Seal of the DSA
Join Us!
Dozenal Society of America
Promoting base twelve and alternative base mathematics
Support the DSA
Donate
Follow Us
Icon for DSA's X Icon for DSA's Facebook Icon for DSA's RSS
Share This Page
Icon for sharing via X Icon for sharing via Facebook Icon for sharing via email
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 51z (61d) | Vol. 2Az (34d) No. 2 | Year 1195z (1985d) ▶️



Click to view PDF

Editor: Dr. Patricia Zirkel

Cover Title: When Does Oct 31 = Dec 25?

Contents:

  • In Memoriam: J. Halcro Johnston
  • Strange Bases (Part I) | Gene Zirkel
    • Introduction
    • Negative Integer Bases
      • Addition
      • Subtraction
      • Multiplication
      • Division
      • Changing Bases
  • Relative Sizes of Decimal and Duodecimal Numbers | Mark Calandra
  • Book Review
    • The Ascent of Mathematics | Raymond Coughlin and David E. Zitarelli
  • Why Europeans Lag in Production | Charles F. Harschner
  • An Unfullfilled Prophecy | Newsday, Long Islands
  • Duodecimal Test (I)
  • Some History | American Metric Journal
  • Dozenal Jottings
    • Naval Weapons Center, China Lake CA
    • New Life Members
      • Albert De Valve
      • Eugene “Skip” Scifres
      • Bill Leonhardt | prefers Pitman symbols
    • Hayden Steele
    • A. Adler Hirsch
    • Pat Zirkel | SUNY Stony Brook publishing workshop
    • Fred Newhall | Annual Student Symposium, Nassau Counting Association of Mathematics Supervisors
    • Don Hammond | editor DSGB Journal
    • Arthur Whillock | ternary arithmetic
    • Tony and Annet Catania | birth of son Michael
    • Bob Foley
    • Kennett Love
    • Mrs. F. Emerson Andrews
    • Vivian Linton
    • B. Klausen
    • David Singmaster
    • Cedric Smith | Colson News (Two-Way Numbers)
    • A. Adler Hirsch | Gregorian leap rules were almost every 132 years
    • Charles and Miriam Bagley
    • Paul Rapoport | dozenal analog watch interest
    • Dr. Anton Glaser
    • Isaac Asimov | accepted honorary membership
    • Gerard Robert Brest
    • Thomas M. O’Neill
  • Symbols | reply to Dudley George | Dr. Paul Rapoport
  • On the Cover | Prof. Rochelle Meyer, Nassau Community College
  • 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.