We visualize the binary word containing these bits as
Each bit is of course either 0 or 1. Check that the table above is computed correctly using this formula. As an example, the numer 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 4.5 shows some of the most common cases.
Table 4.5:Numerical range limits in -bit two’s-complement.
8 -128 127 16 -32768 32767 24 -8,388,608 8,388,607 32 -2,147,483,648 2,147,483,647