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 = Cin xor A xor B
  • Cout = B Cin + A Cin + A B = Cin (A + B) + A B

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