**Half Subtractor-**

Before you go through this article, make sure that you have gone through the previous article on **Half Subtractor**.

We have discussed-

- Half Subtractor is used for the purpose of subtracting two single bit numbers.
- Half subtractors have no scope of taking into account “Borrow-in” from the previous circuit.
- To overcome this drawback, full subtractor comes into play.

In this article, we will discuss about Full Subtractor.

##
**Full ****Subtractor-**

- Full Subtractor is a combinational logic circuit.
- It is used for the purpose of subtracting two single bit numbers.
- It also takes into consideration borrow of the lower significant stage.
- Thus, full subtractor has the ability to perform the subtraction of three bits.
- Full subtractor contains 3 inputs and 2 outputs (Difference and Borrow) as shown-

**Designing a Full Subtractor-**

Full subtractor is designed in the following steps-

**Step-01:**

Identify the input and output variables-

- Input variables = A, B, B
_{in }(either 0 or 1) - Output variables = D, B
_{out}where D = Difference and B_{out}= Borrow

**Step-02:**

Draw the truth table-

Inputs |
Outputs |
|||

A |
B |
B_{in} |
B_{out} (Borrow) |
D (Difference) |

0 | 0 | 0 | 0 | 0 |

0 | 0 | 1 | 1 | 1 |

0 | 1 | 0 | 1 | 1 |

0 | 1 | 1 | 1 | 0 |

1 | 0 | 0 | 0 | 1 |

1 | 0 | 1 | 0 | 0 |

1 | 1 | 0 | 0 | 0 |

1 | 1 | 1 | 1 | 1 |

**Truth Table**

**Step-03:**

Draw K-maps using the above truth table and determine the simplified Boolean expressions-

**Also Read-** **Full Adder**

**Step-04:**

Draw the logic diagram.

The implementation of full adder using 1 XOR gate, 3 AND gates, 1 NOT gate and 1 OR gate is as shown below-

To gain better understanding about Full Subtractor,

**Next Article-** **Ripple Carry Adder**

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