FloatingPointRepresentation

A pattern of all zeros in the fraction eld of a

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Unformatted text preview: ortly. A pattern of all zeros in the fraction eld of a normalized number represents the signi cand 1.0, not 0.0. Zero is not the only special number for which the IEEE standard has a special representation. Another special number, not used on older machines but very useful, is the number 1. This allows the possibility of dividing a nonzero number by 0 and storing a sensible mathematical result, namely 1, instead of terminating with an over ow message. This turns out to be 5 Table 1: IEEE Single Precision a1a2a3 : : :a8 b1b2b3 : : :b23 If exponent bitstring a1 : : :a8 is (00000000)2 = (0)10 (00000001)2 = (1)10 (00000010)2 = (2)10 (00000011)2 = (3)10 # (01111111)2 = (127)10 (10000000)2 = (128)10 # (11111100)2 = (252)10 (11111101)2 = (253)10 (11111110)2 = (254)10 (11111111)2 = (255)10 Then numerical value represented is (0:b1b2 b3 : : :b23)2 2;126 (1:b1b2 b3 : : :b23)2 2;126 (1:b1b2 b3 : : :b23)2 2;125 (1:b1b2 b3 : : :b23)2 2;124 # (1:b1b2b3 : : :b23)2 20 (1:b1b2b3 : : :b23)2 21 # (1:b1b2b3 : : :b23)2 2125 (1:b1b2b3 : : :b23)2 2126 (1:b1b2b3 : : :b23)2 2127 1 if b1 = : : : = b23 = 0, NaN otherwise very useful, as we shall see later, although one must be careful about what is meant by such a result. On...
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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.

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