# Shannon (unit)

Shannon (abbreviated Sh ) is the unit for the information content of a message named after the American mathematician and founder of information theory, Claude Elwood Shannon .

## definition

A Shannon (1 Sh) is a unit of the amount of information in a message. The message is described by a set of characters and by the probabilities p i with which the individual characters appear in the message. By definition, such a message has the following informational content, measured in Shannon, of ${\ displaystyle Z = \ {z_ {1}, z_ {2}, \ dots, z_ {S} \}}$

${\ displaystyle \ mathrm {H} = - \ sum _ {i} {p_ {i} \ cdot \ log _ {2} p_ {i}} \ quad [{\ text {Sh}}]}$

The unit Sh results from the information theory established by Claude Shannon and corresponds to the entropy of the relevant news source and, in biometry, to the Shannon index of a population of different species.

## Examples

• The simplest example: A one-off message from the character set , where both characters occur with a probability of 0.5 each, has the information content .${\ displaystyle Z = \ {0.1 \}}$${\ displaystyle - {\ frac {1} {2}} \; \ log _ {2} \! \ left ({\ frac {1} {2}} \ right) - {\ frac {1} {2} } \; \ log _ {2} \! \ left ({\ frac {1} {2}} \ right) = - \ log _ {2} \! \ left ({\ frac {1} {2}} \ right) = \ log _ {2} (2) = 1 \, {\ text {Sh}}}$
• If the character set consists of ten characters, for example , with all characters occurring again with the same probability, then the information content is . This can be interpreted in such a way that a 4-bit coding is definitely sufficient to transmit such messages (this is implemented, for example, by the BCD code ), but that there is still redundancy . With the BCD code, this redundancy manifests itself in such a way that only 10 of the 16 different characters that can be represented with this code actually occur.${\ displaystyle \ {0,1,2,3,4,5,6,7,8,9 \}}$${\ displaystyle - \ log _ {2} \ left ({\ frac {1} {10}} \ right) = \ log _ {2} (10) \ approx 3 {,} 322 \ \ mathrm {Sh}}$

## standardization

Definitions of the units of decision content in information theory can be found in the international standards IEC 60027-3 and ISO 2382-16. In addition to the Shannon unit based on the logarithm for base 2, the Hartley based on the logarithm of ten (unit symbol: Hart) and the natural information unit based on the natural logarithm (unit symbol: nat) are explained.

"The attempt by the International Organization for Standardization (ISO) to replace the unit bit with the Shannon unit in 1975 [...] was not very successful in retrospect."

- Walter Umstätter

## literature

• Johann Blieberger, Bernd Burgstaller, Gerhard Helge Schildt: Computer Science - Basics . 4th edition, Springer Verlag, Vienna 2002, ISBN 978-3-211-83710-8 .

## Individual evidence

1. ^ News for Documentation 49 (4), 1998, pp. 221–224.