Nit (unit of information)

Nit , also known as Nat or Naperian Digit or nepit , is a seldom used, dimensionless unit for the quantitative specification of decision-making contents in information theory . The designation Nat is specified in the IEC 60027-3 or ISO 2382-16 standard. The name is derived from the name of a developer of logarithmic calculation rules, John Napier . In contrast to the bit , the nit is not based on the dual, but on the natural logarithm , i.e. on the base e instead of the base 2.

The following applies:

{\ displaystyle \ ln (p) \, \ mathrm {nit} {\ mathrel {\ widehat {=}}} \ log _ {2} (p) \, \ mathrm {bit}}

One nit thus corresponds to 1 / ln (2) bits, which is around 1.44 bits. This results from the following calculation:

{\ displaystyle 1 \, \ mathrm {nit} = {\ log _ {2} (p) \ over \ ln (p)} \, \ mathrm {bit} = {1 \ over \ ln 2} \, \ mathrm {bit} \ approx \ 1 {,} 44 \, \ mathrm {bit}}

An application of this unit can be found where in econometrics entropies are calculated based on the natural logarithm. As a rule, however, entropy measures such as the Theil index are given today without any unit.

Natural unit of information

If n mutually exclusive events are considered, the logarithm of n is called decision content. If you choose the natural logarithm for the base e, write the unit symbol Nit or Nat after the numerical value and the number thus obtained indicates the decision content in natural information units .

context

Analogous definitions lead when using the logarithm to base 2 to the Shannon unit , expressed in the unit bit , and in the case of the logarithm to the Hartley unit , expressed in the rarely used unit Ban .

literature

Fazlollah M. Reza: An Introduction to Information Theory . Dover Publications, New York 1995, ISBN 0-486-68210-2 .

swell

^ Henri Theil : Principles of Econometrics , 1971, pp. 637ff, ISBN 978-0471858454

[1] Henri Theil : Principles of Econometrics , 1971, pp. 637ff, ISBN 978-0471858454