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June 2nd, 2017, 03:33 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, 04:24 AM  #2 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,192 Thanks: 871 
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, 04:37 AM  #3 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,313 Thanks: 2447 Math Focus: Mainly analysis and algebra  
June 2nd, 2017, 05:16 AM  #4  
Senior Member Joined: May 2016 From: USA Posts: 1,038 Thanks: 423  Quote:
$A_{12} + B_{12} = (6_{12} + 4_{12}) + (6_{12} + 5_{12}) =$ $(6_{12} + 6_{12}) + (4_{12} + 5_{12}) = 10_{12} + 9_{12} = 19_{12}.$ 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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