Units of information

Last updated

In digital 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 information contained in messages and the entropy of random variables.

Contents

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. Units of information.svg
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 logbN. 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 logcN = (logcb) logbN. 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 portmanteau of binary digit [2] ). 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. [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 log2e (≈ 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 (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). 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. [7]

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 [8] 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.

SymbolPrefix SI Meaning Binary meaningSize difference
kkilo103  = 10001210 = 102412.40%
Mmega106  = 10002220 = 102424.86%
Ggiga109  = 10003230 = 102437.37%
Ttera1012 = 10004240 = 102449.95%
Ppeta1015 = 10005250 = 1024512.59%
Eexa1018 = 10006260 = 1024615.29%
Zzetta1021 = 10007270 = 1024718.06%
Yyotta1024 = 10008280 = 1024820.89%
Rronna1027 = 10009290 = 1024923.79%
Qquetta1030 = 1000102100 = 10241026.77%

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 are commonly used with their decimal values (powers of 10). Many attempts have sought 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 by defining a series of binary prefixes that use 1024 instead of 1000 as the main radix: [9]

SymbolPrefix
Kikibi, binary kilo1 kibibyte (KiB)210 bytes1024 B
Mimebi, binary mega1 mebibyte (MiB)220 bytes1024 KiB
Gigibi, binary giga1 gibibyte (GiB)230 bytes1024 MiB
Titebi, binary tera1 tebibyte (TiB)240 bytes1024 GiB
Pipebi, binary peta1 pebibyte (PiB)250 bytes1024 TiB
Eiexbi, binary exa1 exbibyte (EiB)260 bytes1024 PiB

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

Size examples

Obsolete and unusual units

Several other units of information storage have been named:

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

See also

Notes

  1. ↑ However, if the SI guideline to include a space before the unit is ignored, the IEC 80000-13 abbreviation "o" for octets can be confused with the postfix "o" to indicate octal numbers in Intel convention .

Related Research Articles

The bit is the most basic unit of information in computing and digital communications. The name is a portmanteau of binary digit. The bit represents a logical state with one of two possible values. These values are most commonly represented as either "1" or "0", but other representations such as true/false, yes/no, on/off, or +/− are also widely used.

The byte is a unit of digital information that most commonly consists of eight bits. Historically, the byte was the number of bits used to encode a single character of text in a computer and for this reason it is the smallest addressable unit of memory in many computer architectures. To disambiguate arbitrarily sized bytes from the common 8-bit definition, network protocol documents such as the Internet Protocol refer to an 8-bit byte as an octet. Those bits in an octet are usually counted with numbering from 0 to 7 or 7 to 0 depending on the bit endianness.

<span class="mw-page-title-main">Binary-coded decimal</span> System of digitally encoding numbers

In computing and electronic systems, binary-coded decimal (BCD) is a class of binary encodings of decimal numbers where each digit is represented by a fixed number of bits, usually four or eight. Sometimes, special bit patterns are used for a sign or other indications.

A binary prefix is a unit prefix that indicates a multiple of a unit of measurement by an integer power of two. The most commonly used binary prefixes are kibi (symbol Ki, meaning 210 = 1024), mebi (Mi, 220 = 1048576), and gibi (Gi, 230 = 1073741824). They are most often used in information technology as multipliers of bit and byte, when expressing the capacity of storage devices or the size of computer files.

<span class="mw-page-title-main">Gigabyte</span> Unit of digital information

The gigabyte is a multiple of the unit byte for digital information. The prefix giga means 109 in the International System of Units (SI). Therefore, one gigabyte is one billion bytes. The unit symbol for the gigabyte is GB.

In computer science, an integer is a datum of integral data type, a data type that represents some range of mathematical integers. Integral data types may be of different sizes and may or may not be allowed to contain negative values. Integers are commonly represented in a computer as a group of binary digits (bits). The size of the grouping varies so the set of integer sizes available varies between different types of computers. Computer hardware nearly always provides a way to represent a processor register or memory address as an integer.

The kilobyte is a multiple of the unit byte for digital information. The International System of Units (SI) defines the prefix kilo as a multiplication factor of 1000 (103); therefore, one kilobyte is 1000 bytes. The internationally recommended unit symbol for the kilobyte is kB.

