The ripple-carry adder that we reviewed in Section 3.2.2 may introduce too much delay into a system. The longest path through the adder is from the inputs of the least signiﬁcant full adder to the outputs of the most signiﬁcant full adder.
The process of summing the inputs at each bit position is relatively fast (a small two-level circuit sufﬁces) but the carry propagation takes a long time to work its way through the circuit. In fact, the propagation time is proportional to the number of bits in the operands. This is unfortunate, since more signiﬁcant ﬁgures in an addition translates to more time to perform the addition.In this section, we look at a method of speeding the carry propagation in what is known as a carry lookahead adder. In Appendix B, reduced Boolean expressions for the sum (si) and carry outputs (ci+1) of a full adder are created. These expressions are repeated below, with subscripts added to denote the relative position of a full adder in a ripple-carry adder: