Multiplexer and Adders is one of the important circuits in Electronics.

#### Multiplexer

A multiplexer is a combinational circuit with many data inputs and based on control inputs, single data output are generated.

For N:1 MUX, N number of input lines are required, log2n number of control/selection lines are required.

We can implement various circuits using MUX, to reduce no. of wires, reduce circuit complexity and cost.

#### Full Adder

A full adder is a combinational logic circuit that can add two binary digits plus a carry-in digit to produce a sum and a carry-out digit.There total 3 inputs are required and 2 outputs are generated (sum and carry)

Full Adder is used to perform operations like addition or subtractions. Full Adder is used in the ALU and other processor parts to generate memory addresses, table indices, set the program counter to the next instruction, and many other functions.

**Sometimes we will not get Full Adder in the Market and we have to design Full Adder using another Circuit. The multiplexer is one of the circuits for creating a Full Adder.**

Let's design Full Adder using 8:1 MUX

### Implement Full Adder using 8:1 MUX

First, let's look at the truth table of Full Adder:

A | B | C_{in} |
S | C_{o} |

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 |

Here we can clearly notice only for 4 output, Sum(S) = 1 and are listed below

A | B | S |

0 | 0 | 1 = I_{o} = Cin |

0 | 1 | 1 = I_{1} = Cin' |

1 | 0 | 1 = I_{2 }= Cin' |

1 | 1 | 1 = I_{3} = Cin |

- When A = 0 , B = 0 then Sum = 1 which is same as Cin
- When A = 0 , B = 1 then Sum = 1 which is opposite of Cin ie. Cin'
- When A = 1, B =0 then Sum = 1 which is opposite of Cin ie. Cin'
- When A = 1 , B = 1 then Sum =1 which is same as Cin.

#### Circuit Diagram for Sum:

Also, Here we can clearly notice only for 4 output, Carry(Co) = 1 and are listed below.

A | B | Carry |

0 | 0 | 0 |

0 | 1 | Cin |

1 | 0 | Cin |

1 | 1 | 1 |

#### Circuit Diagram For Carry

As a result, we have implemented Full Adder using only 1 MUX and do not need two XOR gates, as we did when we made Full Adder using Basic Logic Gates.