Digital Electronics: Principles, Devices and Applications

Arithmetic Circuits 257C4P3G3C3P2G2P1C2G1C1Figure 7.31Look-ahead carry generator.Example 7.7If the CARRY GENERATE G i and CARRY PROPAGATE P i are redefined as P i = A i + B i ) andG i = A i B i show that the CARRY output C i+1 and the SUM output S i of a full adder can be expressedby the following Boolean functions:SolutionC i+1 = C i G i + P i = G i + P i C i and S i = P i G i ⊕ C iC i+1 = C i G i + P i = C i A i B i + A i + B i = C i A i B i A i + B i