TABLE OF CONTENTS In this section we derive the equations for carry-look-ahead addition in a more general way. This will allow us to consider various implementations of the carrylook-ahead adder rather than being restricted to a predetermined blocking factor. It will also provide a general framework for deriving expressions for other techniques for fast addition, including carry-select and carry-skip adders.
We first introduce the following notation. Let P i:j and G i:j denote the group-propagated carry and the group-generated carry functions, respectively, for the group of bit positions i, i ?1, , j (with i ? j), as shown in Figure 5.7.
P i:j equals 1 when an incoming carry into the least significant position j, c j, is allowed to propagate through all i ? j+1 bit positions. G i:j equals 1 when a carry is generated in at least one of the bit positions from j to i inclusive and propagates to bit position i+1, i.e., the outgoing carry c i +1 equals 1. These definitions generalize those in Equation (5.5) and include as a special case the single bit-position carry propagate and generate functions P i and G i. The two group-carry functions can be calculated recursively using the two Boolean equations
Note that the notations P i:i
