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 ( P G {\displaystyle P_{G}} ) and group generate ( G G {\displaystyle G_{G}} ) from each of the four CLAs. P G {\displaystyle P_{G}} and G G {\displaystyle G_{G}} have the following expressions for each CLA adder:
P G = P 0 ⋅ P 1 ⋅ P 2 ⋅ P 3 {\displaystyle P_{G}=P_{0}\cdot P_{1}\cdot P_{2}\cdot P_{3}}
G G = G 3 + G 2 ⋅ P 3 + G 1 ⋅ P 2 ⋅ P 3 + G 0 ⋅ P 1 ⋅ P 2 ⋅ P 3 {\displaystyle G_{G}=G_{3}+G_{2}\cdot P_{3}+G_{1}\cdot P_{2}\cdot P_{3}+G_{0}\cdot P_{1}\cdot P_{2}\cdot P_{3}}
The LCU then generates the carry input for each CLA. Assume that P i {\displaystyle P_{i}} is P G {\displaystyle P_{G}} and G i {\displaystyle G_{i}} is G G {\displaystyle G_{G}} from the ith CLA then the output carry bits are
C 4 = G 0 + P 0 ⋅ C 0 {\displaystyle C_{4}=G_{0}+P_{0}\cdot C_{0}}
C 8 = G 4 + P 4 ⋅ C 4 {\displaystyle C_{8}=G_{4}+P_{4}\cdot C_{4}}
C 12 = G 8 + P 8 ⋅ C 8 {\displaystyle C_{12}=G_{8}+P_{8}\cdot C_{8}}
C 16 = G 12 + P 12 ⋅ C 12 {\displaystyle C_{16}=G_{12}+P_{12}\cdot C_{12}}
Substituting C 4 {\displaystyle C_{4}} into C 8 {\displaystyle C_{8}} , then C 8 {\displaystyle C_{8}} into C 12 {\displaystyle C_{12}} , then C 12 {\displaystyle C_{12}} into C 16 {\displaystyle C_{16}} yields the expanded equations:
C 4 = G 0 + P 0 ⋅ C 0 {\displaystyle C_{4}=G_{0}+P_{0}\cdot C_{0}}
C 8 = G 4 + G 0 ⋅ P 4 + C 0 ⋅ P 0 ⋅ P 4 {\displaystyle C_{8}=G_{4}+G_{0}\cdot P_{4}+C_{0}\cdot P_{0}\cdot P_{4}}
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