An Alternative Carry Lookahead Analysis

The equation for the carry bit based on the generate and propagate bits looks very similar to the original formulation of the less-than relation.

$$\begin{eqnarray*} carry_i & = & g_i \lor (p_i \land carry_{i-1}) \\ \mathit{lt}... ...\left( \left( a_n = b_n \right) \land \mathit{lt}(n) \right) \\ \end{eqnarray*}$$

This suggests we can use the same divide and conquer recursive approach as we used with speeding up the less-than relation. This approach gives a circuit of linear size for each carry bit, so the total size is quadratic.