<P> where A + B (\ displaystyle A + B) on the right - hand side of the equation is a logical disjunction (i.e., an or). </P> <P> Sometimes a slightly different definition of propagate is used . By this definition A + B is said to propagate if the addition will carry whenever there is an input carry, but will not carry if there is no input carry . Due to the way generate and propagate bits are used by the carry - lookahead logic, it doesn't matter which definition is used . In the case of binary addition, this definition is expressed by </P> <Dl> <Dd> P ′ (A, B) = A ⊕ B (\ displaystyle P' (A, B) = A \ oplus B) </Dd> </Dl> <Dd> P ′ (A, B) = A ⊕ B (\ displaystyle P' (A, B) = A \ oplus B) </Dd>

Ripple carry adder and carry look ahead adder