The kilobit is a multiple of the unit bit for digital information or computer storage. The prefix kilo- (symbol k) is defined in the International System of Units (SI) as a multiplier of 103 (1 thousand), and therefore,

The megabyte is a multiple of the unit byte for digital information. Its recommended unit symbol is MB. The unit prefix mega is a multiplier of 1000000 (106) in the International System of Units (SI). Therefore, one megabyte is one million bytes of information. This definition has been incorporated into the International System of Quantities.

<span class="mw-page-title-main">Nibble</span> Four-bit unit of digital storage

In computing, a nibble (occasionally nybble, nyble, or nybl to match the spelling of byte) is a four-bit aggregation, or half an octet. It is also known as half-byte or tetrade. In a networking or telecommunication context, the nibble is often called a semi-octet, quadbit, or quartet. A nibble has sixteen (24) possible values. A nibble can be represented by a single hexadecimal digit (0–F) and called a hex digit.

<span class="mw-page-title-main">Character (computing)</span> Primitive data type

In computer and machine-based telecommunications terminology, a character is a unit of information that roughly corresponds to a grapheme, grapheme-like unit, or symbol, such as in an alphabet or syllabary in the written form of a natural language.

An order of magnitude is usually a factor of ten. Thus, four orders of magnitude is a factor of 10,000 or 104.

In computing, a word is the natural unit of data used by a particular processor design. A word is a fixed-sized datum handled as a unit by the instruction set or the hardware of the processor. The number of bits or digits in a word is an important characteristic of any specific processor design or computer architecture.

A unit prefix is a specifier or mnemonic that is prepended to units of measurement to indicate multiples or fractions of the units. Units of various sizes are commonly formed by the use of such prefixes. The prefixes of the metric system, such as kilo and milli, represent multiplication by positive or negative powers of ten. In information technology it is common to use binary prefixes, which are based on powers of two. Historically, many prefixes have been used or proposed by various sources, but only a narrow set has been recognised by standards organisations.

IEEE 1541-2002 is a standard issued in 2002 by the Institute of Electrical and Electronics Engineers (IEEE) concerning the use of prefixes for binary multiples of units of measurement related to digital electronics and computing. IEEE 1541-2021 revises and supersedes IEEE 1541–2002, which is 'inactive'.

The octet is a unit of digital information in computing and telecommunications that consists of eight bits. The term is often used when the term byte might be ambiguous, as the byte has historically been used for storage units of a variety of sizes.

ISO 80000 or IEC 80000, Quantities and units, is an international standard describing the International System of Quantities (ISQ). It was developed and promulgated jointly by the International Organization for Standardization (ISO) and the International Electrotechnical Commission (IEC). It serves as a style guide for using physical quantities and units of measurement, formulas involving them, and their corresponding units, in scientific and educational documents for worldwide use. The ISO/IEC 80000 family of standards was completed with the publication of the first edition of Part 1 in November 2009.

The JEDEC memory standards are the specifications for semiconductor memory circuits and similar storage devices promulgated by the Joint Electron Device Engineering Council (JEDEC) Solid State Technology Association, a semiconductor trade and engineering standardization organization.

This timeline of binary prefixes lists events in the history of the evolution, development, and use of units of measure which are germane to the definition of the binary prefixes by the International Electrotechnical Commission (IEC) in 1998, used primarily with units of information such as the bit and the byte.

In computing, a syllable is a name for a platform-dependent unit of information storage. Depending on the target hardware, various bit widths are associated with it. Commonly used in the 1960s and 1970s, the term has mostly fallen into disuse in favour of terms like byte or word.

