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Math Help - Decimal to Binary

  1. #1
    MHF Contributor chiph588@'s Avatar
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    Decimal to Binary

    Could anyone explain to me how every number in decimal has a unique representation in binary?
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  2. #2
    Master Of Puppets
    pickslides's Avatar
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    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 \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.
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by chiph588@ View Post
    Could anyone explain to me how every number in decimal has a unique representation in binary?
    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
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