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Unformatted text preview: rs.2 (There
is also a decimal version of the standard but we shall not discuss this.)
The IEEE standard has three very important requirements:
ANSI/IEEE Std 754-1985. Thanks to Jim Demmel for introducing the author to the
2 4 consistent representation of oating point numbers across all machines
adopting the standard
correctly rounded arithmetic (to be explained in the next section)
consistent and sensible treatment of exceptional situations such as division by zero (to be discussed in the following section).
We will not describe the standard in detail, but we will cover the main
We start with the following observation. In the last section, we chose to
normalize a nonzero number x so that x = m 2E , where 1 m < 2, i.e. m = (b0:b1b2b3 : : :)2
with b0 = 1. In the simple oating point model discussed in the previous
section, we stored the leading nonzero bit b0 in the rst position of the eld
provided for m. Note, however, that since we know this bit has the value one,
it is not necessary to store...
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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