References

  1. 1 2 3 Abramson, Norman (1963). Information theory and coding. McGraw-Hill.
  2. ↑ Mackenzie, Charles E. (1980). Coded Character Sets, History and Development (PDF). The Systems Programming Series (1 ed.). Addison-Wesley Publishing Company, Inc. p. xii. ISBN   978-0-201-14460-4. LCCN   77-90165. Archived (PDF) from the original on May 26, 2016. Retrieved August 25, 2019.
  3. 1 2 Knuth, Donald Ervin. The Art of Computer Programming: Seminumerical algorithms. Vol. 2. Addison Wesley.
  4. ↑ Shanmugam (2006). Digital and Analog Computer Systems.
  5. ↑ Jaeger, Gregg (2007). Quantum information: an overview.
  6. ↑ Kumar, I. Ravi (2001). Comprehensive Statistical Theory of Communication.
  7. ↑ Nybble at dictionary reference.com; sourced from Jargon File 4.2.0, accessed 2007-08-12
  8. ↑ Beebe, Nelson H. F. (2017-08-22). "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. p. 970. doi:10.1007/978-3-319-64110-2. ISBN   978-3-319-64109-6. LCCN   2017947446. S2CID   30244721.
  9. ↑ 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
  10. ↑ "Dictionary of Terms for Solid State Technology – 7th Edition". JEDEC Solid State Technology Association. February 2018. pp. 100, 118, 135. JESD88F. Retrieved 2021-06-25.
  11. 1 2 3 Horak, Ray (2007). Webster's New World Telecom Dictionary. John Wiley & Sons. p. 402. ISBN   9-78047022571-4.
  12. ↑ "Unibit".
  13. 1 2 Steinbuch, Karl W.; Wagner, Siegfried W., eds. (1967) [1962]. Written at Karlsruhe, Germany. Taschenbuch der Nachrichtenverarbeitung (in German) (2 ed.). Berlin / Heidelberg / New York: Springer-Verlag OHG. pp. 835–836. LCCN   67-21079. Title No. 1036.
  14. 1 2 Steinbuch, Karl W.; Weber, Wolfgang; Heinemann, Traute, eds. (1974) [1967]. Written at Karlsruhe / Bochum. Taschenbuch der Informatik - Band III - Anwendungen und spezielle Systeme der Nachrichtenverarbeitung (in German). Vol. 3 (3 ed.). Berlin / Heidelberg / New York: Springer Verlag. pp. 357–358. ISBN   3-540-06242-4. LCCN   73-80607.
  15. ↑ Bertram, H. Neal (1994). Theory of magnetic recording (1 ed.). Cambridge University Press. ISBN   0-521-44973-1. 9-780521-449731. […] The writing of an impulse would involve writing a dibit or two transitions arbitrarily closely together. […]
  16. ↑ Weisstein, Eric. W. "Crumb". MathWorld . Retrieved 2015-08-02.
  17. ↑ Control Data 8092 TeleProgrammer: Programming Reference Manual (PDF). Minneapolis, Minnesota, US: Control Data Corporation. 1964. IDP 107a. Archived (PDF) from the original on 2020-05-25. Retrieved 2020-07-27.
  18. ↑ Knuth, Donald Ervin. The Art of Computer Programming: Cobinatorial Algorithms part 1. Vol. 4a. Addison Wesley.
  19. 1 2 Svoboda, Antonín; White, Donnamaie E. (2016) [2012, 1985, 1979-08-01]. Advanced Logical Circuit Design Techniques (PDF) (retyped electronic reissue ed.). Garland STPM Press (original issue) / WhitePubs Enterprises, Inc. (reissue). ISBN   0-8240-7014-3. LCCN   78-31384. Archived (PDF) from the original on 2017-04-14. Retrieved 2017-04-15.
  20. ↑ Paul, Reinhold (2013). Elektrotechnik und Elektronik für Informatiker - Grundgebiete der Elektronik (in German). Vol. 2. B.G. Teubner Stuttgart / Springer. ISBN   978-3-32296652-0 . Retrieved 2015-08-03.
  21. ↑ Böhme, Gert; Born, Werner; Wagner, B.; Schwarze, G. (2013-07-02) [1969]. Reichenbach, Jürgen (ed.). Programmierung von Prozeßrechnern. Reihe Automatisierungstechnik (in German). Vol. 79. VEB Verlag Technik  [ de ] Berlin, reprint: Springer Verlag. doi:10.1007/978-3-663-02721-8. ISBN   978-3-663-00808-8. 9/3/4185.
  22. 1 2 "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, US: 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.)
