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Dozenal Society of America
Promoting base twelve and alternative base mathematics
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The Dozenal Society of America
The DSA is a voluntary, nonprofit education corporation, organized for the conduct of research and education of the public in the use of dozenal (also called duodecimal or base-twelve) in calculations, mathematics, weights and measures, and other branches of pure and applied science.

The Duodecimal Bulletin

◀️ Issue: Whole Number 57z (67d) | Vol. 30z (36d) No. 2 | Year 1197z (1987d) ▶️



Click to view PDF

Editor: Dr. Patricia Zirkel

Cover Title: Doman Numerals

Contents:

  • Doman Numerals | Gerard Robert Brost
  • Same Numeral/Different Number | Gene Zirkel
  • Book Reviews | Jean Kelly
    • Elementary Numerical Analysis | W. Allen Smith | Prentice-Hall, 1986
    • Realities of Metrication, A Report | The International Brotherhood of Electrical Workers
    • A Metric America, A Decision Whose Time Has Come | The National Bureau of Standards
  • Duodecimal Constants | Igor C. Valevski
  • Constitution Change | Ballot
  • Funny Coincidence | Bjarke Nielsen
  • Prime Endings
  • Duodecimal Test (part III)
  • Dozenal Jottings
    • Gene Zirkel | won competition by Abacus computer publication to devise a Turing Test
    • Dezhon | denounces Bell-Tone digits, prefers Pitmans
    • Arthur Whillock, DSGB | notified that Tom Pendlebury passed away
    • Theodore Baumeister passed away
    • Lorraine Katz
    • Skip Scifres, Henry Churchman, Thomas M. O’Neill
    • Paul Adams
      • Rae Charles Eltsa
      • Jay Schiffman
      • Joseph U. Alohan
      • Matthew J. Weitendorf
      • H. K. Baumeister
      • Robert P. White
      • Arthur L. Woerner
    • New members
  • Twelves | Answers
  • Why Change?
  • Counting in Dozens
Copyright © 11B9–120Az (2013–2026d). The Dozenal Society of America. Contact Us.
Creative Commons License
This site and the documents on it are licensed under a Creative Commons Attribution 4.0 International License.

This site expresses numbers in alternative bases, particularly dozenal (also called duodecimal, or base twelve).
The DSA does not endorse any particular notation or pronunciation scheme for alternative bases.
However this site defaults to the following to ensure online readability across all platforms:
“Computerese” uppercase letters represent transdecimal digits: A = ten, B = eleven, C = twelve, etc.
Single-character subscripts annotate bases: d = decimal, z = dozenal, x = hexadecimal, etc., e.g., 2014d = 11BAz = 7DEx.

(0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 ...)d
(0 1 2 3 4 5 6 7 8 9  A  B 10 11 12 13 14 15 16 17 18 19 1A 1B 20 21 22 23 24 25 26 27 28 29 2A 2B 30 ...)z
(0 1 2 3 4 5 6 7 8 9  A  B  C  D  E  F 10 11 12 13 14 15 16 17 18 19 1A 1B 1C 1D 1E 1F 20 21 22 23 24 ...)x

PDF documents on this site reflect changing practices among dozenalists over the years:
Various symbols have been used to represent digits ten and eleven:
Dwiggins 𝒳 and Ɛ (often rendered X and E); Bell Telephone * and #; Pitman turned 2 and 3 (↊ and ↋); etc.
Italics were once used to distinguish dozenal numbers from decimal: e.g. 0.5 = 0.6.
Later, semicolon became a separate‑identity “dozenal point”, versus period as “decimal point”: e.g., 0.5 = 0;6.
However, subscript base annotations provide a more versatile solution that is least‑change: e.g., 0.5d = 0.6z = 0.8x

Dozenal offers superior divisibility over decimal, which can make everyday arithmetic easier to learn:
⅙ = 0.2z | ¼ = 0.3z | ⅓ = 0.4z | ½ = 0.6z | ⅔ = 0.8z | ¾ = 0.9z | ⅚ = 0.Az
⅙ = 0.1666…d | ¼ = 0.25d | ⅓ = 0.333…d | ½ = 0.5d | ⅔ = 0.666…d | ¾ = 0.75d | ⅚ = 0.8333…d

EACH ONE, TEACH ONE.