Units of information

In computing and telecommunications, a unit of information is the capacity of some standard data storage system or communication channel, used to measure the capacities of other systems and channels. In information theory, units of information are also used to measure the entropy of random variables and information contained in messages.

The most commonly used units of data storage capacity are the bit, the capacity of a system that has only two states, and the byte (or octet), which is equivalent to eight bits. Multiples of these units can be formed from these with the SI prefixes (power-of-ten prefixes) or the newer IEC binary prefixes (power-of-two prefixes).

Primary units

Comparison of units of information: bit, trit, nat, ban. Quantity of information is the height of bars. Dark green level is the "nat" unit.

In 1928, Ralph Hartley observed a fundamental storage principle,[1] which was further formalized by Claude Shannon in 1945: the information that can be stored in a system is proportional to the logarithm of N possible states of that system, denoted log_b N. Changing the base of the logarithm from b to a different number c has the effect of multiplying the value of the logarithm by a fixed constant, namely log_c N = (log_c b) log_b N. Therefore, the choice of the base b determines the unit used to measure information. In particular, if b is a positive integer, then the unit is the amount of information that can be stored in a system with N possible states.

When b is 2, the unit is the shannon, equal to the information content of one "bit" (a portmanteau of binary digit[2]). A system with 8 possible states, for example, can store up to log₂8 = 3 bits of information. Other units that have been named include:

• Base b = 3: the unit is called "trit", and is equal to log₂ 3 (≈ 1.585) bits.[3]

• Base b = 10: the unit is called decimal digit, hartley, ban, decit, or dit, and is equal to log₂ 10 (≈ 3.322) bits.[1][4][5][6]
• Base b = e, the base of natural logarithms: the unit is called a nat, nit, or nepit (from Neperian), and is worth log₂ e (≈ 1.443) bits.[1]

The trit, ban, and nat are rarely used to measure storage capacity; but the nat, in particular, is often used in information theory, because natural logarithms are mathematically more convenient than logarithms in other bases.

Units derived from bit

Several conventional names are used for collections or groups of bits.

Byte

Historically, a byte was the number of bits used to encode a character of text in the computer, which depended on computer hardware architecture; but today it almost always means eight bits – that is, an octet. A byte can represent 256 (2⁸) distinct values, such as non-negative integers from 0 to 255, or signed integers from −128 to 127. The IEEE 1541-2002 standard specifies "B" (upper case) as the symbol for byte (IEC 80000-13 uses "o" for octet in French,[nb 1] but also allows "B" in English, which is what is actually being used). Bytes, or multiples thereof, are almost always used to specify the sizes of computer files and the capacity of storage units. Most modern computers and peripheral devices are designed to manipulate data in whole bytes or groups of bytes, rather than individual bits.

Nibble

A group of four bits, or half a byte, is sometimes called a nibble or nybble. This unit is most often used in the context of hexadecimal number representations, since a nibble has the same amount of information as one hexadecimal digit.[7]

Crumb

A pair of two bits or a quarter byte was called a crumb,[8] often used in early 8-bit computing (see Atari 2600, ZX Spectrum). It is now largely defunct.

Word, block, and page

Computers usually manipulate bits in groups of a fixed size, conventionally called words. The number of bits in a word is usually defined by the size of the registers in the computer's CPU, or by the number of data bits that are fetched from its main memory in a single operation. In the IA-32 architecture more commonly known as x86-32, a word is 16 bits, but other past and current architectures use words with 4,[9] 8,[9] 9,[9] 12,[9] 13,[9] 16,[9] 18,[9] 20,[9] 21,[9] 22,[9] 24,[9] 25,[9] 26, 29,[9] 30,[9] 31,[9] 32,[9] 33,[9] 35,[9] 36,[9] 38,[9] 39,[9] 40,[9] 42,[9] 44,[9] 48,[9] 50,[9] 52,[9] 54,[9] 56,[9] 60,[9] 64,[9] 72,[9] 80 bits or others.

Some machine instructions and computer number formats use two words (a "double word" or "dword"), or four words (a "quad word" or "quad").

Computer memory caches usually operate on blocks of memory that consist of several consecutive words. These units are customarily called cache blocks, or, in CPU caches, cache lines.

Virtual memory systems partition the computer's main storage into even larger units, traditionally called pages.

Systematic multiples

Terms for large quantities of bits can be formed using the standard range of SI prefixes for powers of 10, e.g., kilo = 10³ = 1000 (as in kilobit or kbit), mega = 10⁶ = 1000000 (as in megabit or Mbit) and giga = 10⁹ = 1000000000 (as in gigabit or Gbit). These prefixes are more often used for multiples of bytes, as in kilobyte (1 kB = 8000 bit), megabyte (1 MB = 8000000bit), and gigabyte (1 GB = 8000000000bit).

However, for technical reasons, the capacities of computer memories and some storage units are often multiples of some large power of two, such as 2²⁸ = 268435456 bytes. To avoid such unwieldy numbers, people have often repurposed the SI prefixes to mean the nearest power of two, e.g., using the prefix kilo for 2¹⁰ = 1024, mega for 2²⁰ = 1048576, and giga for 2³⁰ = 1073741824, and so on. For example, a random access memory chip with a capacity of 2²⁸ bytes would be referred to as a 256-megabyte chip. The table below illustrates these differences.

