Carry-lookahead logic

• Carry generate: gi = Ai Bi

  • must generate carry when A = B = 1

• Carry propagate: pi = Ai xor Bi

  • there will be a carry-out if there is a carry-in

• Sum and Cout can be re-expressed in terms of generate/propagate:

  • Si = Ai xor Bi xor Ci = pi xor Ci
  • Ci+1 = Ai Bi + Ai Ci + Bi Ci = Ai Bi + Ci (Ai + Bi) = Ai Bi + Ci (Ai xor Bi) = gi + Ci pi

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