Carry select adder

In electronics, an adder is a combinatorial or sequential logic element which computes the n-bit sum of two n-bit numbers. The carry-select adder is simple but rather fast, having a gate level depth of $O(sqrt\; n)$.

The Carry select adder generally consists of two Ripple Carry Adder and one multiplexer. Adding two n-bit numbers with a Carry select adder is done with two adders (therefore 2 Ripple Carry Adder) in order to perform the calculation twice, one time with the assumption of the carry being zero and the other being one. After the two results are calculated the correct sum, as well as the correct carry is then selected with the multiplexer, which is usually controlled by the carry from the previous Ripple carry adder.

The number of bits can be uniform, or variable. In the former case, the optimal delay occurs for a block size of $lfloor\; sqrt\; n\; floor$. In the latter, the block size should be 1-bit for the least-significant block, 2-bits for the next one, and so on. In both cases, the gate delays of the two phases are equal and the total gate delay is minimal.