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A ban, sometimes called a hartley (symbol Hart) or a dit (abbreviation of decimal digit), is a logarithmic unit which measures information
Information

Information as a Conveyed concept has a diversity of meanings, from everyday usage to technical settings. Generally speaking, the concept of information is closely related to notions of constraint, communication, control system, data, form, instruction, knowledge, Meaning , stimulation, pattern, perception, and knowledge representation....
 or entropy
Information entropy

In information theory, entropy is a measure of the uncertainty associated with a random variable. The term by itself in this context usually refers to the Shannon entropy, which quantifies, in the sense of an expected value, the self-information contained in a message, usually in units such as bits....
, based on base 10 logarithm
Logarithm

In mathematics, the logarithm of a number to a given base is the Power or exponent to which the base must be raised in order to produce the number....
s and powers of 10, rather than the powers of 2 and base 2 logarithms
Binary logarithm

In mathematics, the binary logarithm is the logarithm for base 2. It is the inverse function of ....
 which define the bit
Bit

A bit is a binary numeral system numerical digit, taking a value of either 0 or 1. Binary digits are a basic unit of information Computer data storage and transmission in digital computing and digital information theory....
. Like a bit corresponds to a binary digit, a ban is a decimal digit. A deciban is one tenth of a ban.

One ban corresponds to about 3.32 bit
Bit

A bit is a binary numeral system numerical digit, taking a value of either 0 or 1. Binary digits are a basic unit of information Computer data storage and transmission in digital computing and digital information theory....
s (log2(10)), or 2.30 nat
Nat (information)

A nat is a logarithmic unit of information or information entropy, based on natural logarithms and powers of e , rather than the powers of 2 and binary logarithm which define the bit....
s (ln(10)).






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A ban, sometimes called a hartley (symbol Hart) or a dit (abbreviation of decimal digit), is a logarithmic unit which measures information
Information

Information as a Conveyed concept has a diversity of meanings, from everyday usage to technical settings. Generally speaking, the concept of information is closely related to notions of constraint, communication, control system, data, form, instruction, knowledge, Meaning , stimulation, pattern, perception, and knowledge representation....
 or entropy
Information entropy

In information theory, entropy is a measure of the uncertainty associated with a random variable. The term by itself in this context usually refers to the Shannon entropy, which quantifies, in the sense of an expected value, the self-information contained in a message, usually in units such as bits....
, based on base 10 logarithm
Logarithm

In mathematics, the logarithm of a number to a given base is the Power or exponent to which the base must be raised in order to produce the number....
s and powers of 10, rather than the powers of 2 and base 2 logarithms
Binary logarithm

In mathematics, the binary logarithm is the logarithm for base 2. It is the inverse function of ....
 which define the bit
Bit

A bit is a binary numeral system numerical digit, taking a value of either 0 or 1. Binary digits are a basic unit of information Computer data storage and transmission in digital computing and digital information theory....
. Like a bit corresponds to a binary digit, a ban is a decimal digit. A deciban is one tenth of a ban.

One ban corresponds to about 3.32 bit
Bit

A bit is a binary numeral system numerical digit, taking a value of either 0 or 1. Binary digits are a basic unit of information Computer data storage and transmission in digital computing and digital information theory....
s (log2(10)), or 2.30 nat
Nat (information)

A nat is a logarithmic unit of information or information entropy, based on natural logarithms and powers of e , rather than the powers of 2 and binary logarithm which define the bit....
s (ln(10)). A deciban is about 0.33 bits.

History


The ban and the deciban were invented by Alan Turing
Alan Turing

Alan Mathison Turing, Order of the British Empire, Fellow of the Royal Society was a British mathematician, logician and Cryptanalysis....
 with I. J. Good
I. J. Good

Irving John Good is a British statistician who worked also as a cryptographer at Bletchley Park. He was born Isidore Jacob Gudak to a Jewish family in London....
 in 1940, to measure the amount of information that could be deduced by the codebreakers at Bletchley Park
Bletchley Park

Bletchley Park, also known as Station X, is an estate located in the town of Bletchley, in Buckinghamshire. Since 1967, Bletchley has been part of Milton Keynes, England....
 using the Banburismus
Banburismus

Banburismus was a cryptology process invented by Alan Turing at Bletchley Park in England during the Second World War. It was used by Bletchley Park's Hut 8 to help break German Kriegsmarine messages enciphered on an Enigma machine....
 procedure, towards determining each day's unknown setting of the German naval Enigma
Enigma machine

The Enigma machine is any of a family of related electro-mechanical rotor machines that have been used to generate ciphers for the encryption and decryption of secret messages....
 cipher machine. The name was inspired by the enormous sheets of card, printed in the town of Banbury
Banbury

Banbury is a market town and civil parish in the district of Cherwell in northern Oxfordshire, England, located on the River Cherwell. It lies northwest of London, southeast of Birmingham, south of Coventry and north northwest of the county town of Oxford....
 about 30 miles away, that were used in the process.

The term hartley is after Ralph Hartley
Ralph Hartley

Ralph Vinton Lyon Hartley was an electronics researcher. He invented the Hartley oscillator and the Hartley transform, and contributed to the foundations of information theory....
, who suggested this unit in 1928 (Reza [1961] 1994:7).

The units pre-date Shannon's bit by at least eight years.

Usage as a unit of probability


The deciban is a particularly useful measure of information in odds-ratios or weights of evidence. 10 decibans corresponds to an odds ratio of 10:1; 20 decibans to 100:1 odds, etc. According to I. J. Good
I. J. Good

Irving John Good is a British statistician who worked also as a cryptographer at Bletchley Park. He was born Isidore Jacob Gudak to a Jewish family in London....
, a change in a weight of evidence of 1 deciban (i.e., a change in an odds ratio from evens to about 5:4), or perhaps half a deciban, is about as finely as humans can reasonably be expected to quantify their degree of belief in a hypothesis.

The unit was not adopted as a metric for measuring and comparing digital error correction systems, nor was it adopted as an information density (or entropy) unit for image compression.