Brent-Kung adder

In electronics, an adder is a combinatorial or sequential logic element which computes the n-bit sum of two n-bit numbers. The Brent-Kung adder is one of the more advanced designs, having a gate level depth of $O(log\_2(n))$.

Adding two n-bit numbers is performed as adding in parallel the lower halves of the addends, the upper halves with input carry $0$, and the upper halves with input carry $1$, then selecting the appropriate upper half sum based on the output carry from the lower half sum. Thus the gate level depth of the n-bit adder is equal to the depth of the half-width adder plus the depth of a mux.