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Re: Is there a name for this notation?
Posted:
Oct 9, 2011 1:30 AM


On Sun, 9 Oct 2011, Steven D'Aprano wrote:
> Long ago, I came across a book that mentioned a particular notation for > writing numbers in terms of sums of powers of some base, but *not* in the > conventional form. > > For example, using 2 as the base and comparing to decimal: > > 1 = 2^0 => "0" > 2 = 2^1 => "1" > 3 = 2^1 + 2^0 => "10" > 4 = 2^2 => "2" > 5 = 2^2 + 2^0 => "20" > 6 = 2^2 + 2^1 => "21"
7 = 2^2 + 2^1 + 2^0 = 210 8 = 2^3 = 3 9 = 2^3 + 2^0 = 30 ... 33 = 50
How do you write 2^100 + 2^10 + 2^50?
Every positive integer is a sum of nonnegative powers of two. No integer other than two has that property.
We could write 1/2 = 1 1/4 = 2; 1/8 = 3; 1/16 = 4; 0 = oo
3/4 = 1 2 1/3 = 2 4 ...; an infinite series.
Let's try adding. 21 + 31 = 3211 = 322 = 33 = 4. Check. 6 + 10 = 16.
210 + 210 = 221100 = 321 2 * abcd = a+1 b+1 c+1 d+1
Looks like fun. If you can't remember the details, let's reinvent them.
> and so forth. Obviously there is no way of writing zero, and the order of > the digits is arbitrary: I could have written either "12" or "21" for > decimal 6. > > Unfortunately I have forgotten all details about this except the basic > notation, including the name of the book. > > Is there a name for this notation, is it useful for anything, and where > might I find out more about it?



