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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- Spring '09
- oating point