We are using k-levels of carry look-ahead adder. For example,
Suppose we have 16 bits numbers to add and 4 bit carry look-ahead adder, then we’ll need 2 levels of carry look-ahead adder to compute all the carries.
$Level-2\rightarrow\:\: |\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:Generator 5\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:|$
$Level-1\rightarrow \: \: |\:generator4\:|\:generator 3\:|\:generator 2\:|\:generator 1|$
$Level-0\rightarrow \: \: |a_{15}a_{14}a_{13}a_{12}|\: \: a_{11}a_{10}a_{9}a_{8}\: |\: \: \: a_{7}a_{6}a_{5}a_{4}\: \: \: |\: \: a_{3}a_{2}a_{1}a_{0}\: \:\:\:|$
Also, each level’s carry generator can work in parallel. Therefore, each level causes ‘d’ delay. And therefore, total delay = k*d.