**Full Subtractor-**

- Full Subtractor is a combinational logic circuit that is used for the purpose of subtracting two single bit numbers taking into consideration borrow of the lower significant stage.
- Thus, Full Subtractor has the ability to perform the subtraction of three bits unlike half subtractor which can subtract only two bits.
- It contains 3 inputs and 2 outputs (Difference and Borrow).

**Designing a Full Subtractor-**

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

**Step-04:**

Draw the logic diagram-

**Logic Diagram**

Here, Full Subtractor has been implemented using 1 XOR gate, 3 AND gates and 1 OR gate.

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Summary

Article Name

Full Subtractor

Description

Full Subtractor is a combinational logic circuit that is used for the purpose of subtracting two single bit numbers with a borrow of the lower significant stage unlike half subtractor which can subtract only two bits. It contains 3 inputs and 2 outputs (Difference and Borrow).

Author

Akshay Singhal

Publisher Name

Gate Vidyalay

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