FloatingPointRepresentation

Now we see the reason for the 2126 in the rst line it

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Unformatted text preview: we 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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