16-bit Adder
By combining four 4-bit CLAs, a 16-bit adder can be created but additional logic is needed in the form of an LCU.
The LCU accepts the group propagate and group generate from each of the four CLAs. and have the following expressions for each CLA adder:
The LCU then generates the carry input for each CLA.
Assume that is and is from the ith CLA then the output carry bits are
Substituting into, then into, then into yields the expanded equations:
corresponds to the carry input into the second CLA; to the third CLA; to the fourth CLA; and to overflow carry bit.
In addition, the LCU can calculate its own propagate and generate:
Read more about this topic: Lookahead Carry Unit