Bi-quinary coded decimal

<h2 id="examples">Examples</h2>
<p>Several different representations of bi-quinary coded decimal have been used by different machines. The two-state component is encoded as one or two <a href="/facts/Bit/S972NSaD">bits</a>, and the five-state component is encoded using three to five bits. Some examples are:
</p>
<ul><li>Roman and Chinese <a href="/facts/Abacus/ThMQBsel">abacuses</a></li>
<li><a href="/facts/George_Stibitz/M6pUBsqx">Stibitz</a><a class="footnote-ref" id="fnref:2" href="#fn:2"><sup>2</sup></a> relay calculators at Bell Labs from <a href="/facts/Bell_Labs/fKP5Gk0H">Model II</a> onwards</li>
<li><a href="/facts/FACOM_128/kvY6z3dq">FACOM 128</a> relay calculators at <a href="/facts/Fujitsu/6e5gvNSa">Fujitsu</a></li></ul>
<h3>IBM 650</h3>
<p>
The <a href="/facts/IBM_650/l5mCAMIF">IBM 650</a> uses seven bits: two <i>bi</i> bits (0 and 5) and five <i>quinary</i> bits (0, 1, 2, 3, 4), with error checking.
</p><p>Exactly one <i>bi</i> bit and one <i>quinary</i> bit is set in a valid digit. The bi-quinary encoding of the internal workings of the machine are evident in the arrangement of its lights – the <i>bi</i> bits form the top of a T for each digit, and the <i>quinary</i> bits form the vertical stem.
</p>
<table><tbody><tr><th>Value</th><th>05-01234 bits<a class="footnote-ref" id="fnref:3" href="#fn:3"><sup>3</sup></a></th><td rowspan="11"></td></tr><tr><td>0</td><td>10-10000</td></tr><tr><td>1</td><td>10-01000</td></tr><tr><td>2</td><td>10-00100</td></tr><tr><td>3</td><td>10-00010</td></tr><tr><td>4</td><td>10-00001</td></tr><tr><td>5</td><td>01-10000</td></tr><tr><td>6</td><td>01-01000</td></tr><tr><td>7</td><td>01-00100</td></tr><tr><td>8</td><td>01-00010</td></tr><tr><td>9</td><td>01-00001</td></tr></tbody></table>
<h3>Remington Rand 409</h3>
<p>The <a href="/facts/Remington_Rand_409/6wGbpKoU">Remington Rand 409</a> has five bits: one <i>quinary</i> bit (tube) for each of 1, 3, 5, and 7 - only one of these would be on at the time. The fifth <i>bi</i> bit represented 9 if none of the others were on; otherwise it added 1 to the value represented by the other <i>quinary</i> bit. The machine was sold in the two models <a href="/facts/UNIVAC_60/6wGbpKoU">UNIVAC 60</a> and <a href="/facts/UNIVAC_120/6wGbpKoU">UNIVAC 120</a>.
</p>
<table><tbody><tr><th>Value</th><th>1357-9 bits</th></tr><tr><td>0</td><td>0000-0</td></tr><tr><td>1</td><td>1000-0</td></tr><tr><td>2</td><td>1000-1</td></tr><tr><td>3</td><td>0100-0</td></tr><tr><td>4</td><td>0100-1</td></tr><tr><td>5</td><td>0010-0</td></tr><tr><td>6</td><td>0010-1</td></tr><tr><td>7</td><td>0001-0</td></tr><tr><td>8</td><td>0001-1</td></tr><tr><td>9</td><td>0000-1</td></tr></tbody></table>
<h3>UNIVAC Solid State</h3>
<p>The <a href="/facts/UNIVAC_Solid_State/X7Sse7Tp">UNIVAC Solid State</a> uses four bits: one <i>bi</i> bit (5), three binary coded <i>quinary</i> bits (4 2 1)<a class="footnote-ref" id="fnref:4" href="#fn:4"><sup>4</sup></a><a class="footnote-ref" id="fnref:5" href="#fn:5"><sup>5</sup></a><a class="footnote-ref" id="fnref:6" href="#fn:6"><sup>6</sup></a><a class="footnote-ref" id="fnref:7" href="#fn:7"><sup>7</sup></a><a class="footnote-ref" id="fnref:8" href="#fn:8"><sup>8</sup></a><a class="footnote-ref" id="fnref:9" href="#fn:9"><sup>9</sup></a> and one <a href="/facts/Parity_bit/peFp3Wau">parity check bit</a>
</p>
<table><tbody><tr><th>Value</th><th>p-5-421 bits</th></tr><tr><td>0</td><td>1-0-000</td></tr><tr><td>1</td><td>0-0-001</td></tr><tr><td>2</td><td>0-0-010</td></tr><tr><td>3</td><td>1-0-011</td></tr><tr><td>4</td><td>0-0-100</td></tr><tr><td>5</td><td>0-1-000</td></tr><tr><td>6</td><td>1-1-001</td></tr><tr><td>7</td><td>1-1-010</td></tr><tr><td>8</td><td>0-1-011</td></tr><tr><td>9</td><td>1-1-100</td></tr></tbody></table>
<h3>UNIVAC LARC</h3>
<p>The <a href="/facts/UNIVAC_LARC/qdqLSEgt">UNIVAC LARC</a> has four bits:<a class="footnote-ref" id="fnref:10" href="#fn:10"><sup>10</sup></a> one <i>bi</i> bit (5), three <a href="/facts/Johnson_counter/TWedHbrQ">Johnson counter</a>-coded <i>quinary</i> bits and one parity check bit.
</p>
<table><tbody><tr><th>Value</th><th>p-5-qqq bits</th></tr><tr><td>0</td><td>1-0-000</td></tr><tr><td>1</td><td>0-0-001</td></tr><tr><td>2</td><td>1-0-011</td></tr><tr><td>3</td><td>0-0-111</td></tr><tr><td>4</td><td>1-0-110</td></tr><tr><td>5</td><td>0-1-000</td></tr><tr><td>6</td><td>1-1-001</td></tr><tr><td>7</td><td>0-1-011</td></tr><tr><td>8</td><td>1-1-111</td></tr><tr><td>9</td><td>0-1-110</td></tr></tbody></table>
<h2 id="see-also">See also</h2>
<ul><li><a href="/facts/Binary-coded_decimal/dWTaE7ES">Binary-coded decimal</a></li>
<li><a href="/facts/Binary_number/a6JDSRPs">Binary number</a></li>
<li><a href="/facts/Chisanbop/N02RFI7o">Chisanbop</a></li>
<li><a href="/facts/Finger_binary/zdMDr5Tw">Finger binary</a></li>
<li><a href="/facts/Quinary/m1hTPFA0">Quinary</a></li>
<li><a href="/facts/Two-out-of-five_code/5QmldTRV">Two-out-of-five code</a></li>
<li><a href="/facts/FACOM_128/kvY6z3dq">FACOM 128</a></li></ul>

