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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 58z (68d) | Vol. 30z (36d) No. 3 | Year 1197z (1987d) ▶️



Click to view PDF

Editor: Dr. Patricia Zirkel

Cover Title: Two Subroutines

Contents:

  • Schedule, 1987 Annual Meeting
  • Constitution Change Passes
  • An Accuracy Scale | Fred Newhall
  • Dozenal Nude Numbers | Jean Kelly
    • Definition: nude = every digit is a factor
    • The Degree of a Nude Number
    • Large Nude Number
    • Consecutive Nude Numbers
  • Two FORTRAN Subroutines for Base Conversion | Nassau Communitiy College students
    • A Subroutine to Convert from Base Twelve to Base Ten | Brian Doherty
    • A Subroutine to Convert from Base Ten to Base Twelve | Regina DeBonis
  • Dozenal Jottings
    • Paul Rapoport
      • letter from Don Hammond, DSGB | dozenal clock
      • disagrees with Igor Valevsky about 2 dozen hours, prefers 1 dozen to be pure dozenal metric
    • Nelson Gray
    • Dean Koonts | Strangers | novel with a dozenal reference near the end
    • Gene and Pat Zirkel | visited Dudley and Kay George in Seattle
    • Father Joachim Watrin, D.S.B. passed away
  • Dek and El
  • Cinderella Dek-El-Do | a poem | Henry Churchman
  • 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.