Suppose . We can represent it
as by simply discarding (``chopping'')
the digits which do not fit the mantissa format
(here the remaining digits are 625).
We see that the FP representation is precisely ,
and we have .
Now, if was negative, ,
the chopped representation would be ,
but now this is . Note that in this situation
.
In consequence, with chopping, we choose if and
is . In both situations the floating point number is
closer to 0 than the real number , so chopping is also called
*rounding toward 0*.

Chopping has the advantage of being very simple to implement
in hardware. The roundoff error for
chopping satisfies

For example:

and

Adrian Sandu 2001-08-26