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FloatingPointRepresentation

# Again illustrate with an example 4 the expression

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Unformatted text preview: strate with an example. 4 The expression round(x) is de ned in the next section. 9 Table 2: IEEE Double Precision a1a2 a3 : : :a11 b1b2b3 : : :b52 If exponent bitstring is a1 : : :a11 (00000000000)2 = (0)10 (00000000001)2 = (1)10 (00000000010)2 = (2)10 (00000000011)2 = (3)10 # (01111111111)2 = (1023)10 (10000000000)2 = (1024)10 # (11111111100)2 = (2044)10 (11111111101)2 = (2045)10 (11111111110)2 = (2046)10 (11111111111)2 = (2047)10 Then numerical value represented is (0:b1b2 b3 : : :b52)2 2;1022 (1:b1b2 b3 : : :b52)2 2;1022 (1:b1b2 b3 : : :b52)2 2;1021 (1:b1b2 b3 : : :b52)2 2;1020 # (1:b1b2 b3 : : :b52)2 20 (1:b1b2 b3 : : :b52)2 21 # (1:b1b2b3 : : :b52)2 21021 (1:b1b2b3 : : :b52)2 21022 (1:b1b2b3 : : :b52)2 21023 1 if b1 = : : : = b52 = 0, NaN otherwise For many applications, single precision numbers are quite adequate. However, double precision is a commonly used alternative. In this case each oating point number is stored in a 64-bit double word. Details are shown in Table 2. The ideas are all the...
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