Base 12

23-Dec-2020


A base twelve counting system seems to be better suited for humans, as opposed to computers, than the base ten we currently use. Base twelve is a good balance between small enough for humans to handle but big enough to make maths easier, simpler and convenient. Base 12 has less fractions and less infinite repeating decimals, or perhaps infinite duodecimals, the system's name is not set, I've seen "dozenal" which is good but it doesn't sound great, don't know, maybe it just needs getting used to. I'll call it the "duodecimal system" until a better name sets in.

Ideally we would have two brand new symbols to represent ten and eleven but for now, like in the hexadecimal system, we'll use letters A and B to represent these numbers.

Table translating four systems:

                   
Decimal
                   
                   
Duodecimal
                   
                   
Binary
                   
                   
Hexadecimal
                   
0 0 0 0
1 1 1 1
2 2 10 2
3 3 11 3
4 4 100 4
5 5 101 5
6 6 110 6
7 7 111 7
8 8 1000 8
9 9 1001 9
10 A 1010 A
11 B 1011 B
12 10 1100 C
13 11 1101 D
14 12 1110 E
15 13 1111 F
16 14 10000 10
17 15 10001 11
18 16 10010 12
19 17 10011 13
20 18 10100 14
21 19 10101 15
22 1A 10110 16
23 1B 10111 17
24 20 11000 18
25 21 11001 19
26 22 11010 1A
27 23 11011 1B
28 24 11100 1C
29 25 11101 1D
30 26 11110 1E
31 27 11111 1F
32 28 100000 20
33 29 100001 21
34 2A 100010 22
35 2B 100011 23


There're already many pages on the Web including a Wikipedia page about the duodecimal system and why it's better, all easily googlable. They explain it better than I could. There are also online calculators. I'll just mention this one good site worth visiting with plenty info and a nice offline duodecimal/dozenal calculator for Windows:

http://www.dozenalsociety.org.uk/apps/calculator.html.

I've saved the ZCalculator.exe program many years ago and never had a virus issue but my saved file is dated Apr-2004. They could have gone rogue since then or been hacked. Any .exe file downloaded from the Internet is always very suspect so be careful.


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