Hartley (unit)

The hartley (symbol Hart), also called a ban, or a dit (short for "decimal digit"),^[1][2][3] is a logarithmic unit that measures information or entropy, based on base 10 logarithms and powers of 10. One hartley is the information content of an event if the probability of that event occurring is 1⁄10.^[4] It is therefore equal to the information contained in one decimal digit (or dit), assuming a priori equiprobability of each possible value. It is named after Ralph Hartley.

If base 2 logarithms and powers of 2 are used instead, then the unit of information is the shannon or bit, which is the information content of an event if the probability of that event occurring is 1⁄2. Natural logarithms and powers of e define the nat.

One ban corresponds to ln(10) nat = log₂(10) Sh, or approximately 2.303 nat, or 3.322 bit (3.322 Sh).^[a] A deciban is one tenth of a ban (or about 0.332 Sh); the name is formed from ban by the SI prefix deci-.

Though there is no associated SI unit, information entropy is part of the International System of Quantities, defined by International Standard IEC 80000-13 of the International Electrotechnical Commission.

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