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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 A1z (121d) | Vol. 51z (61d) No. 1 | Year 11B9z (2013d) ▶️



Click to view PDF

Editor: Michael DeVlieger

Cover Title: The Nomenclature Issue: Systematic Dozenal Nomenclature

Contents:

  • President’s Message | Don Goodman III
  • Welcome, Newscast!
  • The Nomenclature Issue
  • Dozenal in Plain English | Michale DeVlieger
  • Closing Time
  • Expanded DSA Website | Don Goodman III
  • Feature: Systematic Dozenal Nomenclature | John Volan
    • Introduction
    • Digit Roots
    • Digit Strings and Element Names
    • SDN Prefixes
      • Multiplier Prefixes
      • Power Prefixes
      • Combining Multiplier and Power Prefixes
    • Adding a Dash of “Dit” ...
    • .. and a Pinch of “Per”
    • Conclusions
  • Editorial: The 12/12/12 Effect
  • Minutes of the 11B8z (2012d) Annual and Board Meetings
  • Minutes of the 11B9z (2013d) Annual and Board Meetings
    • Ralph Beard Memorial Award, 11B9z (2013d): Jen Seron
    • Speech: Dozenal Integer Sequences | Jay Schiffman
    • Speech: Systematic Dozenal Nomenclature | Don Goodman III
    • Workshop: American Society of Engineering Educators
  • The Practical Dozenalist
  • Problem Corner | Prof. Gene Zirkel
  • The Lamadrid Base Name System | Michael DeVlieger
  • Mathematics and Computer Education (Advertisement)
  • Mailbag
    • Gage Middaugh
    • Michael Keller
    • Paul Rapoport
    • Robert Maxfield
  • Preview of Next Issue
  • Join the DSA Today!
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.