**Arithmetic circuits** can perform seven different arithmetic operations using a single composite circuit.

It uses a full adder (FA) to perform these operations. A multiplexer (MUX) is used to provide different inputs to the circuit in order to obtain different arithmetic operations as outputs.

**4-bit Arithmetic Circuit : **

Consider the following 4-bit Arithmetic circuit with inputs A and B. It can perform seven different arithmetic operations by varying the inputs of the multiplexer and the carry (C_{0}).

**Truth Table for the above Arithmetic Circuit :**

S_{0} | S_{1} | C_{0} | MUX Output | Full Adder Output |
---|---|---|---|---|

0 | 0 | 0 | B | A + B |

0 | 0 | 1 | B | A + B + 1 |

0 | 1 | 0 | B’ | A + B’ |

0 | 1 | 1 | B’ | A + B’ + 1 = A – B |

1 | 0 | 0 | 0 | A |

1 | 0 | 1 | 0 | A + 1 |

1 | 1 | 0 | 1 | A – 1 |

1 | 1 | 1 | 1 | A – 1 + 1 = A |

Hence, the different operations for the inputs A and B are –

- A + B (adder)
- A + B + 1
- A + B’
- A – B (subtracter)
- A
- A + 1 (incrementer)
- A – 1 (decrementer)