In this article I will show you how can you implement full adder in 4:1 and 8:1 multiplexer.

Truth table for full adder is shown below. This truth table is written by the concept of binary addition. That is

0 + 0 = 0

0 + 1 = 1

1 + 0 = 1

1 + 1 = 0, carry = 1.

A | B | C | Sum | Carry |

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 |

## Full Adder using 8:1 mux

Now we will implement this full adder in 8:1 MUX. We will need to have two different multiplexers. The first one for implementing sum and the other one for implementing carry.

**The implementation of Sum is shown in the circuit below –**

**The implementation of Carry is shown in the circuit below –**

## Full Adder using 4:1 mux

Since the 4:1 MUX has only four inputs and the truth table shows 8 inputs. The truth table shown above needs to be converted.

Again we will do separate conversion for both sum and carry. Also there will be separate circuit diagrams.

The conversion for Sum is shown in the figure below

Here, D_{0}, D_{1}, D_{2} & D_{3} are the inputs that will be given to 4:1 multiplexer. The boxes 0 – 7 shows the seven inputs from the truth table. The input signals are taken in terms of A and A’. The boxes with logic 1 selects signals ( A or A’ ).

**Implementation of Full adder ( Sum ) in 4:1 MUX is shown in the Circuit below**

**The conversion for Carry is shown in the figure below-**

Similarly for carry, D_{0}, D_{1}, D_{2} & D_{3} are the inputs that will be given to 4:1 multiplexer. The boxes 0 – 7 shows the seven inputs from the truth table. The input signals are taken in terms of A and A’. The boxes with logic 1 selects signals ( A or A’ )

**Implementation of Full adder ( Carry ) in 4:1 MUX is shown in the Circuit below**

#### Frequently Asked Questions

**What is full adder ?**

- It is a combinational logic circuit. A full adder has three inputs ( each of one bit ) termed as A, B and C
_{in}that generates sum ( S ) and carry ( C ) in the output. A full adder circuit is designed using two AND gate, two XOR gate, and one OR gate. The XOR gate gives the output for sum and the OR gate gives the output for carry.

**What is Multiplexer ( MUX ) ?**

- A MUX or a multiplexer is a digital logic circuit ( combinational circuit ). A multiplexer has many inputs and only one output. The output depends upon the input given to the select lines.

**What is 8:1 Multiplexer ?**

- A Multiplexer that has 8 inputs and only one output is known as 8:1 Multiplexer.

**What is 4:1 Multiplexer ?**

- A Multiplexer that has 4 inputs and only one output is known as 4:1 Multiplexer.

**Author**

Akash Sharma

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