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Suppose that the signi cand eld has room only to

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Unformatted text preview: . Suppose that the signi cand eld has room only to store b0:b1b2, and that the only possible values for the exponent E are ;1, 0 and 1. We shall call this system our toy oating point system. The set of toy oating point numbers is shown in Figure 1 Actually, the usual de nition of precision is one half of this quantity, for reasons that will become apparent in the next section. We prefer to omit the factor of one half in the de nition. 1 3 : : :: : : 0 1 2 3 Figure 1: The Toy Floating Point Numbers The largest number is (1:11)2 21 = (3:5)10, and the smallest positive normalized number is (1:00)2 2;1 = (0:5)10. All of the numbers shown are normalized except zero. Since the next oating point number bigger than 1 is 1.25, the precision of the toy system is = 0:25. Note that the gap between oating point numbers becomes smaller as the magnitude of the numbers themselves get smaller, and bigger as the numbers get bigger. Note also that the gap between between zero and the smallest positive number is much bigger than the gap between the smallest positive number and the next positive number. We sh...
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