<h2 id="further-reading">Further reading</h2>
<ul><li><a href="http://everyspec.com/MIL-HDBK/MIL-HDBK-0200-0299/download.php?spec=MIL_HDBK_231A.1809.pdf"><i>Military Handbook: Encoders - Shaft Angle To Digital</i></a> (PDF). <a href="/facts/United_States_Department_of_Defense/dWAvf7e3">United States Department of Defense</a>. 1991-09-30. MIL-HDBK-231A. <a href="https://web.archive.org/web/20200725051128/http://everyspec.com/MIL-HDBK/MIL-HDBK-0200-0299/download.php?spec=MIL_HDBK_231A.1809.pdf">Archived</a> (PDF) from the original on 2020-07-25. Retrieved 2020-07-25. (NB. Supersedes MIL-HDBK-231(AS) (1970-07-01).)</li></ul>

<h2 id="references">References</h2>

<ol>
<li id="fn:1"><p>"Why Use Binary? - Computerphile". YouTube. 2015-12-04. Archived from the original on 2021-12-12. Retrieved 2020-12-10. <a href="https://www.youtube.com/watch?v=thrx3SBEpL8&list=WL&index=17&t=0s" target="_blank">https://www.youtube.com/watch?v=thrx3SBEpL8&list=WL&index=17&t=0s</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li>
<li id="fn:2"><p>Stibitz, George Robert; Larrivee, Jules A. (1957).  Written at Underhill, Vermont, US. Mathematics and Computers (1 ed.). New York, US / Toronto, Canada / London, UK: McGraw-Hill Book Company, Inc. p. 105. LCCN 56-10331. (10+228 pages) <a href="/wiki/George_Robert_Stibitz" target="_blank">/wiki/George_Robert_Stibitz</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></p></li>
<li id="fn:3"><p>Ledley, Robert Steven; Rotolo, Louis S.; Wilson, James Bruce (1960). "Part 4. Logical Design of Digital-Computer Circuitry; Chapter 15. Serial Arithmetic Operations; Chapter 15-7. Additional Topics". Digital Computer and Control Engineering (PDF). McGraw-Hill Electrical and Electronic Engineering Series (1 ed.). New York, US: McGraw-Hill Book Company, Inc. (printer: The Maple Press Company, York, Pennsylvania, US). pp. 517–518. ISBN 0-07036981-X. ISSN 2574-7916. LCCN 59015055. OCLC 1033638267. OL 5776493M. SBN 07036981-X. ISBN 978-0-07036981-8. ark:/13960/t72v3b312. Archived (PDF) from the original on 2021-02-19. Retrieved 2021-02-19. p. 518: […] The use of the biquinary code in this respect is typical. The binary part (i.e., the most significant bit) and the quinary part (the other 4  bits) are first added separately; then the quinary carry is added to the binary part. If a binary carry is generated, this is propagated to the quinary part of the next decimal digit to the left. […] {{cite book}}: ISBN / Date incompatibility (help) [1] (xxiv+835+1 pages) <a href="0-07036981-X07036981-X" target="_blank">0-07036981-X07036981-X</a> <a href="#fnref:3" class="footnote-back-ref">↩</a></p></li>
<li id="fn:4"><p>Berger, Erich R. (1962). "1.3.3. Die Codierung von Zahlen".  Written at Karlsruhe, Germany. In Steinbuch, Karl W. (ed.). Taschenbuch der Nachrichtenverarbeitung (in German) (1 ed.). Berlin / Göttingen / New York: Springer-Verlag OHG. pp. 68–75. LCCN 62-14511. <a href="/wiki/Karl_W._Steinbuch" target="_blank">/wiki/Karl_W._Steinbuch</a> <a href="#fnref:4" class="footnote-back-ref">↩</a></p></li>