  23. 1 2 3 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.
  24. ↑ 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.
  25. ↑ Crispin, Mark R. (2005). RFC 4042: UTF-9 and UTF-18.
  26. ↑ IEEE Standard for Floating-Point Arithmetic. 2008-08-29. pp. 1–70. doi:10.1109/IEEESTD.2008.4610935. ISBN   978-0-7381-5752-8 . Retrieved 2016-02-10.
  27. ↑ 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.
  28. ↑ 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.
  29. ↑ Kneusel, Ronald T. (2015). Numbers and Computers. Springer Verlag. ISBN   9783319172606. 3319172603. Retrieved 2016-02-10.
  30. ↑ Zbiciak, Joe. "AS1600 Quick-and-Dirty Documentation" . Retrieved 2013-04-28.
  31. ↑ "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.
  32. ↑ Bardin, Hillel (1963). "NCR 315 Seminar" (PDF). Computer Usage Communique. 2 (3). Archived (PDF) from the original on 2016-05-24.
  33. ↑ Schneider, Carl (2013) [1970]. Datenverarbeitungs-Lexikon [Lexicon of information technology] (in German) (softcover reprint of hardcover 1st ed.). Wiesbaden, Germany: Springer Fachmedien Wiesbaden GmbH / Betriebswirtschaftlicher Verlag Dr. Th. Gabler GmbH. pp. 201, 308. doi:10.1007/978-3-663-13618-7. ISBN   978-3-409-31831-0 . 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)]
  34. 1 2 3 4 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 . Retrieved 2016-02-10. (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.)
  35. 1 2 3 Knuth, Donald Ervin (2004-02-15) [1999]. Fascicle 1: MMIX (PDF) (0th printing, 15th ed.). Stanford University: Addison-Wesley. Archived (PDF) from the original on 2017-03-30. Retrieved 2017-03-30.
  36. 1 2 Raymond, Eric S. (1996). The New Hacker's Dictionary (3 ed.). MIT Press. p. 333. ISBN   0262680920.
  37. ↑ Böszörményi, László; Hölzl, Günther; Pirker, Emaneul (February 1999). Written at Salzburg, Austria. Zinterhof, Peter; Vajteršic, Marian; Uhl, Andreas (eds.). Parallel Cluster Computing with IEEE1394–1995. Parallel Computation: 4th International ACPC Conference including Special Tracks on Parallel Numerics (ParNum '99) and Parallel Computing in Image Processing, Video Processing, and Multimedia. Proceedings: Lecture Notes in Computer Science 1557. Berlin, Germany: Springer Verlag.
  38. ↑ Nicoud, Jean-Daniel (1986). Calculatrices (in French). Vol. 14 (2 ed.). Lausanne: Presses polytechniques romandes. ISBN   2-88074054-1.
  39. ↑ Proceedings. Symposium on Experiences with Distributed and Multiprocessor Systems (SEDMS). Vol. 4. USENIX Association. 1993.
  40. 1 2 "1. Introduction: Segment Alignment". 8086 Family Utilities - User's Guide for 8080/8085-Based Development Systems (PDF). Revision E (A620/5821 6K DD ed.). Santa Clara, California, US: Intel Corporation. May 1982 [1980, 1978]. p. 1-6. Order Number: 9800639-04. Archived (PDF) from the original on 2020-02-29. Retrieved 2020-02-29.
  41. ↑ Dewar, Robert Berriedale Keith; Smosna, Matthew (1990). Microprocessors - A Programmer's View (1 ed.). Courant Institute, New York University, New York, US: McGraw-Hill Publishing Company. p. 85. ISBN   0-07-016638-2. LCCN   89-77320. (xviii+462 pages)
  42. ↑ Brousentsov, N. P.; Maslov, S. P.; Ramil Alvarez, J.; Zhogolev, E. A. "Development of ternary computers at Moscow State University" . Retrieved 2010-01-20.
  43. ↑ US 4319227,Malinowski, Christopher W.; Rinderle, Heinz& Siegle, Martin,"Three-state signaling system",issued 1982-03-09, assigned to AEG-Telefunken
  44. ↑ "US4319227". Google.
  45. ↑ "US4319227" (PDF). Patentimages.
This page is based on this Wikipedia article
Text is available under the CC BY-SA 4.0 license; additional terms may apply.
Images, videos and audio are available under their respective licenses.