
Elementary Math Fractions, Percentages, Word Problems, Equations, Inequations, Factorization, Expansion 
 LinkBack  Thread Tools  Display Modes 
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: 2,576 Thanks: 668 
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: 6,876 Thanks: 2240 Math Focus: Mainly analysis and algebra  
June 2nd, 2017, 05:16 AM  #4  
Senior Member Joined: May 2016 From: USA Posts: 755 Thanks: 303  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.  

Tags 
base, duodecimal, system 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Base e number system  Loren  Number Theory  23  October 20th, 2016 05:16 PM 
General rule for passing from base 10 to any other base B  ajayullal  Number Theory  1  December 16th, 2015 09:25 AM 
A little confused about converting from base 10 to base 2(new to binary)?  chakana  Computer Science  2  June 19th, 2015 09:14 PM 
Why does base 60 have a lower number of terminating decimals than base 10?  caters  Number Theory  9  May 22nd, 2014 02:46 AM 
Finding smallest n : (base^n + base^(n1) + ... base^1) > x  momesana  Algebra  4  December 3rd, 2009 06:13 PM 