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 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 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.