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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 33z (39d) | Vol. 19z (21d) No. 1 | Year 117Az (1966d) ▶️



Click to view PDF

Editor: Jamison “Jux” Handy, Jr.

Contents:

  • Decimal Currency and Inflation (page 1z)
  • Decimal Coinage — A Lost Cause? | B. A. M. Moon and K. P. C. Mears (page 3z)
    • Forword (page 4z)
    • Men or Machines? (page 5z)
    • Coinage, Currency, Weights & Measures (page 6z)
      • £200,000,000 Investment or £1,000,000,000 Loss? (page 6z)
      • Compulsion or Choice? (page 7z)
      • Competition or Co-Operation (page 9z)
      • Cost Considerations (page 10z)
      • Dozens, Dozens Arithmetic, Duodecimals and Duodecimal Systems (page 16z)
      • Evolutionary Processes (page 17z)
        • Evolution of currency (page 17z)
        • Evolution of arithmetic teaching (page 18z)
        • Development of use of dozens arithmetic (page 19z)
      • Education (page 1Az)
      • Economic Consequences of Changes in Currency and Systems of Measurement (page 20z)
  • A Base Conversion Algorithm | B. A. M. Moon (page 23z)
    • Conversion from base Ten to base Twelve (page 23z)
    • Conversion from base Twelve to base Ten (page 24z)
    • Conversion from base Eight to base Twelve (page 25z)
    • Conclusion (page 25z)
  • Counting in Dozens (page 26z)
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.