Arithmetic Circuits
257
C 4
C 3
C 2
P 3
G 3
P 2
G 2
P 1
G 1
C 1
Figure 7.31 Look-ahead carry generator.
Example 7.7
If the CARRY GENERATE G i and CARRY PROPAGATE P i are redefined as P i = A i + B i ) and
G 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 expressed
by the following Boolean functions:
C i+1 = C i G i + P i = G i + P i C i and S i = P i G i ⊕ C i
Solution
C i+1 = C i G i + P i = C i A ii B i + A i + B i
= C i A i B i A i + B i
257
C 4
C 3
C 2
P 3
G 3
P 2
G 2
P 1
G 1
C 1
Figure 7.31 Look-ahead carry generator.
Example 7.7
If the CARRY GENERATE G i and CARRY PROPAGATE P i are redefined as P i = A i + B i ) and
G 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 expressed
by the following Boolean functions:
C i+1 = C i G i + P i = G i + P i C i and S i = P i G i ⊕ C i
Solution
C i+1 = C i G i + P i = C i A ii B i + A i + B i
= C i A i B i A i + B i