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<title>Aiken code</title>

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Aiken code

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</style><table class="infobox"><tbody><tr><th colspan="2" class="infobox-above">Aiken code</th></tr><tr><th scope="row" class="infobox-label">Digits</th><td class="infobox-data">4<a href="#cite_note-Steinbuch_1962-1">[1]</a><a href="#cite_note-Steinbuch-Weber_1974-2">[2]</a></td></tr><tr><th scope="row" class="infobox-label">Tracks</th><td class="infobox-data">4<a href="#cite_note-Steinbuch_1962-1">[1]</a><a href="#cite_note-Steinbuch-Weber_1974-2">[2]</a></td></tr><tr><th scope="row" class="infobox-label"><a href="Digit_value" class="mw-redirect" title="Digit value">Digit values</a></th><td class="infobox-data">2 4 2 1<a href="#cite_note-Steinbuch_1962-1">[1]</a><a href="#cite_note-Steinbuch-Weber_1974-2">[2]</a></td></tr><tr><th scope="row" class="infobox-label"><a href="Hamming_weight" title="Hamming weight">Weight(s)</a></th><td class="infobox-data">0..4<a href="#cite_note-Steinbuch_1962-1">[1]</a><a href="#cite_note-Steinbuch-Weber_1974-2">[2]</a></td></tr><tr><th scope="row" class="infobox-label">Continuity</th><td class="infobox-data">no</td></tr><tr><th scope="row" class="infobox-label"><a href="Cyclic_code" title="Cyclic code">Cyclic</a></th><td class="infobox-data">no<a href="#cite_note-Steinbuch_1962-1">[1]</a><a href="#cite_note-Steinbuch-Weber_1974-2">[2]</a></td></tr><tr><th scope="row" class="infobox-label"><a href="Hamming_distance" title="Hamming distance">Minimum distance</a></th><td class="infobox-data">1<a href="#cite_note-Steinbuch_1962-1">[1]</a><a href="#cite_note-Steinbuch-Weber_1974-2">[2]</a></td></tr><tr><th scope="row" class="infobox-label">Maximum distance</th><td class="infobox-data">4<a href="#cite_note-Steinbuch_1962-1">[1]</a><a href="#cite_note-Steinbuch-Weber_1974-2">[2]</a></td></tr><tr><th scope="row" class="infobox-label"><a href="Redundancy_(information_theory)" title="Redundancy (information theory)">Redundancy</a></th><td class="infobox-data">0.7</td></tr><tr><th scope="row" class="infobox-label"><a href="Lexicographical_order" class="mw-redirect" title="Lexicographical order">Lexicography</a></th><td class="infobox-data">yes<a href="#cite_note-Steinbuch_1962-1">[1]</a><a href="#cite_note-Steinbuch-Weber_1974-2">[2]</a></td></tr><tr><th scope="row" class="infobox-label"><a href="Method_of_complements" title="Method of complements">Complement</a></th><td class="infobox-data">9<a href="#cite_note-Steinbuch_1962-1">[1]</a><a href="#cite_note-Steinbuch-Weber_1974-2">[2]</a></td></tr><tr><td colspan="2" class="infobox-navbar"><style data-mw-deduplicate="TemplateStyles:r1129693374">

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The Aiken code (also known as 2421 code)<a href="#cite_note-Steinbuch_1962-1">[1]</a><a href="#cite_note-Steinbuch-Weber_1974-2">[2]</a> is a complementary <a href="Binary-coded_decimal" title="Binary-coded decimal">binary-coded decimal</a> (BCD) code. A group of four bits is assigned to the decimal digits from 0 to 9 according to the following table. The code was developed by <a href="Howard_Hathaway_Aiken" class="mw-redirect" title="Howard Hathaway Aiken">Howard Hathaway Aiken</a> and is still used today in <a href="Digital_clock" title="Digital clock">digital clocks</a>, <a href="Pocket_calculator" class="mw-redirect" title="Pocket calculator">pocket calculators</a> and similar devices.

The Aiken code differs from the standard <a href="8421_BCD" class="mw-redirect" title="8421 BCD">8421</a> BCD code in that the Aiken code does not weight the fourth digit as 8 as with the standard BCD code but with 2.

The following weighting is obtained for the Aiken code: 2-4-2-1.

