Let
denote the number of bits. Then the value of a two's
complement integer fixed-point number can be expressed in terms of its
bits
as
Each bit
while the number -3 is expressed as
and so on.
The most-significant bit in the word,
, can be interpreted as the
``sign bit''. If
is ``on'', the number is negative. If it is
``off'', the number is either zero or positive.
The least-significant bit is
. ``Turning on'' that bit adds 1 to
the number, and there are no fractions allowed.
The largest positive number is when all bits are on except
, in
which case
. The largest (in magnitude) negative number is
, i.e.,
and
for all
. Table G.4 shows
some of the most common cases.
|