# Half-Adder

Half-adder is a simple combinational circuit that can add only two bits together. It is a combination of XOR gate and AND gate where XOR gate is used to perform addition and AND gate is used to get the *carry output*.

### Boolean Function

Sum = X XOR Y;

Carry = XY

### Truth Table

Input | Output | ||
---|---|---|---|

x | y | sum | carry |

0 | 0 | 0 | 0 |

0 | 1 | 1 | 0 |

1 | 0 | 1 | 0 |

1 | 1 | 0 | 1 |

Half-adder receives two inputs and produces two outputs. The inputs are the two bits to be added and the outputs are sum and carry.

The logic diagram for half-adder has two gates: XOR and AND. The XOR gates produces sum and AND get produces carry. For example if the inputs are 0 and 1 then the output of XOR gate will be the sum, 1 and carry, 0.

The disadvantage is that it will not be useful for adding large binary numbers.