ban (unit)

The ban is a dimensionless unit of measurement for the amount of data that is no longer in use today . It is also called hartley (abbreviation: Hart ) or as a dit ( word intersection of d ecimal and dig it ; literally German: decimal), respectively. A quantity of information of n ban requires n decimal digits to be represented or transmitted.

origin

The ban was established during the Second World War in 1940 by the English mathematician and cryptologist Alan Turing together with his colleague Irving John Good during their cryptanalytic work on German encryption methods , such as the rotor key machine Enigma , in particular for the cryptanalysis of the Enigma used by the German Navy -M4 , conceived in Bletchley Park , England . The name of the information unit was inspired by the English city of Banbury , which is near Bletchley , and in which for the code breakers (English: codebreakers ) important tools, the so-called Banbury sheets (German: "Banbury sheets") were produced.

The alternative name hartley this unit is based on the name of the founder of information theory , the US electrical engineer Ralph Hartley .

definition

The ban as a dimensionless information unit is defined as the decadic logarithm (lg = logarithm to base ten) of the ratio of two data sets and : ${\ displaystyle P}$ ${\ displaystyle P_ {0}}$

{\ displaystyle L = \ lg {\ frac {P} {P_ {0}}} \, \ mathrm {ban}}

The data volume is usually set to 1 (reference data volume) and for practical reasons - similar to the related unit Bel - one tenth of it is used instead of the unit itself. Using the unit prefix deci (one tenth), ban so becomes deciban with the abbreviation db (not to be confused with the abbreviation dB for decibels ). The definition equation thus simplifies to: ${\ displaystyle P_ {0}}$

${\ displaystyle L = 10 \ lg P \, \ mathrm {db}}$

For example, an amount of data from a thousand to

{\ displaystyle L = 10 \ lg (1000) \, \, \ mathrm {db} = 30 \, \ mathrm {db}}

can be specified as 30 db.

Conversion in bit

The ban as a unit of information is historically older than the bit more commonly used today (word crossing from bi nary dig it ; German literally: binary digit ), which is formed using the logarithm of two ld (logarithm to base 2; abbreviation comes from Latin: l ogarithmus d ualis ):

{\ displaystyle L = \ mathop {\ mathrm {ld}} \, P \, \ mathrm {bit}}

The conversion between bit and deciban (e.g. for P = 2) results from the identity as follows: ${\ displaystyle L = \ mathop {\ mathrm {ld}} \, P \, \ mathrm {bit} = 10 \ lg P \, \ mathrm {db}}$

{\ displaystyle 1 \, \ mathrm {bit} = 10 \ lg (2) \, \ mathrm {db} \ approx \ 3 {,} 010 \, \ mathrm {db}}

The amount of data considered above as an example of thousands therefore corresponds to

{\ displaystyle L \ approx {\ frac {30 \, \ mathrm {db}} {3 {,} 010 \, {\ mbox {db}}}} \, \ mathrm {bit} \ approx 9 {,} 966 \, \ mathrm {bit},}

so almost 10 bit. 10 bits correspond exactly to 1024.

meaning

From today's perspective, the ban unit is primarily of historical importance. The two British Turing and Good used it years before the American Claude Shannon introduced the bit based on the binary system. Because of the paramount importance of the dual place value system in our time due to the binary representation of numbers in computer technology, the bit is used almost exclusively today, and the unit ban has been more and more forgotten. But it deserves the credit of being the historically older unit of data volume.

literature

Francis Harry Hinsley , Alan Stripp: Codebreakers - The inside story of Bletchley Park . Oxford University Press, Reading (Berkshire) 1993, ISBN 0-19-280132-5 .
David JC MacKay: Information Theory, Inference, and Learning Algorithms . Cambridge University Press, 2003, p. 265, cam.ac.uk (PDF; 11.7 MB)
Gordon Welchman : The Hut Six Story - Breaking the Enigma Codes . Allen Lane, London 1982; Cleobury Mortimer M&M, Baldwin Shropshire 2000, ISBN 0-947712-34-8 .