Full subtractor using multiplexer. A full subtractor is a combinational logic circuit. It has three inputs ( each of one bit ) termed as A, B and C_{in} that generates difference ( D ) and borrow ( B_{r} ) in the output. A full subtractor circuit is designed using two AND gate, two NOT gate, two XOR gate, and one OR gate. The XOR gate gives the output for difference and the OR gate gives the output for borrow.

In this article I will show you how can you implement full subtractor using multiplexer. The implementation of full subtractor in 4:1 and 8:1 multiplexer is explained with truth table, conversion & circuit diagram.

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

0 – 0 = 0

1 – 0 = 1

0 – 1 = 1, borrow = 1

1 – 1 = 0

A | B | C | Difference | Borrow |

0 | 0 | 0 | 0 | 0 |

0 | 0 | 1 | 1 | 1 |

0 | 1 | 0 | 1 | 1 |

0 | 1 | 1 | 0 | 1 |

1 | 0 | 0 | 1 | 0 |

1 | 0 | 1 | 0 | 0 |

1 | 1 | 0 | 0 | 0 |

1 | 1 | 1 | 1 | 1 |

## Full Subtractor using Multiplexer ( 8:1 )

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

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

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

### Full Subtractor using Multiplexer ( 4:1 )

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 difference and borrow. Also, there will be separate circuit diagrams.

**The conversion for difference 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 to 7 shows the eight 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 subtractor ( Difference ) in 4:1 MUX is shown in the Circuit below**

**The conversion for borrow is shown in the figure below –**

Similarly for borrow, 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 eight inputs from the truth table. The input signals are taken in terms of A, A’, 0 & 1. The boxes with logic 1 selects signals ( A or A’ )

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

#### Frequently Asked Questions

**What is Multiplexer ( MUX ) ?**

- A multiplexer ( MUX ) is a digital combinational circuit ( logic circuit ). A multiplexer has multiple inputs and a single output. The output signal depends upon the input signal given to the select lines.

**What is 8:1 Multiplexer ?**

- A Multiplexer ( MUX ) that has 8 inputs and a single output is known as 8:1 Multiplexer.

**What is 4:1 Multiplexer ?**

- A Multiplexer ( MUX ) that has 4 inputs and single output is known as 4:1 Multiplexer.

**Author**

Akash Sharma

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