TABLE OF CONTENTS Ling adders [19] are a variation of the carry-look-ahead adders. They use a simpler version of the group-generated carry signal and thus provide an opportunity to reduce the associated delay. We will see the principle behind Ling adders through a simple example. Suppose that we start with a carry-look-ahead adder with groups of size 2, i.e., we produce the signals G 1 : 0, P 1 : 0, G 3: 2, P 3:2 and so on. The outgoing carry for position 3 can be expressed as
where
We either assume that c 0=0 or set G 0 =x 0 y 0 +P 0 c 0. Expressing G 3: 0 in terms of the individual carry generate and propagate signals we obtain
Since G 3 P 3= G 3 all terms in the above equation have P 3 as a common factor, and we can therefore rewrite the expression for G 3:0 as
where H 3:0 is defined as
and
Note that P 2:1 is used in (5.24) in contrast to P 3: 2 which is used in (5.22). Equation (5.24) defines H as an alternative to the carry generate G and shows that H can be calculated in a similar manner. However, H does not have a simple interpretation like G. On the other hand, H is simpler to calculate. For example, expressing H 3:0 in...
