FloatingPointRepresentation

E in this case b23 b24 are all zero for example the

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Unformatted text preview: in this case, b23 b24 : : : are all zero. For example, the number 11=2 = (1:011)2 22 would be represented by 0 E=2 1.0110000000000000000000 1 and the number would be represented by 0 71 = (1:000111)2 26 E=6 1.0001110000000000000000 : To avoid confusion, the exponent E , which is actually stored in a binary representation, is shown in decimal for the moment. The oating point representation of a nonzero number is unique as long as we require that 1 m < 2. If it were not for this requirement, the number 11=2 could also be written (0:01011)2 24 and could therefore be represented by 0 E=4 0.0101100000000000000000 : However, this is not allowed since b0 = 0 and so m < 1. A more interesting example is 1=10 = (0:0001100110011 : : :)2: Since this binary expansion is in nite, we must truncate the expansion somewhere. (An alternative, namely rounding, is discussed later.) The simplest way to truncate the expansion to 23 bits would give the representation 0 E=0 0.0001100110011001100110 but this means m < 1 since b0 = 0. An eve...
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