5.8 Carry-Select Adders

In a carry-select adder the n bits are divided into nonoverlapping groups of possibly different lengths. The underlying strategy is similar to that of the conditional-sum adder described in Section 5.3. Each group generates two sets of sum bits and an outgoing carry. One set assumes that the incoming carry into the group is 0, the other assumes that it is 1. When the incoming carry into the group is assigned its final value it selects one of the two sets as is shown in Figure 5.3. Figure 5.13 is a more detailed version of Figure 5.3 depicting the lth group which consists of k bit positions starting with bit position j and ending with bit position i where i=j+ k ?1.

Figure 5.13: The i th group, consisting of the k bit positions j, j+1, , i, in a carry-select adder.

The outputs of the group are the sum bits s _i , s _{i ?1}, , s _j and the lth group outgoing carry c _{i +1}. The corresponding Boolean equations are

and

where is the mth sum bit under the condition that the incoming carry into the lth group is 0. This is the same notation that we have used for the conditional-sum adder. The notations , and are defined similarly.

The two separate sets of outputs can be calculated in a ripple-carry manner. Thus, for bit...