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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 8Bz (107d) | Vol. 45z (53d) No. 2 | Year 11B0z (2004d) ▶️



Click to view PDF

Editor: Prof. Jay Schiffman

Contents:

  • President’s Message | Jay Schiffman
  • Reprint: The Reverse Notation | J. Halcro Johnson
  • Calculator a Boon to Proofreading! | Michael Punter (England)
  • Problem Corner
  • π Mnemonic | Dylan Martinez
  • Annual Award: Rob Roy McPherson
  • News from our British Friends
    • BWMA press release: U.S. Dept. of Commerce to abolish pounds, ounces, pints for packaged foods/goods
    • BWMA press statement: Bad News: NIST to end inch-pound units
    • Britain’s Disastrous Experience of Metric
    • RIP Metric Martyr Steven Thoburn
    • More Bad News: standards officers launch raids against market traders in Lewisham
    • Some Good News: Press Release of Conservative Party. Conservative Stance
    • Notes to Editors about the Metrication Directive
  • Do You Have a Better Idea?
    • Dozenal words corresponding to: decade, century, millennium?
  • 5 Dozenth Annual Meeting
  • Solutions to Problem Corner
  • Mail Bag
    • Michael Thomas De Vlieger, AIA | first twenty Argam numerals
    • Bryan Perry | dozenal number system with -twe, -do, gross, grand, milliad
    • Jeff Wells | dozenal clock with 0 midnight at bottom
    • Eitan Adam Pechenick | 2Doh! Game; dozenal number words system
    • Jim Hartley
    • Rakesh Khanna, India
  • One Small Success: Main DOT converts back from metric to USC
  • Why Change?
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.