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Units of information

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Short description: Unit of measure for digital data
"tribit" redirects here. It is not to be confused with tibit or trit.

A unit of information is any unit of measure of digital data size. In digital computing, a unit of information is used to describe the capacity of a digital data storage device. In telecommunications, a unit of information is used to describe the throughput of a communication channel. In information theory, a unit of information is used to measure information contained in messages and the entropy of random variables.

Due to the need to work with data sizes that range from small to large, units of information cover a wide range of data sizes. Units are defined as multiples of a smaller unit except for the smallest unit which is based on convention and hardware design. Multiplier prefixes are used to describe relatively large sizes.

For binary hardware, the most common hardware today, the smallest unit is the bit, which represents a value that is one of two possibilities, typically shown as 0 and 1. The nibble, 4 bits, represents the value of a single hexadecimal digit. The byte (8 bits, 2 nibbles) is possibly the most commonly known and used base unit to describe data size. The word is a size that varies by and has a special importance for a particular hardware context. On modern hardware, a word is typically 2, 4 or 8 bytes, but the size varies dramatically on older hardware. Larger sizes can be expressed as multiples of a base unit via SI metric prefixes (powers of ten) or the newer and generally more accurate IEC binary prefixes (powers of two).

Information theory

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

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 logb 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 logc N = (logc b) logb 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 b possible states.

When b is 2, the unit is the shannon, equal to the information content of one "bit". A system with 8 possible states, for example, can store up to log2 8 = 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.[2]
Base b = 10
the unit is called decimal digit, hartley, ban, decit, or dit, and is equal to log2 10 (≈ 3.322) bits.[1][3][4][5]
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. An 8-bit byte can represent 256 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, but also allows "B" in English). 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, nybble or nyble. This unit is most often used in the context of hexadecimal number representations, since a nibble has the same number of possible values as one hexadecimal digit has.[6]

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 32 bits, but other past and current architectures use words with 4, 8, 9, 12, 13, 16, 18, 20, 21, 22, 24, 25, 29, 30, 31, 32, 33, 35, 36, 38, 39, 40, 42, 44, 48, 50, 52, 54, 56, 60, 64, 72[7] 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.

Multiplicative prefixes

A unit for a large amount of data can be formed using either a metric or binary prefix with a base unit. For storage, the base unit is typically a byte. For communication throughput, a base unit of bit is common. For example, using the metric kilo prefix, a kilobyte is 1000 bytes and a kilobit is 1000 bits.

Use of metric prefixes is common. In the context of computing, some of these prefixes (primarily kilo, mega and giga) are used to refer to the nearest power of two. For example, 'kilobyte' often refers to 1024 bytes even though the standard meaning of kilo is 1000.[8]

Symbol Prefix Multiple
k kilo 1000
M mega 10002
G giga 10003
T tera 10004
P peta 10005
E exa 10006
Z zetta 10007
Y yotta 10008
R ronna 10009
Q quetta 100010

The International Electrotechnical Commission (IEC) standardized binary prefixes for binary multiples to avoid ambiguity through their similarity to the standard metric terms. These are based on powers of 1024, which is a power of 2.[9]

Symbol Prefix Multiple Example
Ki kibi 210, 1024 kibibyte (KiB)
Mi mebi 220, 10242 mebibyte (MiB)
Gi gibi 230, 10243 gibibyte (GiB)
Ti tebi 240, 10244 tebibyte (TiB)
Pi pebi 250, 10245 pebibyte (PiB)
Ei exbi 260, 10246 exbibyte (EiB)
Zi zebi 270, 10247 zebibyte (ZiB)
Yi yobi 280, 10248 yobibyte (YiB)
Ri robi 290, 10249 robibyte (RiB)
Qi quebi 2100, 102410 quebibyte (QiB)

The JEDEC memory standard JESD88F notes that its inclusion of the definitions of kilo (K), mega (M) and giga (G) based on powers of two are included only to reflect common usage, but that these are otherwise deprecated.[10]

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 = 0.5 KiB: The typical sector size of an old style hard disk drive (modern Advanced Format sectors are 4096 bytes).
  • 1024 bytes = 1 KiB: A block size in some older UNIX filesystems
  • 2048 bytes = 2 KiB: A CD-ROM sector
  • 4096 bytes = 4 KiB: A memory page in x86 (since Intel 80386) and many other architectures, also the modern Advanced Format hard disk drive sector size.
  • 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
  • 16 GB: DDR5 DRAM laptop memory under $40 (as of early 2024)
  • 32/64/128 GB: Three common sizes of USB flash drives
  • 1 TB: The size of a $30 hard disk (as of early 2024)
  • 6 TB: The size of a $100 hard disk (as of early 2022)
  • 16 TB: The size of a small/cheap $130 (as of early 2024) enterprise SAS hard disk drive
  • 24 TB: The size of $440 (as of early 2024) "video" hard disk drive
  • 32 TB: Largest hard disk drive (as of mid-2024)
  • 100 TB: Largest commercially available solid-state drive (as of mid-2024)
  • 200 TB: Largest solid-state drive constructed (prediction for mid-2022)
  • 1.6 PB (1600 TB): Amount of possible storage in one 2U server (world record as of 2021, using 100 TB solid-states drives).[11]
  • 1.3 ZB: Prediction of the volume of the whole internet in 2016

