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see the reason for the 2;126 in the rst line. It allows us to represent numbers
in the range immediately below the smallest normalized number. Subnormal
numbers cannot be normalized, since that would result in an exponent which
does not t in the eld.
Let us return to our example of a machine with a tiny word size, illustrated
in Figure 1, and see how the addition of subnormal numbers changes it. We
get three extra numbers: (0:11)2 2;1 = 3=8, (0:10)2 2;1 = 1=4 and
(0:01)2 2;1 = 1=8: these are shown in Figure 2.
8 : : :: : : 0 1 2 3 Figure 2: The Toy System including Subnormal Numbers
Note that the gap between zero and the smallest positive normalized number
is nicely lled in by the subnormal numbers, using the same spacing as that
between the normalized numbers with exponent ;1.
Subnormal numbers are less accurate, i.e. they have less room for nonzero
bits in the fraction eld, than normalized numbers. Indeed, the accuracy
drops as the size of the subnormal number decreases. Thus (1=1...
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- Spring '09