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I know that $3/8$ can be written as $0*1/2+1*1/4+1*1/8$. But there is another way of expanding it in binary.

Can anyone help finding that?

Thanks!

Elizabeth Schmidt
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  • That's the binary expansion. Could they be looking for a floating-point representation? I suppose they could be looking for a nearest-estimate sort of expansion, in which case it would be $\frac 1 2 - \frac 1 8$. – Gabriel Burns Nov 09 '16 at 22:06
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    Similar to $1=0.999999\ldots$, we have ${3\over8}={1\over4}+{1\over16}+{1\over32}+{1\over64}+\cdots$. – Barry Cipra Nov 09 '16 at 22:18
  • Maybe you are looking for $0.011_2$, where I used the subscript to indicate a binary fraction. To the right side of the "decimal" point, we have the halves place, the fourths place, the eighths place, etc. It's the same expansion, but when it is written with the point it is called a binary fraction, as opposed to a decimal fraction or a common fraction. – LouisB Nov 09 '16 at 22:35
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    Binary expansions are unique! The same is true for $m$-ary expansions. – Oiler Nov 09 '16 at 22:39

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