FloatingPointRepresentation

An even worse choice of representation would be the

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Unformatted text preview: n worse choice of representation would be the following: since 1=10 = (0:00000001100110011 : : :)2 24 the number could be represented by 0 E = 4 0.0000000110011001100110 : This is clearly a bad choice since less of the binary expansion of 1=10 is stored, due to the space wasted by the leading zeros in the signi cand eld. This is the reason why m < 1, i.e. b0 = 0, is not allowed. The only allowable representation for 1=10 uses the fact that 1=10 = (1:100110011 : : :)2 2;4 2 giving the representation 0 E = ;4 1.1001100110011001100110 : This representation includes more of the binary expansion of 1=10 than the others, and is said to be normalized, since b0 = 1, i.e. m > 1. Thus none of the available bits is wasted by storing leading zeros. We can see from this example why the name oating point is used: the binary point of the number 1=10 can be oated to any position in the bitstring we like by choosing the appropriate exponent: the normalized representation, with b0 = 1, is the one which should be always be used when possible. I...
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