One might think that double codes are possible for a number, for example 1011 and 0101 could represent 5. However, here one makes sure that the digits 0 to 4 are mirror image complementary to the numbers 5 to 9.

<th colspan="4" bgcolor="#ffc0c0">Aiken code

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<th bgcolor="#e0ffff">Decimal digit

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<th bgcolor="#e0ffff">Aiken 2 4 2 1 code<a href="#cite_note-Steinbuch_1962-1">[1]</a><a href="#cite_note-Steinbuch-Weber_1974-2">[2]</a>

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<td align="center">0

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<td align="center">0 0 0 0

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<td align="center">1

</td>

<td align="center">0 0 0 1

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<td align="center">2

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<td align="center">0 0 1 0

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<td align="center">3

</td>

<td align="center">0 0 1 1

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<td align="center">4

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<td align="center">0 1 0 0

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<td align="center">5

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<td align="center">1 0 1 1

</td></tr>

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<td align="center">6

</td>

<td align="center">1 1 0 0

</td></tr>

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<td align="center">7

</td>

<td align="center">1 1 0 1

</td></tr>

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<td align="center">8

</td>

<td align="center">1 1 1 0

</td></tr>

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<td align="center">9

</td>

<td align="center">1 1 1 1

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<ul><li><a href="Excess-3_code" class="mw-redirect" title="Excess-3 code">Excess-3 code</a></li>

<li><a href="O'Brien_code_type_I" class="mw-redirect" title="O'Brien code type I">O'Brien code type I</a></li></ul>

<div class="mw-heading mw-heading2"><h2 id="References">References</h2></div>

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</style><cite id="CITEREFSteinbuch1962" class="citation book cs1 cs1-prop-foreign-lang-source"><a href="Karl_W._Steinbuch" class="mw-redirect" title="Karl W. Steinbuch">Steinbuch, Karl W.</a>, ed. (1962). Taschenbuch der Nachrichtenverarbeitung [Handbook for Signal Processing] (in German) (1 ed.). Berlin / Göttingen / New York: <a href="Springer-Verlag_OHG" class="mw-redirect" title="Springer-Verlag OHG">Springer-Verlag OHG</a>. pp. 71–74. <a href="LCCN_(identifier)" class="mw-redirect" title="LCCN (identifier)">LCCN</a> <a rel="nofollow" class="external text" href="https://lccn.loc.gov/62-14511">62-14511</a>.</cite>

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<cite id="CITEREFSteinbuchWeberHeinemann1974" class="citation book cs1 cs1-prop-foreign-lang-source"><a href="Karl_W._Steinbuch" class="mw-redirect" title="Karl W. Steinbuch">Steinbuch, Karl W.</a>; Weber, Wolfgang; Heinemann, Traute, eds. (1974) [1967]. Struktur und Programmierung von EDV-Systemen [Handbook for Information Systems - Volume II - Structure and programming of computer systems]. Taschenbuch der Informatik – Band II (in German). Vol. II (3 ed.). Berlin, Germany: <a href="Springer_Verlag" class="mw-redirect" title="Springer Verlag">Springer Verlag</a>. pp. 98–100. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>3-540-06241-6</bdi>. <a href="LCCN_(identifier)" class="mw-redirect" title="LCCN (identifier)">LCCN</a> <a rel="nofollow" class="external text" href="https://lccn.loc.gov/73-80607">73-80607</a>.</cite>

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<div class="mw-heading mw-heading2"><h2 id="Further_reading">Further reading</h2></div>

<ul><li><cite id="CITEREFWhite1953" class="citation journal cs1">White, Garland S. (October 1953). "Coded Decimal Number Systems for Digital Computers". <a href="Proceedings_of_the_Institute_of_Radio_Engineers" class="mw-redirect" title="Proceedings of the Institute of Radio Engineers">Proceedings of the Institute of Radio Engineers</a>. 41 (10). <a href="Institute_of_Radio_Engineers" title="Institute of Radio Engineers">Institute of Radio Engineers</a> (IRE): 1450–1452. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1109%2FJRPROC.1953.274330">10.1109/JRPROC.1953.274330</a>. <a href="EISSN_(identifier)" class="mw-redirect" title="EISSN (identifier)">eISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/2162-6634">2162-6634</a>. <a href="ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0096-8390">0096-8390</a>. <a href="S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:51674710">51674710</a>.</cite> (3 pages)</li></ul></div><div><div class="zim-footer">

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