## The Half Adder

We can construct a half adder, an essential component of binary arithmetic, which take a two one bit binary numbers – 0's or 1's – add the result and outputs the result as a two bit binary number (CARRY BIT)( SUM BIT) (the SUM is like the units in decimal arithmetic) where the CARRY and SUM BIT's are either 0's or 1's.The SUM BIT is the output of a XOR gate. In binary arithmetic, a 1 is left in the units column as a result of adding 0 and 1 or 1 and 0 and a carry is only produced if both A and B are 1.

The truth table for a half adder is shown below.

A | B | CARRY BIT | SUM BIT |

0 | 0 | 0 | 0 |

1 | 0 | 0 | 1 |

0 | 1 | 0 | 1 |

1 | 1 | 1 | 0 |