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 June 2nd, 2017, 04:33 AM #1 Newbie   Joined: Jun 2017 From: Croatia Posts: 2 Thanks: 0 Duodecimal System base 12 Hello, I am barely familiar with Duodecimal System so here are few questions: 1. how to Calculate within Duodecimal base 12? 2. interesting facts/repetitions/stuff in Numerical sequences using Duodecimal? 3. interesting facts Welcomed
 June 2nd, 2017, 05:24 AM #2 Math Team   Joined: Jan 2015 From: Alabama Posts: 2,940 Thanks: 794 You have asked two questions that are simply much too vague and general. Make your question more precise. As for "how to calculate using the duodecimal (base 12) system: The duodecimal system adds two new "digits" representing 10 and 11. Usually those are represented by "A" and "B" respectively. So the numbers in duodecimal are 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, 10, 11, 12, 13 14, 15, 16, 17, 18, 19, 1A, 1B, 20, ... Note that, here, "10" means "1 times 12" or 12 decimal, "11" means "1 times 12 plus 1" or 13 decimal, etc. To add in duodecimal, you have to remember that you only "carry" if the sum of two digits is greater than 11. 3+ 4= 7 but 7+ 8= (6+ 1)+ (6+ 2)= (6+6)+ (1+ 2)= 13. That, of course, in decimal, would be 7+ 8= 12+ 3= 15.
June 2nd, 2017, 05:37 AM   #3
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 Originally Posted by Country Boy 7+ 8= (6+ 1)+ (6+ 2)= (6+6)+ (1+ 2)= 13
What an extraordinary way to represent the sum! I'd have thought $7+8=7+(5+3)=(7+5)+3=13$ would be more normal.

June 2nd, 2017, 06:16 AM   #4
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 Originally Posted by v8archie What an extraordinary way to represent the sum! I'd have thought $7+8=7+(5+3)=(7+5)+3=13$ would be more normal.
I wouldn't say extraordinary. I'd rather say a bit complicated for the simple case given, but perhaps helpful in more complicated cases. Moreover, both presentations seem to me to skip the crucial step and the hard cases.

$A_{12} + B_{12} = (6_{12} + 4_{12}) + (6_{12} + 5_{12}) =$

$(6_{12} + 6_{12}) + (4_{12} + 5_{12}) = 10_{12} + 9_{12} = 19_{12}.$

This may make clear that when you add two numbers both less than six, duodecimal addition looks like decimal addition. When you add two numbers under twelve with at least one that is larger than five, you can decompose the larger numbers into a sum of six and some smaller number. The sum of six and six is always $10_{12}.$

And that lets you construct the entire addition table for duodecimal digits.

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