Let
denote the number of bits. Then the value of a
two's
complement integer
fixedpoint number can be expressed in terms of its
bits
as

(G.1) 
We visualize the
binary word containing these bits as
Each bit
is of course either 0 or 1. Check that the
case
in Table
G.3 is computed correctly using this formula. As an
example, the number 3 is expressed as
while the number 3 is expressed as
and so on.
The mostsignificant 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 leastsignificant 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.
Table G.4:
Numerical range limits in bit two'scomplement.



8 
128 
127 
16 
32768 
32767 
24 
8,388,608 
8,388,607 
32 
2,147,483,648 
2,147,483,647 

Next Section: Signal Energy and PowerPrevious Section: Two's Complement FixedPoint Format