Circuits for binary addition

• Half adder (add 2 1-bit numbers)

  • Sum = Ai' Bi + Ai Bi' = Ai xor Bi
  • Cout = Ai Bi

• Full adder (carry-in to cascade for multi-bit adders)

  • Sum = Ci xor A xor B
  • Cout = B Ci + A Ci + A B = Ci (A + B) + A B

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