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Digital Electronics
Figure 7.32 Four-bit full adder with a look-ahead carry generator.
= C i + A i B i A i + B i = C i A i + B i + A i B i A i + B i
= C i A i + B i + A i B i = P i C i + G i
S i = A i ⊕ B i ⊕ C i = A i B i + A i B i ⊕ C i
Also
P i G i ⊕ C i = A i + B i A i B i ⊕ C i
= A i + B i A i + B i ⊕ C i = A i B i + A i B i ⊕ C i
Therefore, S i = P i G i ⊕ C i .