# How to calculate a floating point of negative number?

In IEEE double precision n=53. So to represent 16 I can do the following:
The next biggest number from $16=+(.10 \dots 01)_22^5=2^{-1}2^5+2^{-53}2^5=16+2^{-48}$

Now the biggest number from $-16=-16+2^{-49}$, but how to show this formally like i did above for positive $16$ case?

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$\large+(1.00...01)_2\cdot2^4 = 16\cdot(1+2^{-52}) = 16+2^{-48}$
$\large+(1.11...11)_2\cdot2^3 = 16\cdot(1-2^{-53}) = 16-2^{-49}$
$\large-(1.11...11)_2\cdot2^3 = -16\cdot(1-2^{-53}) = -16+2^{-49}$
I kind of figured it out already, THANK YOU for the answer. The only thing, everything looks correct but $1$s should be after decimal point, I edited it already :) –  ASROMA Dec 3 '12 at 1:47