Obsolete and unusual units

Some notable unit names that are today obsolete or only used in limited contexts.

  • 5 bits: pentad, pentade,[23]
  • 6 bits: byte (in early IBM machines using BCD alphamerics), hexad, hexade,[23][24] sextet[20]
  • 7 bits: heptad, heptade[23]
  • 9 bits: nonet,[27] rarely used
  • 18 bits: chomp, chawmp (on a 36-bit machine)[38]
  • 96 bits: bentobox (in ITRON OS)
  • 256 bytes: page (on Intel 4004,[44] 8080 and 8086 processors,[42] also many other 8-bit processors – typically much larger on many 16-bit/32-bit processors)

See also

  • File size
  • ISO 80000-13 (Quantities and units – Part 13: Information science and technology)

References

Citations

  1. ↑ 1.0 1.1 1.2 Information theory and coding. McGraw-Hill. 1963. 
  2. ↑ 2.0 2.1 The Art of Computer Programming: Seminumerical algorithms. 2. Addison Wesley. 
  3. ↑ Shanmugam (2006). Digital and Analog Computer Systems. 
  4. ↑ Quantum information: an overview. 2007. https://www.springer.com/physics/quantum+physics/book/978-0-387-35725-6. 
  5. ↑ Comprehensive Statistical Theory of Communication. 2001. 
  6. ↑ Nybble at dictionary reference.com; sourced from Jargon File 4.2.0, accessed 2007-08-12
  7. ↑ "Chapter I. Integer arithmetic". The Mathematical-Function Computation Handbook – Programming Using the MathCW Portable Software Library (1 ed.). Salt Lake City, UT, US: Springer International Publishing AG. 2017-08-22. p. 970. doi:10.1007/978-3-319-64110-2. ISBN 978-3-319-64109-6. 
  8. ↑ "Metric (SI) Prefixes" (in en). 2010-01-13. https://www.nist.gov/pml/owm/metric-si-prefixes. 
  9. ↑ Quantities and units – Part 13: Information science and technology, https://www.iso.org/standard/87648.html 
  10. ↑ "Dictionary of Terms for Solid State Technology – 7th Edition". JEDEC Solid State Technology Association. February 2018. pp. 100,118,135. https://www.jedec.org/standards-documents/docs/jesd-88c. 
  11. ↑ Maleval, Jean Jacques (2021-02-12). "Nimbus Data SSDs Certified for Use With Dell EMC PowerEdge Servers" (in en-US). https://www.storagenewsletter.com/2021/02/12/nimbus-data-ssds-certified-by-dell-emc-for-poweredge-servers/. 
  12. ↑ 12.0 12.1 12.2 Webster's New World Telecom Dictionary. John Wiley & Sons. 2007. p. 402. ISBN 9-78047022571-4. https://books.google.com/books?id=L18YaEomzjMC&pg=PA402. 
  13. ↑ "Unibit". http://www.yourdictionary.com/unibit#computer. 
  14. ↑ 14.0 14.1 (in de) Taschenbuch der Nachrichtenverarbeitung (2 ed.). Berlin / Heidelberg / New York: Springer-Verlag OHG. 1967. pp. 835–836. Title No. 1036. 
  15. ↑ 15.0 15.1 (in de) Taschenbuch der Informatik – Band III – Anwendungen und spezielle Systeme der Nachrichtenverarbeitung. 3 (3 ed.). Berlin / Heidelberg / New York: Springer Verlag. 1974. pp. 357–358. ISBN 3-540-06242-4. 
  16. ↑ Theory of magnetic recording (1 ed.). Cambridge University Press. 1994. 9-780521-449731. ISBN 0-521-44973-1. "[...] The writing of an impulse would involve writing a dibit or two transitions arbitrarily closely together. [...]" 
  17. ↑ "Crumb". MathWorld. http://mathworld.wolfram.com/Crumb.html. 
  18. ↑ Control Data 8092 TeleProgrammer: Programming Reference Manual. Minneapolis, Minnesota, US: Control Data Corporation. 1964. IDP 107a. http://bitsavers.org/pdf/cdc/809x/IDP107a_8092pgmRef_1964.pdf. Retrieved 2020-07-27. 
  19. ↑ The Art of Computer Programming: Cobinatorial Algorithms part 1. 4a. Addison Wesley. 
