiO", "1024   octet",                      "1024 octet",  "0,000000000000000000078396937239 J/K".
"Mebioctet", "MiO", "1024 Kioctet",                   "1048576 octet",  "0,000000000000000080278463733028 J/K".
"Gibioctet", "GiO", "1024 Mioctet",                "1073741824 octet",  "0,0000000000000822051468626207   J/K".
"Tebioctet", "TiO", "1024 Gioctet",             "1099511627776 octet",  "0,0000000000841780703873236      J/K".
"Pebioctet", "PiO", "1024 Tioctet",          "1125899906842624 octet",  "0,0000000861983440766193         J/K".
"Exbioctet", "EiO", "1024 Pioctet",       "1152921504606846976 octet",  "0,0000882671043344582            J/K".
"Zebioctet", "ZiO", "1024 Eioctet",    "1180591620717411303424 octet",  "0,0903855148384852               J/K".
"Yobioctet", "YiO", "1024 Zioctet", "1208925819614629174706176 octet", "92,5547671946                     J/K".

Thus, 1 J/K is approximately 13061734757245900000000 octet (approx. 11 Zebioctet).

The bit is also a good measure for information. It might be combined with the prefixes given, too.

Inventions of this page

The following words could not be found in the web using Google ™ (as of 2003-10) before this page was published: Yibyte, Zibyte (in the sense used here), Pebioctet, Exbioctet, Zebioctet, and Yobioctet. The symbols PiO, EiO, ZiO, and YiO probably also have not been used before in this sense.

Resources

0: Letter symbols to be used in electrical technology - Part 2: Telecommunications and electronics; https://domino.iec.ch/webstore/webstore.nsf/artnum/026554; IEC 60027-2 Ed. 2.0 (2000-11); ICS code: 01.060 - TC 25 -; 66 pages
1: (IUCr) 1995 Report - IUPAC Interdivisional Committee on Nomenclature and Symbols (IDCNS); http://www.il.iucr.org/iucr-top/cexec/rep95/idcns.htm
2: Definitions of the SI units: The binary prefixes; http://physics.nist.gov/cuu/Units/binary.html