# Duodecimal System



## Meldon (May 28, 2012)

Has anyone tried transcribing decimal numbers into duodecimal numbers?

I've tried something a few days ago and i wanted to share this.
This are the dates of Tolkien's birth and death

Duodecimal: 11-1-1118
Decimal:13-1-1892

Duodecimal: 2-9-1185
Decimal: 2-9-1973

How this works is:

Duodecimal 1118 is

Decimal: 1x12x12x12+1x12x12+1x12+8=1728+144+12+8=1892

From Decimal to Duodecimal is a bit harder, you have to take the gratest amount possible,
write it down and so on.

Decimal: 1973
Duodecimal: 1728 so 1
144 so 1
96 so 8
the remainder: 5 so 5

Any questions? Feel free to ask.


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## Erestor Arcamen (May 30, 2012)

Very interesting but I think the section you want is 'The Floating Log' since it's not Tolkien related at all.

I remember using the Duodecimal system in school and hating it lol because I didn't have very good teachers. Then I got to college and fell in love with math when I had the best teacher ever!


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## Meldon (May 30, 2012)

Well thank you, and I hope one of the moderators will move this thread


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## Prince of Cats (May 31, 2012)

I do a lot of base 2 (binary) and base 16 (hexadecimal) math working with communications and computers; what's base 12 used for?

I think these types of math are a lot of fun  I taught myself (by reading and playing) hex and binary in middle school for reverse engineering computer games.

Say you have a string in binary *11*0*1*0000
thats 2^7(*1*) + 2^6(*1*) + 2^5(0) + 2^4(*1*) + 2^3(0) + 2^2(0) + 2^1(0) + 2^0(0)

It's easier just to memorize what 2^7 is etc and you can do the math quickly in your head, so you have the numbers 

128, 64, 32, 16, 8, 4, 2, 1 for 2^7, 2^6, 2^5, 2^4 etc. for each binary digit

So to convert to decimal (base 10) from binary 11010000 would be
128 + 64 + 0 + 16 + 0 + 0 + 0 + 0 or 208

Working from decimal into binary is pretty much the same thing ... 208 can be expressed with no less than 8 bits (binary digits) knowing that the maximum value for 8 bits is 256 (including 0) and 128 for 7 bits (including 0) .. and then from there you start with the largest bit (128 at position 8 -- 2^7). For each bit that can be subtracted from the number that remains, a 1 is entered for that bit. 208 - 128 leaves 80, 80 - 64 leaves 16, you can't subtract 32 from 16, so the third bit is 0, 16 - 16 works so the fourth bit is a 1, and now that the remainder is 0 your number is expressed by writing zero for the last 4 bits (which would be decimal 8 4 2 and 1).

Our birth year for Tolkien is 1892 in decimal, or 0000011101100100 (which is the same as 11101100100 (drop the leading zeros) but in computing we typically express binary in groups of 8 bits (a byte)). 2^10 is 1024 (FYI a Kilobyte (KB) is 1024 Bytes), double that (2^11) would be larger than our decimal number, so we know that it takes 11 bits (2^10 is the 11th bit because 2^0 is the first bit, not 2^1) to express 1892 in binary and work down from there.

Here in the US I was never taught duodecimal in school - I'm assuming it uses a and b for numbers 11 and 12? 

Fun times


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## Meldon (May 31, 2012)

Yes, that's right, I know binary and hexadecimal too, but i only posted duodecimal because it was the system the elves used


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