  20. ↑ 20.0 20.1 Advanced Logical Circuit Design Techniques (retyped electronic reissue ed.). Garland STPM Press (original issue) / WhitePubs Enterprises, Inc. (reissue). 2016. ISBN 0-8240-7014-3. http://www.donnamaie.com/Advanced_logic_ckt/Advanced_Logical_Circuit_Design_Techniques%20sm.pdf. Retrieved 2017-04-15.  [1][2]
  21. ↑ (in de) Elektrotechnik und Elektronik für Informatiker – Grundgebiete der Elektronik. 2. B.G. Teubner Stuttgart / Springer. 2013. ISBN 978-3-32296652-0. https://books.google.com/books?id=-fzKBgAAQBAJ. Retrieved 2015-08-03. 
  22. ↑ Reichenbach, Jürgen, ed (2013-07-02) (in de). Programmierung von Prozeßrechnern. Reihe Automatisierungstechnik. 79. VEB Verlag Technik (de) Berlin, reprint: Springer Verlag. doi:10.1007/978-3-663-02721-8. 9/3/4185. ISBN 978-3-663-00808-8. https://books.google.com/books?id=T-S0BgAAQBAJ. 
  23. ↑ 23.0 23.1 23.2 (in de) Digitale Rechenanlagen – Grundlagen / Schaltungstechnik / Arbeitsweise / Betriebssicherheit (2 ed.). ETH Zürich, Zürich, Switzerland: Springer-Verlag / IBM. 1965. pp. 6, 34, 165, 183, 208, 213, 215. 0978. 
  24. ↑ Steinbuch, Karl W., ed (1962). written at Karlsruhe, Germany (in de). Taschenbuch der Nachrichtenverarbeitung (1 ed.). Berlin / Göttingen / New York: Springer-Verlag OHG. p. 1076. 
  25. ↑ British Commercial Computer Digest: Pergamon Computer Data Series. Pergamon Press. 1969-01-01. 978-148312210-6. ISBN 1-48312210-7. 
  26. ↑ "Philips – Philips Data Systems' product range – April 1971". Philips. 1971. http://www.intact-reunies.nl/pdf/product1971.pdf. 
  27. ↑ UTF-9 and UTF-18 Efficient Transformation Formats of Unicode, April 1, 2005, doi:10.17487/RFC4042, RFC 4042, https://tools.ietf.org/html/rfc4042 
  28. ↑ IEEE Standard for Floating-Point Arithmetic. 2008-08-29. pp. 1–70. doi:10.1109/IEEESTD.2008.4610935. ISBN 978-0-7381-5752-8. 
  29. ↑ Handbook of Floating-Point Arithmetic (1 ed.). Birkhäuser. 2010. doi:10.1007/978-0-8176-4705-6. ISBN 978-0-8176-4704-9. https://cds.cern.ch/record/1315760. 
  30. ↑ Erle, Mark A. (2008-11-21). Algorithms and Hardware Designs for Decimal Multiplication (Thesis). Lehigh University (published 2009). ISBN 978-1-10904228-3. 1109042280. Retrieved 2016-02-10.
  31. ↑ Numbers and Computers. Springer Verlag. 2015. 3319172603. ISBN 9783319172606. https://books.google.com/books?id=FPlICAAAQBAJ. Retrieved 2016-02-10. 
  32. ↑ "AS1600 Quick-and-Dirty Documentation". http://spatula-city.org/~im14u2c/intv/jzintv-1.0-beta3/doc/utilities/as1600.txt. 
  33. ↑ "315 Electronic Data Processing System". NCR. November 1965. http://www.thecorememory.com/NCR_315_EDPS.pdf. 
  34. ↑ "NCR 315 Seminar". Computer Usage Communique 2 (3). 1963. http://www.thecorememory.com/NCR_315_Seminar.pdf. 
  35. ↑ (in de) Datenverarbeitungs-Lexikon (softcover reprint of hardcover 1st ed.). Wiesbaden, Germany: Springer Fachmedien Wiesbaden GmbH / Betriebswirtschaftlicher Verlag Dr. Th. Gabler GmbH. 2013. pp. 201, 308. doi:10.1007/978-3-663-13618-7. ISBN 978-3-409-31831-0. https://books.google.com/books?id=3aN9BwAAQBAJ. Retrieved 2016-05-24. "[...] slab, Abk. aus syllable = Silbe, die kleinste adressierbare Informationseinheit für 12 bit zur Übertragung von zwei Alphazeichen oder drei numerischen Zeichen. (NCR) [...] Hardware: Datenstruktur: NCR 315-100 / NCR 315-RMC; Wortlänge: Silbe; Bits: 12; Bytes: –; Dezimalziffern: 3; Zeichen: 2; Gleitkommadarstellung: fest verdrahtet; Mantisse: 4 Silben; Exponent: 1 Silbe (11 Stellen + 1 Vorzeichen) [...] [slab, abbr. for syllable = syllable, smallest addressable information unit for 12 bits for the transfer of two alphabetical characters or three numerical characters. (NCR) [...] Hardware: Data structure: NCR 315-100 / NCR 315-RMC; Word length: Syllable; Bits: 12; Bytes: –; Decimal digits: 3; Characters: 2; Floating point format: hard-wired; Significand: 4 syllables; Exponent: 1 syllable (11 digits + 1 prefix)]" 
