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{{short description|Unit of information}}
{{fundamental info units}}

The '''shannon''' (symbol: Sh) is a [[unit of information]] named after [[Claude Shannon]], the founder of [[information theory]]. [[IEC 80000-13]] defines the shannon as the [[information content]] associated with an event when the probability of the event occurring is {{sfrac|1|2}}. It is understood as such within the realm of [[information theory]], and is conceptually distinct from the [[bit]], a term used in [[data processing]] and storage to denote a single instance of a binary [[Digital signal|signal]]. A sequence of ''n'' binary symbols (such as contained in computer memory or a binary data transmission) is properly described as consisting of ''n'' bits, but the information content of those ''n'' symbols may be more or less than ''n'' shannons depending on the ''a priori'' probability of the actual sequence of symbols.{{efn|Since the information associated with an event outcome that has ''a priori'' probability ''p'', e.g. that a single given data bit takes the value 0, is given by {{nowrap|1=''H'' = −log ''p''}}, and ''p'' can lie anywhere in the range {{nowrap|0 < ''p'' ≤ 1}}, the information content can lie anywhere in the range {{nowrap|0 ≤ ''H'' < ∞}}.}}

The shannon also serves as a unit of the [[information entropy]] of an event, which is defined as the [[expected value]] of the information content of the event (i.e., the probability-weighted average of the information content of all potential events). Given a number of possible outcomes, unlike information content, the entropy has an upper bound, which is reached when the possible outcomes are equiprobable. The maximum entropy of ''n'' bits is ''n'' Sh. A further quantity that it is used for is [[channel capacity]], which is generally the maximum of the expected value of the information content encoded over a channel that can be transferred with negligible probability of error, typically in the form of an information rate.

Nevertheless, the term ''bits of information'' or simply ''bits'' is more often heard, even in the fields of information and [[A Mathematical Theory of Communication#Contents|communication theory]], rather than ''shannons''; just saying ''bits'' can therefore be ambiguous. Using the unit ''shannon'' is an explicit reference to a quantity of information content, information entropy or channel capacity, and is not restricted to binary data,{{refn|{{cite journal |author=Olivier Rioul |year=2018 |title=This is IT: A primer on Shannon's entropy and Information |journal=L'Information, Séminaire Poincaré |volume=XXIII |pages=43–77 |url=https://perso.telecom-paristech.fr/rioul/publis/201811rioul.pdf |access-date=2021-05-23 |quote=The ''Système International d'unités'' recommends the use of the ''shannon'' (Sh) as the information unit in place of the ''bit'' to distinguish the amount of information from the quantity of data that may be used to represent this information. Thus, according to the SI standard, ''H''(''X'') should be expressed using the shannon as the unit. The entropy of one bit lies between 0 and 1 Sh. }}}} whereas ''bits'' can as well refer to the number of binary symbols involved, as is the term used in fields such as data processing.

== Similar units ==

The shannon is connected through constants of proportionality to two other units of information:{{refn|{{cite web |title=IEC 80000-13:2008 |url=http://www.iso.org/iso/catalogue_detail?csnumber=31898 |publisher=[[International Organization for Standardization]] |accessdate=21 July 2013 }}}}
{{block indent|1=1 Sh ≈ 0.693 [[Nat (unit)|nat]] ≈ 0.301 [[hartley (unit)|Hart]].}}

The ''[[hartley (unit)|hartley]]'', a seldom-used unit, is named after [[Ralph Hartley]], an electronics engineer interested in the capacity of communications channels. Although of a more limited nature, his early work, preceding that of Shannon, makes him recognized also as a pioneer of information theory. Just as the shannon describes the maximum possible information capacity of a binary symbol, the hartley describes the information that can be contained in a 10-ary symbol, that is, a digit value in the range 0 to 9 when the ''a priori'' probability of each value is {{sfrac|1|10}}. The conversion factor quoted above is given by log10(2).

In mathematical expressions, the [[Nat (unit)|nat]] is a more natural unit of information, but 1 nat does not correspond to a case in which all possibilities are equiprobable, unlike with the shannon and hartley. In each case, formulae for the quantification of information capacity or [[Entropy (information theory)|entropy]] involve taking the [[logarithm]] of an expression involving probabilities. If base-2 logarithms are employed, the result is expressed in shannons, if base-10 ([[common logarithm]]s) then the result is in hartleys, and if [[natural logarithm]]s (base [[e (mathematical constant)|e]]), the result is in nats. For instance, the information capacity of a 16-bit sequence (achieved when all 65536 possible sequences are equally probable) is given by log(65536), thus {{nowrap|1=log10(65536) Hart ≈ 4.82 Hart}}, {{nowrap|1=loge(65536) nat ≈ 11.09 nat}}, or {{nowrap|1=log2(65536) Sh = 16 Sh}}.

== Information measures ==
{{main|Quantities of information}}

In [[information theory]] and derivative fields such as [[coding theory]], one cannot quantify the 'information' in a single message (sequence of symbols) out of context, but rather a reference is made to the model of a channel (such as [[bit error rate]]) or to the underlying statistics of an information source. There are thus [[Quantities of information|various measures of or related to information]], all of which may use the shannon as a unit.{{cn|date=December 2022}}

For instance, in the above example, a 16-bit channel could be said to have a [[channel capacity]] of 16 Sh, but when connected to a particular information source that only sends one of 8 possible messages, one would compute the [[Entropy (information theory)|entropy]] of its output as no more than 3 Sh. And if one already had been informed through a side channel in which set of 4 possible messages the message is, then one could calculate the [[mutual information]] of the new message (having 8 possible states) as no more than 2 Sh. Although there are infinite possibilities for a [[real number]] chosen between 0 and 1, so-called [[differential entropy]] can be used to quantify the information content of an analog signal, such as related to the enhancement of [[signal-to-noise ratio]] or confidence of a [[hypothesis test]].{{cn|date=December 2022}}

== Notes ==
{{notelist}}

== References ==
{{reflist}}

[[Category:Units of information]]
[[Category:Claude Shannon|unit]]
[[Category:2 (number)]]

Shannon (unit) - Revision history

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