Could anyone explain to me how every number in decimal has a unique representation in binary?

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- Nov 23rd 2009, 07:49 PMchiph588@Decimal to Binary
Could anyone explain to me how every number in decimal has a unique representation in binary?

- Nov 23rd 2009, 08:00 PMpickslides
Its been a long time since i've done some conversions and they were mainly integers but I would suggest the place value for binary could be represented by $\displaystyle \dots ,2^3,2^2,2^1,2^0,2^{-1},2^{-2},2^{-3},\dots$ etc.. The negative indicies representing decimals.

Someone please correct me if I am giving the poster a bum steer. - Nov 23rd 2009, 08:06 PMCaptainBlack
Every natural number has a unique representation in any positive integral base, there is nothing special about decimal (or binary for that matter). If you are happy that every number (integer, natural?) has a unique representation in decimal then exactly the same reasoning is applicable to any other base.

(note: not all decimal and binary fractions have unique representations in their corresponding bases)

CB