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   Base 13 subtraction
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   Author  Topic: Base 13 subtraction  (Read 2101 times)
minniekp
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Base 13 subtraction  
« on: Aug 17th, 2007, 1:59am »
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How do you subtract two numbers in base 13 given below:
 
 (A023AC5B)
-(129B5321) to the base 13
 
This was asked in Adobe written test.
 
Thanks
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inexorable
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Re: Base 13 subtraction  
« Reply #1 on: Aug 17th, 2007, 2:54am »
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8A55593A        
can't it be answered by just doing by hand?
the carry will be 13 as its base 13
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towr
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Re: Base 13 subtraction  
« Reply #2 on: Aug 17th, 2007, 3:12am »
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Simple way is to convert both to integers, subtract, and return to base 13.
 
Another way is to turn it into an addition, for the number you want to subtract, change every digit to 13- that digit. Add the two numbers base-13 and ermm, add 1 extra for good measure? And mind the overflow.  
There's some details to bare in mind (for which I don't have time now); but basically adapt what you'd do for binary.
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Grimbal
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Re: Base 13 subtraction  
« Reply #3 on: Aug 17th, 2007, 5:13am »
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OK, here is how it's done.  Remember A=10, B=11, etc.  Start from the right.
 
B-1 = A.
5-2 = 3
C-3 = 12-3 = 9
A-5 = 10-5 = 5
 
so far so good.
 
3-B = 3-11 = uh... it gets negative
  so add 13 to 3 and remember the carry
  16-11 = 5
 
2-1(carry)-9 = ...
  add 13 to 2 = 15, remember carry
  15-1-9 = 5
 
0-1-2 = ...
  add 13 to 0 = 13, remember carry
  13-1-2 = 10 = A
 
A-1-1 = 8
 
put it together: 8A55593A
« Last Edit: Aug 17th, 2007, 7:40am by Grimbal » IP Logged
towr
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Re: Base 13 subtraction  
« Reply #4 on: Aug 17th, 2007, 7:17am »
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Here's my approach worked out:
 
 A023AC5B
-129B5321
--------- (modulo 10000000)
 A023AC5B
+BA3179AB (12's/C's complement -> 129B5321+BA3179AB = CCCCCCCC)
+     1 (because CCCCCCCC + 1 = 10000000)
---------
18A55593A
--------- mod 10000000
 8A55593A
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Grimbal
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Re: Base 13 subtraction  
« Reply #5 on: Aug 17th, 2007, 7:43am »
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Of course, when you add BA3179AB+1, in fact you add BA3179AB.CCC...
Because CCCCCCCC.CCC... = 0 (mod 100000000)
 Wink
« Last Edit: Aug 17th, 2007, 7:45am by Grimbal » IP Logged
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