A ban, sometimes called a hartley (symbol Hart) or a dit (abbreviation of decimal digit), is a logarithmic unit which measures information or entropy, based on base 10 logarithms and powers of 10, rather than the powers of 2 and base 2 logarithms which define the bit. Information as a concept has a diversity of meanings from everyday usage to technical settings 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 In Mathematics, the binary logarithm (log2 n) is the Logarithm for Base 2 A bit is a binary digit, taking a value of either 0 or 1 Binary digits are a basic unit of Information storage and communication 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 bits (log2(10)), or 2. A bit is a binary digit, taking a value of either 0 or 1 Binary digits are a basic unit of Information storage and communication 30 nats (ln(10)). A nat (sometimes also nit or even nepit) is a Logarithmic unit of Information or entropy, based on Natural logarithms and A deciban is about 0. 33 bits.

## History

The ban and the deciban were invented by Alan Turing with I. J. Good in 1940, to measure the amount of information that could be deduced by the codebreakers at Bletchley Park using the Banburismus procedure, towards determining each day's unknown setting of the German naval Enigma cipher machine. Alan Mathison Turing, OBE, FRS (ˈt(jʊ(ərɪŋ (23 June 1912 &ndash 7 June 1954 was an English Mathematician Irving John (Jack Good (born 9 December 1916) is a British Statistician who worked also as a Cryptographer at Bletchley Park Year 1940 ( MCMXL) was a Leap year starting on Monday (link will display the full 1940 calendar of the Gregorian calendar. Bletchley Park, also known as Station X, is an estate located in the town of Bletchley, in Buckinghamshire, and (since 1967 part of Milton Keynes Banburismus was a process invented by Alan Turing at Bletchley Park in England during the Second World War. The Enigma machine is any one of a family of related electro-mechanical Rotor machines used to generate Ciphers for the Encryption and decryption of The name was inspired by the enormous sheets of card, printed in the town of Banbury about 30 miles away, that were used in the process. Banbury is a Market town located on the River Cherwell in northern Oxfordshire, England.

The term hartley is after Ralph Hartley, who suggested this unit in 1928 (Reza [1961] 1994:7). Ralph Vinton Lyon Hartley ( November 30, 1888 – May 1, 1970) was an Electronics researcher

The units pre-date Shannon's bit by at least eight years. Claude Elwood Shannon (April 30 1916 – February 24 2001 an American Electronic engineer and Mathematician, is "the father of Information

## Usage as a unit of probability

The deciban is a particularly useful measure of information in odds-ratios or weights of evidence. The odds ratio is a measure of Effect size particularly important in Bayesian statistics and Logistic regression. In Statistics, the use of Bayes factors is a Bayesian alternative to classical Hypothesis testing. 10 decibans corresponds to an odds ratio of 10:1; 20 decibans to 100:1 odds, etc. According to I. J. Good, a change in a weight of evidence of 1 deciban (i. Irving John (Jack Good (born 9 December 1916) is a British Statistician who worked also as a Cryptographer at Bletchley Park 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.

## References

• Hartley, R. V. L. , "Transmission of Information," Bell System Technical Journal, July 1928
• Reza, Fazlollah M. An Introduction to Information Theory. New York: Dover, 1994. ISBN 0-486-68210-2
• David J. C. MacKay. Information Theory, Inference, and Learning Algorithms Cambridge: Cambridge University Press, 2003. ISBN 0-521-64298-1. This on-line textbook includes a chapter on the units of information content, and the game of Banburismus that the codebreakers played when cracking each day's Enigma codes. Banburismus was a process invented by Alan Turing at Bletchley Park in England during the Second World War.

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