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Fig. 7.6 An IEEE 754 floating point value in big-endian and little-endian format
the 23 bit normalised significand, which when interpreted, should have an a addi-
tional bit set to 1 added to the left most position making it 24 bits. When the octets
are swapped, the location of the sign, exponent and the significand change consid-
erably and hence either the octet order or the specific locations of the bits must be
specified.
A formula can be written for representing the exact nature of the interpre-
tation of the floating point value. The formula for IEEE 754 floating point
numbers is:
erhf
In Fig. 7.6 the value of the floating point value is calculated by adding a bit
to the left most side of the significand (1.00101011001010101100110) and then
converting it directly to its decimal value (IEEE 754 uses Sign and Magnitude as
the interpretation scheme for the significand) which gives 1.168621778.
The exponent is also treated as an unsigned integer and converted directly to its
decimal value which gives 70. The bias is -127 so the actual exponent is 70 -127
=
-57. The sign bit is 1 which indicates a negative number.
10 -18 .
As already mentioned there are bit patterns reserved for exception values. For
IEEE 754 32 bit floating point values when a number is too large to be expressed in
the 32 bit range then the sign bit is set to 0 the exponent to 11111111 and the bits
in the significand are all set to zero. This bit pattern would appear in stored binary
2 -57
Using the formula one has -1.168621778
×
=
-8.108942535
×
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