  36. ↑ 36.0 36.1 36.2 36.3 IEEE Standard for a 32-bit Microprocessor Architecture. The Institute of Electrical and Electronics Engineers, Inc.. 1995. pp. 5–7. doi:10.1109/IEEESTD.1995.79519. ISBN 1-55937-428-4.  (NB. The standard defines doublets, quadlets, octlets and hexlets as 2, 4, 8 and 16 bytes, giving the numbers of bits (16, 32, 64 and 128) only as a secondary meaning. This might be important given that bytes were not always understood to mean 8 bits (octets) historically.)
  37. ↑ 37.0 37.1 37.2 Fascicle 1: MMIX (0th printing, 15th ed.). Stanford University: Addison-Wesley. 2004-02-15. http://profs.scienze.univr.it/~manca/storia-informatica/mmix.pdf. Retrieved 2017-03-30. 
  38. ↑ 38.0 38.1 Raymond, Eric S. (1996). The New Hacker's Dictionary (3 ed.). MIT Press. p. 333. ISBN 0262680920. 
  39. ↑ Zinterhof, Peter; Vajteršic, Marian; Uhl, Andreas, eds (February 1999). "Parallel Cluster Computing with IEEE1394–1995". written at Salzburg, Austria. Parallel Computation: 4th International ACPC Conference including Special Tracks on Parallel Numerics (ParNum '99) and Parallel Computing in Image Processing, Video Processing, and Multimedia. Berlin, Germany: Springer Verlag. 
  40. ↑ (in fr) Calculatrices. 14 (2 ed.). Lausanne: Presses polytechniques romandes. 1986. ISBN 2-88074054-1. https://books.google.com/books?id=3hGZ2qxxby8C&pg=PR3. 
  41. ↑ "Proceedings". Symposium on Experiences with Distributed and Multiprocessor Systems (SEDMS). 4. USENIX Association. 1993. 
  42. ↑ 42.0 42.1 "1. Introduction: Segment Alignment". 8086 Family Utilities – User's Guide for 8080/8085-Based Development Systems (A620/5821 6K DD ed.). Santa Clara, California, US: Intel Corporation. May 1982. p. 1-6. Order Number: 9800639-04. http://bitsavers.trailing-edge.com/pdf/intel/ISIS_II/9800639-04E_8086_Famility_Utilities_Users_Guide_May82.pdf. Retrieved 2020-02-29. 
  43. ↑ Microprocessors – A Programmer's View (1 ed.). Courant Institute, New York University, New York, US: McGraw-Hill Publishing Company. 1990. p. 85. ISBN 0-07-016638-2.  (xviii+462 pages)
  44. ↑ "Terms And Abbreviations / 4.1 Crossing Page Boundaries". MCS-4 Assembly Language Programming Manual – The INTELLEC 4 Microcomputer System Programming Manual (Preliminary ed.). Santa Clara, California, US: Intel Corporation. December 1973. pp. v, ((2-6)), ((4-1)). MCS-030-1273-1. http://bitsavers.trailing-edge.com/components/intel/MCS4/MCS-4_Assembly_Language_Programming_Manual_Dec73.pdf. 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.)
  45. ↑ "Development of ternary computers at Moscow State University". http://www.computer-museum.ru/english/setun.htm. 
  46. ↑ Malinowski, Christopher W.; Heinz Rinderle & Martin Siegle, "Three-state signaling system", US patent 4319227, issued 1982-03-09
  47. ↑ "US4319227". Google. https://patents.google.com/patent/US4319227. 
  48. ↑ "US4319227". Patentimages. http://patentimages.storage.googleapis.com/pdfs/US4319227.pdf. 



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