Lookahead carry unit

A lookahead carry unit (LCU) is a logical unit in digital circuit design used to decrease calculation time in adder units and used in conjunction with carry look-ahead adders (CLAs).
4-bit adder.
A single 4-bit CLA is shown below:
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 (formula_1) and group generate (formula_2) from each of the four CLAs. formula_1 and formula_2 have the following expressions for each CLA adder:
The LCU then generates the carry input for each CLA.
Assume that formula_7 is formula_1 and formula_9 is formula_2 from the ith CLA then the output carry bits are
Substituting formula_15 into formula_16, then formula_16 into formula_18, then formula_18 into formula_20 yields the expanded equations:
formula_15 corresponds to the carry input into the second CLA; formula_16 to the third CLA; formula_18 to the fourth CLA; and formula_20 to overflow carry bit.
In addition, the LCU can calculate its own propagate and generate:
64-bit adder.
By combining 4 CLAs and an LCU together creates a 16-bit adder.
Four of these units can be combined to form a 64-bit adder.
An additional (second-level) LCU is needed that accepts the propagate (formula_32) and generate (formula_33) from each LCU and the four carry outputs generated by the second-level LCU are fed into the first-level LCUs.