How to Do Duodecimal, Dozenal, Base 12 Number System Conversions  Includes Examples
If you understand the everyday decimal (base 10) number system, then you already understand the duodecimal, base 12, dozenal counting and numbering system. You just don’t know you know yet. The complete lesson immediately follows the short introduction.
And at the end of the page is a video, What Is the Sound of Pi in Base 12. Kind of induces a strange feeling after awhile...
How to Learn the Duodecimal, Dozenal, Base 12 Numbering System
And a "political" note.
The base 12 numerical system, also known as the duodecimal or dozenal system, is just like all the other base numbering and counting systems. However, this is the only base numbering system which has a "political" aspect to it. This has to do with the number 12 being a very useful number and as to which symbols to use for the base 10 numbers "10" and "11".
If one wishes to remain within the standardized structure of hexadecimal and all the other base X numbering / counting systems up to and including base 36, then the use of sequential numbers and letters should be used. Thus, as in hexadecimal, base 10 "10" is equal to base 12 "A", and base 10 "11" is equal to base 12 "B".
Others advocate the use of different symbols, some examples being:
 10 = T
 10 = X
 11 = E
This howto tutorial will stick with the base 2 through base 36 mathematical "standard" of 10 being designated by "A" and 11 being designated by "B".
Complete Lesson and Examples
Duodecimal Base 12 Numbering System
Duodecimal Orders of Magnitude
1 · 12 · 144 · 1728 · 20736 · 248832
Positional
248832 · 20736 · 1728 · 144 · 12 · 1
We use the base 10 numbering / counting system in our daytoday living. Base 10 has ten numbers (09) and orders of magnitude that are times ten. The lowestorder number represents itself times one. The nextorder number represents itself times 10. The next order number represents itself times 10 x 10, or itself times 100. The next order of magnitude would be 10 x 10 x 10, or 1000. And so on.
An example would be the number 7824. This number means there are:
Four 1’s,
two 10’s,
eight 100’s,
and seven 1000's.
Which represents 4 + 20 + 800 + 7000; for a total of 7824.
The duodecimal (base12 ) or dozenal numbering system...
...uses the same structure, the only difference being the orders of magnitude. Base 12 aka duodecimal has twelve numbers (0 through B).
The numbers are 0 = 0, 1 = 1, 2 = 2, 3 = 3, 4 = 4, 5 = 5, 6 = 6, 7 = 7, 8 = 8, 9 = 9, A = 10, B = 11.
The orders of magnitude are times twelve. The lowestorder number represents itself times one. The nextorder number represents itself times 12. The next order number represents itself times 12 x 12, or itself times 144. The next order number represents itself times 12 x 12x 12, or itself times 1728 And so on.
An example would be the number 2B9A. This number means there are:
ten 1’s,
nine 12’s,
eleven 144’s,
and two 1728’s.
Which represents 10+108+1584+3456; for a total of 5158.
Another example would be the number A51B. This number means there are:
eleven 1’s,
one 12,
five 144’s,
and ten 1728’s.
Which represents 11+12+720+17280; for a total of 18023.
More Duodecimal, Dozenal, Base 12 to Base 10 Conversion Examples
Column headings in the following table are simply a convenience relist of the relevant positional orders of magnitude as applies to each column.
12 · 1
 144 · 12 · 1
 1728 · 144 · 12 · 1


0=0
 92=110
 B00=1584

1=1
 100=144
 BBB=1727

5=5
 101=145
 1000=1728

9=9
 110=156
 1001=1729

A=10
 200=288
 1010=1740

B=11
 202=290
 1100=1872

10=12
 20A=298
 1111=1885

11=13
 20B=299
 2000=3456

18=20
 210=300
 42BB=7343

20=24
 7B6=1146
 AB2B=18899

5A=70
 A00=1440
 B460=19656

5B=71
 A2B=1475
 BBBB=20735

Many people advocate the teaching of base 12 as a societal standard.
Do you think this is a good idea?
See results without votingThe Dozenal Society of America has all sorts of information regarding the mathematical and societal aspects of the base twelve number / counting system.
What Is the Sound of Pi in Duodecimal
And last, but not least. Here is a video, The Sound of Pi in Base 12.
More by this Author
 9
No website hoops. On the front page. Math rules for algebra. Algebra and equations for beginners. Complete lessons.
 1
Ternary aka Trinary aka Base 3 numerical system lesson and examples.
 15
Here is a compilation of all known methods to get rid of gophers. If you know of one that is not here, please add it.
Comments 2 comments
I'm a bit weird about the number 12. As a kid I used pounds, shillings and pence for money with 12 pennies in the shilling and twenty shillings in the pound (decimalized when I was 12, lol).
This might be why I often think about the oddities of 12's. Money and time are rather important.
I was brought up in the UK pre decimal money, same as will apse but its still difficult for me to get my head round the idea of base 12. Useful hub.