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All the lines of Table 1 except the rst and the last refer to the normalized
numbers, i.e. all the oating point numbers which are not special in some way.
Note especially the relationship between the exponent bitstring a1a2 a3 : : :a8
and the actual exponent E , i.e. the power of 2 which the bitstring is intended
to represent. We see that the exponent representation does not use any of
sign-and-modulus, 2's complement or 1's complement, but rather something
called biased representation: the bitstring which is stored is simply the binary
representation of E + 127. In this case, the number 127 which is added to
the desired exponent E is called the exponent bias. For example, the number
1 = (1:000 : : : 0)2 20 is stored as
0 01111111 00000000000000000000000 :
Here the exponent bitstring is the binary representation for 0 + 127 and the
fraction bitstring is the binary representation for 0 (the fractional part of 1:0).
The number 11=2 = (1:011)2 22 is stored as
0 10000001 0110000000000000000000
and the number 1=10 = (1:100110011 : : :)2 2;4 is stored as
0 01111011 10011001100110011001100 :
We see that the range of exponent eld bitstrings for normalized numbers
is 00000001 to 11111110 (the decimal numbers 1 through 254), representing
3 These numbers were called denormalized in early versions of the standard....
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- Spring '09
- oating point