# FHSST Physics/Electronics/Counting Circuits

# Counting circuits[edit]

An arithmetic and logical unit (ALU) adder provides the basic functionality of arithmetic operations within a computer, and is a significant component of the arithmetic and logical unit. Adders are composed of half adders and full adders, which add two-bit binary pairs, and ripple carry adders and carry look ahead adders which do addition operations to a series of binary numbers.

*Note: Pictures on wikipedia under GFDL*

## Half Adder[edit]

A half adder is a logical circuit that performs an addition operation on two binary digits. The half adder produces a sum and a carry value which are both binary digits.

Sum(s) = A xor B Cot(c) = A and B

Following is the logic table for a half adder:

A | B | Sum | Cot |

0 | 0 | 0 | 0 |

0 | 1 | 1 | 0 |

1 | 0 | 1 | 0 |

1 | 1 | 0 | 1 |

## Full adder[edit]

A full adder is a logical circuit that performs an addition operation on three binary digits. The full adder produces a sum and carry value, which are both binary digits.

Sum = (A xor B) xor Cin

Cot = (A nand B) nand (Cin nand (A xor B))

A | B | Cin | Sum | Cot |

0 | 0 | 0 | 0 | 0 |

0 | 0 | 1 | 1 | 0 |

0 | 1 | 0 | 1 | 0 |

0 | 1 | 1 | 0 | 1 |

1 | 0 | 0 | 1 | 0 |

1 | 0 | 1 | 0 | 1 |

1 | 1 | 0 | 0 | 1 |

1 | 1 | 1 | 1 | 1 |