Carry Look-Ahead Adders -- Basic Idea

Recall that ci = xiyi + xici-1 + yici-1

= xiyi + xiyici-1 + xiyi?ci-1 + xiyici-1 + xi ?yici-1

= xiyi + xiyi?ci-1 + xi ?yici-1

= xiyi + (xiyi? + xi ?yi)ci-1

= xiyi + (xi ? yi)ci-1

Let gi = xiyi [carry generate] (4.33)

pi = xi ? yi [carry propagate] (4.34)

Then ci = gi + pi ci-1

si = pi ? ci-1 (4.38)

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