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Unformatted text preview: 7 actual exponents from Emin = ;126 to Emax = 127. The smallest normalized
number which can be stored is represented by
0 00000001 00000000000000000000000
meaning (1:000 : : : 0)2 2;126 , i.e. 2;126, which is approximately 1:2 10;38,
while the largest normalized number is represented by
0 11111110 11111111111111111111111
meaning (1:111 : : : 1)2 2127, i.e. (2 ; 2;23 ) 2127, which is approximately
3:4 1038.
The last line of Table 1 shows that an exponent bitstring consisting of all
ones is a special pattern used for representing 1 and NaN, depending on
the value of the fraction bitstring. We will discuss the meaning of these later.
Finally, let us return to the rst line of the table. The idea here is as
follows: although 2;126 is the smallest normalized number which can be represented, we can use the combination of the special zero exponent bitstring
and a nonzero fraction bitstring to represent smaller numbers called subnormal numbers. For example, 2;127, which is the same as (0:1)2 2;126, is
represented as
0 00000000 10000000000000000000000
while 2;149 = (0:0000 : : : 01)2
point) is stored as 2;126 (with 22 zero bits after the binary 0 00000000 00000000000000000000001 :
This last number is the smallest nonzero number which can be stored. Now...
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This note was uploaded on 02/12/2014 for the course MATH 4800 taught by Professor Lie during the Spring '09 term at Rensselaer Polytechnic Institute.
 Spring '09
 LIE

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