Multiples of bits
Decimal Value SI 1000 10^3 kbit kilobit 1000^2 10^6 Mbit megabit 1000^3 10^9 Gbit gigabit 1000^4 10^12 Tbit terabit 1000^5 10^15 Pbit petabit 1000^6 10^18 Ebit exabit 1000^7 10^21 Zbit zettabit 1000^8 10^24 Ybit yottabit	Binary Value IEC JEDEC 1024 2^10 Kibit kibibit Kbit kilobit 1024^2 2^20 Mibit mebibit Mbit megabit 1024^3 2^30 Gibit gibibit Gbit gigabit 1024^4 2^40 Tibit tebibit - 1024^5 2^50 Pibit pebibit - 1024^6 2^60 Eibit exbibit - 1024^7 2^70 Zibit zebibit - 1024^8 2^80 Yibit yobibit -
See also Nibble Byte Orders of magnitude of data

Symbol	Prefix	SI Meaning	Binary meaning	Size difference
k	kilo	10^3   = 1000^1	2^10 = 1024^1	2.40%
M	mega	10^6   = 1000^2	2^20 = 1024^2	4.86%
G	giga	10^9   = 1000^3	2^30 = 1024^3	7.37%
T	tera	10^12 = 1000^4	2^40 = 1024^4	9.95%
P	peta	10^15 = 1000^5	2^50 = 1024^5	12.59%
E	exa	10^18 = 1000^6	2^60 = 1024^6	15.29%
Z	zetta	10^21 = 1000^7	2^70 = 1024^7	18.06%
Y	yotta	10^24 = 1000^8	2^80 = 1024^8	20.89%

In the past, uppercase K has been used instead of lowercase k to indicate 1024 instead of 1000. However, this usage was never consistently applied.

On the other hand, for external storage systems (such as optical discs), the SI prefixes were commonly used with their decimal values (powers of 10). There have been many attempts to resolve the confusion by providing alternative notations for power-of-two multiples. In 1998 the International Electrotechnical Commission (IEC) issued a standard for this purpose, namely a series of binary prefixes that use 1024 instead of 1000 as the main radix:[10]

Symbol	Prefix
Ki	kibi, binary kilo	1 kibibyte (KiB)	2^10 bytes	1024 B
Mi	mebi, binary mega	1 mebibyte (MiB)	2^20 bytes	1024 KiB
Gi	gibi, binary giga	1 gibibyte (GiB)	2^30 bytes	1024 MiB
Ti	tebi, binary tera	1 tebibyte (TiB)	2^40 bytes	1024 GiB
Pi	pebi, binary peta	1 pebibyte (PiB)	2^50 bytes	1024 TiB
Ei	exbi, binary exa	1 exbibyte (EiB)	2^60 bytes	1024 PiB

The JEDEC memory standards however define uppercase K, M, and G for the binary powers 2¹⁰, 2²⁰ and 2³⁰ to reflect common usage.[11]

Size examples

• 1 bit: Answer to a yes/no question.
• 1 byte: A number from 0 to 255.
• 90 bytes: Enough to store a typical line of text from a book.
• 512 bytes = ½ KiB: The typical sector of a hard disk.
• 1024 bytes = 1 KiB: The classical block size in UNIX filesystems.
• 2048 bytes = 2 KiB: A CD-ROM sector.
• 4096 bytes = 4 KiB: A memory page in x86 (since Intel 80386).
• 4 kB: About one page of text from a novel.
• 120 kB: The text of a typical pocket book.
• 1 MiB: A 1024×1024 pixel bitmap image with 256 colors (8 bpp color depth).
• 3 MB: A three-minute song (133 kbit/s).
• 650–900 MB – a CD-ROM.
• 1 GB: 114 minutes of uncompressed CD-quality audio at 1.4 Mbit/s.
• 8/16 GB: Two common sizes of USB flash drives.
• 4 TB: The size of a $100 hard disk (as of early 2018).
• 12 TB: Largest hard disk drive (as of early 2018)
• 16 TB: Largest commercially available solid state drive (as of early 2018)
• 100 TB: Largest solid state drive constructed (as of early 2018)
• 1.3 ZB: Prediction of the volume of the whole internet in 2016.

Obsolete and unusual units

Several other units of information storage have been named:[7]