<li id="fn:5"><p>Berger, Erich R.; Händler, Wolfgang (1967) [1962]. Steinbuch, Karl W.; Wagner, Siegfried W. (eds.). Taschenbuch der Nachrichtenverarbeitung (in German) (2 ed.). Berlin, Germany: Springer-Verlag OHG. LCCN 67-21079. Title No. 1036. <a href="/wiki/Wolfgang_H%C3%A4ndler" target="_blank">/wiki/Wolfgang_H%C3%A4ndler</a> <a href="#fnref:5" class="footnote-back-ref">↩</a></p></li>
<li id="fn:6"><p>Steinbuch, Karl W.; Weber, Wolfgang; Heinemann, Traute, eds. (1974) [1967]. Taschenbuch der Informatik - Band II - Struktur und Programmierung von EDV-Systemen (in German). Vol. 2 (3 ed.). Berlin, Germany: Springer-Verlag. ISBN 3-540-06241-6. LCCN 73-80607. {{cite book}}: |work= ignored (help) <a href="3-540-06241-6" target="_blank">3-540-06241-6</a> <a href="#fnref:6" class="footnote-back-ref">↩</a></p></li>
<li id="fn:7"><p>Dokter, Folkert; Steinhauer, Jürgen (1973-06-18). Digital Electronics. Philips Technical Library (PTL) / Macmillan Education (Reprint of 1st English ed.). Eindhoven, Netherlands: The Macmillan Press Ltd. / N. V. Philips' Gloeilampenfabrieken. doi:10.1007/978-1-349-01417-0. ISBN 978-1-349-01419-4. SBN 333-13360-9. Retrieved 2020-05-11.[permanent dead link] (270 pages) (NB. This is based on a translation of volume I of the two-volume German edition.) <a href="978-1-349-01419-4333-13360-9" target="_blank">978-1-349-01419-4333-13360-9</a> <a href="#fnref:7" class="footnote-back-ref">↩</a></p></li>
<li id="fn:8"><p>Dokter, Folkert; Steinhauer, Jürgen (1975) [1969]. Digitale Elektronik in der Meßtechnik und Datenverarbeitung: Theoretische Grundlagen und Schaltungstechnik. Philips Fachbücher (in German). Vol. I (improved and extended 5th ed.). Hamburg, Germany: Deutsche Philips GmbH. p. 50. ISBN 3-87145-272-6. (xii+327+3 pages) (NB. The German edition of volume I was published in 1969, 1971, two editions in 1972, and 1975. Volume II was published in 1970, 1972, 1973, and 1975.) <a href="3-87145-272-6" target="_blank">3-87145-272-6</a> <a href="#fnref:8" class="footnote-back-ref">↩</a></p></li>
<li id="fn:9"><p>Savard, John J. G. (2018) [2006]. "Decimal Representations". quadibloc. Archived from the original on 2018-07-16. Retrieved 2018-07-16. <a href="http://www.quadibloc.com/comp/cp0203.htm" target="_blank">http://www.quadibloc.com/comp/cp0203.htm</a> <a href="#fnref:9" class="footnote-back-ref">↩</a></p></li>
<li id="fn:10"><p>Savard, John J. G. (2018) [2006]. "Decimal Representations". quadibloc. Archived from the original on 2018-07-16. Retrieved 2018-07-16. <a href="http://www.quadibloc.com/comp/cp0203.htm" target="_blank">http://www.quadibloc.com/comp/cp0203.htm</a> <a href="#fnref:10" class="footnote-back-ref">↩</a></p></li>
</ol>

Bi-quinary coded decimal open-in-new

Bi-quinary coded decimal