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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
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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This note was uploaded on 02/12/2014 for the course MATH 4800 taught by Professor Lie during the Spring '09 term at Rensselaer Polytechnic Institute.
- Spring '09