Get Units of Information essential facts below. View Videos or join the Units of Information discussion. Add Units of Information to your PopFlock.com topic list for future reference or share this resource on social media.
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).
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, 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 . 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 .
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). 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 (? 1.585) bits.
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.
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.
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 amount of information as one hexadecimal digit.
A pair of two bits or a quarter byte was called a crumb, 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, 8, 9, 12, 13, 16, 18, 20, 21, 22, 24, 25, 26, 29, 30, 31, 32, 33, 35, 36, 38, 39, 40, 42, 44, 48, 50, 52, 54, 56, 60, 64, 72, 80 bits or others.
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.
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). 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:
^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
^ abSteinbuch, Karl W.; Weber, Wolfgang; Heinemann, Traute, eds. (1974) . Written at Karlsruhe / Bochum. Taschenbuch der Informatik - Band III - Anwendungen und spezielle Systeme der Nachrichtenverarbeitung. Taschenbuch der Nachrichtenverarbeitung (in German). 3 (3 ed.). Berlin / Heidelberg / New York: Springer Verlag. pp. 357-358. ISBN3-540-06242-4. LCCN73-80607.
^Bertram, H. Neal (1994). Theory of magnetic recording (1 ed.). Cambridge University Press. ISBN0-521-44973-1. 9-780521-449731. [...] The writing of an impulse would involve writing a dibit or two transitions arbitrarily closely together. [...]
^ ab"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 . [...] 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.)
^Böszörményi, László; Hölzl, Günther; Pirker, Emaneul (February 1999). Written at Salzburg, Austria. Zinterhof, Peter; Vajter?ic, 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.
^Nicoud, Jean-Daniel (1986). Calculatrices. Traité d'électricité de l'École polytechnique fédérale de Lausanne (in French). 14 (2 ed.). Lausanne: Presses polytechniques romandes. ISBN2-88074054-1.
^Proceedings. Symposium on Experiences with Distributed and Multiprocessor Systems (SEDMS). 4. USENIX Association. 1993.
^US4319227, Malinowski, Christopher W.; Heinz Rinderle & Martin Siegle, "Three-state signaling system", issued 1982-03-09, assigned to Department of Research and Development, AEG-Telefunken, Heilbronn, Germany