• 1 bit: unibit,[12][13] sniff.
• 2 bits: dibit,[14][15][12][16] crumb,[8] quartic digit,[17] quad, quarter, taste, tayste, tidbit, tydbit, lick, lyck, semi-nibble, snort.
• 3 bits: tribit,[14][15][12] triad,[18] triade,[19][20] tribble.
• 4 bits: character (on Intel 4004[21] – however, characters are typically 8 bits wide or larger on other processors), for other terms denoting 4 bits see nibble.
• 5 bits: pentad, pentade,[22] nickel, nyckle.
• 6 bits: byte (in early IBM machines using BCD alphamerics), hexad, hexade,[22][23] sextet.[18]
• 7 bits: heptad, heptade.[22]
• 8 bits: octet, commonly also called byte.
• 9 bits: nonet,[24] rarely used.
• 10 bits: declet,[25][26][27][28] decle,[29] deckle, dyme.
• 12 bits: slab.[30][31][32]
• 15 bits: parcel (on CDC 6600 and CDC 7600).
• 16 bits: doublet,[33] wyde,[3][34] parcel (on Cray-1), plate, playte, chomp, chawmp (on a 32-bit machine).
• 18 bits: chomp, chawmp (on a 36-bit machine).
• 32 bits: quadlet,[33][35][36] tetra,[34] dinner, dynner, gawble (on a 32-bit machine).
• 48 bits: gobble, gawble (under circumstances that remain obscure).
• 64 bits: octlet,[33] octa.[34]
• 96 bits: bentobox (in ITRON OS).
• 128 bits: hexlet.[33][37]
• 16 bytes: paragraph (on Intel x86 processors).[38][39]
• 256 bytes: page (on Intel 4004,[21] 8080 and 8086 processors,[38] also many other 8-bit processors – however, pages are typically much larger on many 16-bit/32-bit processors).
• 6 trits: tryte.[40]
• combit, comword.[41][42][43]

Some of these names are jargon, obsolete, or used only in very restricted contexts.

See also

• Metric prefix
• File size

Notes

1. However, the IEC 80000-13 abbreviation "o" for octets can be confused with the postfix "o" to indicate octal numbers in Intel convention.

References

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10. ISO/IEC standard is ISO/IEC 80000-13:2008. This 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. ISO Online Catalogue
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21. "Terms And Abbreviations / 4.1 Crossing Page Boundaries". MCS-4 Assembly Language Programming Manual - The INTELLEC 4 Microcomputer System Programming Manual (PDF) (Preliminary ed.). Santa Clara, California, USA: Intel Corporation. December 1973. pp. v, 2-6, 4-1. MCS-030-1273-1. Archived (PDF) from the original on 2020-03-01. Retrieved 2020-03-02. […] Bit - The smallest unit of information which can be represented. (A bit may be in one of two states I 0 or 1). […] Byte - A group of 8 contiguous bits occupying a single memory location. […] Character - A group of 4 contiguous bits of data. […] programs are held in either ROM or program RAM, both of which are divided into pages. Each page consists of 256 8-bit locations. Addresses 0 through 255 comprise the first page, 256-511 comprise the second page, and so on. […] (NB. This Intel 4004 manual uses the term character referring to 4-bit rather than 8-bit data entities. Intel switched to use the more common term nibble for 4-bit entities in their documentation for the succeeding processor 4040 in 1974 already.)
22. Speiser, Ambrosius Paul (1965) [1961]. Digitale Rechenanlagen - Grundlagen / Schaltungstechnik / Arbeitsweise / Betriebssicherheit [Digital computers - Basics / Circuits / Operation / Reliability] (in German) (2 ed.). ETH Zürich, Zürich, Switzerland: Springer-Verlag / IBM. pp. 6, 34, 165, 183, 208, 213, 215. LCCN 65-14624. 0978.
23. Steinbuch, Karl W., ed. (1962). Written at Karlsruhe, Germany. Taschenbuch der Nachrichtenverarbeitung (in German) (1 ed.). Berlin / Göttingen / New York: Springer-Verlag OHG. p. 1076. LCCN 62-14511.
24. Crispin, Mark R. (2005). RFC 4042: UTF-9 and UTF-18.
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26. Muller, Jean-Michel; Brisebarre, Nicolas; de Dinechin, Florent; Jeannerod, Claude-Pierre; Lefèvre, Vincent; Melquiond, Guillaume; Revol, Nathalie; Stehlé, Damien; Torres, Serge (2010). Handbook of Floating-Point Arithmetic (1 ed.). Birkhäuser. doi:10.1007/978-0-8176-4705-6. ISBN 978-0-8176-4704-9. LCCN 2009939668.
27. Erle, Mark A. (2008-11-21). Algorithms and Hardware Designs for Decimal Multiplication (Thesis). Lehigh University: ProQuest (published 2009). ISBN 978-1-10904228-3. 1109042280. Retrieved 2016-02-10.
28. Kneusel, Ronald T. (2015). Numbers and Computers. Springer Verlag. ISBN 9783319172606. 3319172603. Retrieved 2016-02-10.
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30. "315 Electronic Data Processing System" (PDF). NCR. November 1965. NCR MPN ST-5008-15. Archived (PDF) from the original on 2016-05-24. Retrieved 2015-01-28.
31. Bardin, Hillel (1963). "NCR 315 Seminar" (PDF). Computer Usage Communique. 2 (3). Archived (PDF) from the original on 2016-05-24.
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External links

• Representation of numerical values and SI units in character strings for information interchanges
• Bit Calculator – Make conversions between bits, bytes, kilobits, kilobytes, megabits, megabytes, gigabits, gigabytes, terabits, terabytes, petabits, petabytes, exabits, exabytes, zettabits, zettabytes, yottabits, yottabytes.
• Paper on standardized units for use in information technology
• Data Byte Converter