converting numbers between number systems  | Moderator | | Join Date: Aug 2008 Location: Leipzig, Germany
Posts: 3,652
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I recently found a problem I haven't seen a good solution yet.
this is just the general conversion from a number between number/notation systems (e.g. decimal, binary, octadecimal notation) - ∞ ∞
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Σ{a(i)⋅n^i} = Σ{b(j)⋅m^j}
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–∞ –∞
n, m – base of the number system
a(i) – given coefficients of number in system n
b(j) – unknown coefficients of number in system m
ex: - 10110 (2) = 28 (10)
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n = 2, a(1) = a(2) = a(4) = 1, a(x) = 0 (x not 1,2 or 4)
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m = 10, b(0) = 8, b(1) = 2, b(x) = 0 (x not 0 or 1)
the solution I know is an iterative one, but I wonder if there is an analytical solution to this equation at all.
maybe something like:
Dormi
| | Moderator | | Join Date: Mar 2006
Posts: 1,103
| | | re: converting numbers between number systems
Are you trying to find a specific a(i) given variable i, and fixed m, n, and b(j)'s? If so, the solution probably uses specific mod rules, dependent on m and n.
| | Moderator | | Join Date: Aug 2008 Location: Leipzig, Germany
Posts: 3,652
| | | re: converting numbers between number systems
Quote:
Originally Posted by jkmyoung  Are you trying to find a specific a(i) given variable i, and fixed m, n, and b(j)'s? no, I want all coefficients a, but I guess the coefficient for a given i (a(i)) depends on i, m, n and all coefficients b. (just feels like that)
(I mixed up a and b in the last code block, but it doesn't matter as long as you imagine b as given, instead of a) Quote:
Originally Posted by jkmyoung If so, the solution probably uses specific mod rules, dependent on m and n. that's what the iteration way uses.
|  | Expert | | Join Date: Jun 2007 Location: Israel
Posts: 2,584
| | | re: converting numbers between number systems
Quote:
Originally Posted by Dormilich
Dormi I guess this could not be resolved unless logn(m) is an integer and j*(logn(m)-1)-1 <= i <= j*logn(m)-1.
Did you mean | | Moderator | | Join Date: Aug 2008 Location: Leipzig, Germany
Posts: 3,652
| | | re: converting numbers between number systems
Quote:
Originally Posted by FishVal Did you mean
I don't have an idea, what the result function depends on, that's really only a guess.
note: b(j) means "b with index j", but I couldn't make it display this way
| | Moderator | | Join Date: Mar 2006
Posts: 1,103
| | | re: converting numbers between number systems
What is the criteria for solving this? Do you want a faster algorithm? One that takes less space on a computer?
Recursive, eg,
a(i) = f(m,n,i,b a(i-1))
or relate it somehow to another function?
| | Moderator | | Join Date: Aug 2008 Location: Leipzig, Germany
Posts: 3,652
| | | re: converting numbers between number systems
Quote:
Originally Posted by jkmyoung What is the criteria for solving this? not the iterative way (means applying mod n recursively, a.k.a. a(i) = f(m,n,a(i-1)) ), just a solution where each coefficient can be computed separately.
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