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Floating points

  1. Feb 19, 2009 #1
    This should be an easy one, but my PC is bugging me!!! Based on the floating point definition:

    F = [tex]\pm[/tex]( [tex]\stackrel{m}{\overline{B^{t}}}[/tex])[tex]B^{e}[/tex]

    Where B is the base (usually 2), m is the mantissa and varies from 1 [tex]\leq[/tex] [tex]B^{t}[/tex] - 1. e is the exponent (1024 for double and 128 for single precision machines).

    Quetion: what is the smallest intenger that DOES NOT belong to this floating point definition.

    Solution: Since we want to minimize the denominator term we will let t=1, This would again let m =1. Hence, we can conclude that this said integer is 2[tex]^{1023}[/tex]. However, I cannot verify this on the computer. In matlab, if I have this number and I add 1 to it, it gives me back the same number instead of Inf as I expect it. Can someone tell me how to verify this on a computer, or if my analysis is wrong?

  2. jcsd
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