Consider a carry lookahead adder for adding two $n$-bit integers, built using gates of fan-in at most two. The time to perform addition using this adder is (A) $\Theta(1)$ (B) $\Theta(\log(n))$ (C) $\Theta(\sqrt{n})$ (D) $\Theta(n)$

1. In an $n$-bit Carry Lookahead Adder (CLA):

   • Bit-generate ($G_i = A_i B_i$) and bit-propagate ($P_i = A_i \oplus B_i$) signals are calculated in parallel in $\Theta(1)$ time using 2-input gates.

   • The carry terms require computing prefix operations (AND/OR trees) over $n$ variables.

2. When the fan-in of logic gates is limited to a constant (at most 2), an associative binary operation over $n$ inputs can be computed using a balanced binary tree of gates.

3. The depth (height) of such a binary tree with $n$ inputs is $\Theta(\log_2 n)$.

4. Hence, the total propagation delay to compute all carries and finalize the sum bits using 2-input gates is $\Theta(\log n)$.

Therefore, the correct option is (B).