Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Is there a way to perform these operations in a particular base b but 10? I can convert it back to base 10 and perform the operation, however, I think it's kinda odd by doing this way.

Thanks,
Chan

share|improve this question
add comment

1 Answer

up vote 4 down vote accepted

If what you are interested in are paper-and-pencil methods, then the same algorithms that one uses in base 10 work in base $b$, provided you remember to perform all operations in base $b$. (Of course, it may be that the proliferation of calculators has atrophied some people's ability to do it even in base $10$...)

For example, if you want to add $573641$ and $561373$ in base $9$ (I just made them up), then we add can add them right to left, with carries; note that in base $9$, $7+4 = 12$, $6+3=10$, etc. So we get: $$\begin{array}{r} 573641\\\ \underline{+\ 561373}\\\ 1245124 \end{array}$$ Similar with subtraction, multiplication, and long division.

share|improve this answer
    
Thanks a lot, I do want to use paper and pencil. –  Chan Feb 4 '11 at 4:12
1  
@Chan: Great, then. Multiplication is a bit difficult, because if you know the multiplication tables in base 10, you'll have a hard time remembering things like the fact that, if you are working in base $7$, then $6\times 5$ is $42$, but if you keep that in mind, the good old base 10 algorithms work. –  Arturo Magidin Feb 4 '11 at 4:16
    
I find when I do this I convert back to base 10 for each single digit calculation (except for binary). I did a math puzzle years ago that was so based in 6's that it made sense to do all the arithmetic in base 6. –  Ross Millikan Feb 4 '11 at 5:00
1  
@Ross: I suspect with enough practice one would be able to do it almost without thinking for any particular base, but yes, that's pretty much what I do. Except, as you say, base 2, though I would extend that to base $2^k$, which I do by converting to binary and back (the latter via groupings, which is pretty easy). –  Arturo Magidin Feb 4 '11 at 5:02
    
I don't do hex enough to know that 7*8=38 or even that A+B=15. But I know many people can. It is said that the stage calculators worked in base 100 and knew the multiplication table for that. –  Ross Millikan Feb 4 '11 at 5:08
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.