**IMPLEMENTATION OF HALF SUBTRACTOR & FULL SUBTRACTOR**

**AIM:**

**To design and verify the truth table of the Half Subtractor & Full Subtractor circuits.**

**APPARATUS REQUIRED:**

S.No | Name of the Apparatus | Range | Quantity |

1. | Digital IC trainer kit | | 1 |

2. | AND gate | IC 7408 | |

3. | OR gate | IC 7432 | |

4. | NOT gate | IC 7404 | |

5. | EX-OR gate | IC 7486 | |

6. | Connecting wires | As required | |

**THEORY:**

**The arithmetic operation, subtraction of two binary digits has four possible elementary operations, namely,**

**0 - 0 = 0**

**0 - 1 = 1 with 1 borrow**

**1 - 0 = 1**

**1 - 1 = 0**

**In all operations, each subtrahend bit is subtracted from the minuend bit. In case of the second operation the minuend bit is smaller than the subtrahend bit, hence 1 is borrowed.**

**HALF SUBTRACTOR:**

**A combinational circuit which performs the subtraction of two bits is called half subtractor. The input variables designate the minuend and the subtrahend bit, whereas the output variables produce the difference and borrow bits.**

**FULL SUBTRACTOR:**

**A combinational circuit which performs the subtraction of three input bits is called full subtractor. The three input bits include two significant bits and a previous borrow bit. A full subtractor circuit can be implemented with two half subtractors and one OR gate.**

__HALF SUBTRACTOR__**TRUTH TABLE:**

S.No | INPUT | OUTPUT | ||

A | B | DIFF | BORR | |

1. | 0 | 0 | 0 | 0 |

2. | 0 | 1 | 1 | 1 |

3. | 1 | 0 | 1 | 0 |

4. | 1 | 1 | 0 | 0 |

**DESIGN:**

**From the truth table the expression for difference and borrow bits of the output can be obtained as,**

**Difference, DIFF = A**

**B**

**Borrow, BORR = A’ . B**

**CIRCUIT DIAGRAM:**

__FULL SUBTRACTOR__**TRUTH TABLE:**

S.No | INPUT | OUTPUT | |||

A | B | C | DIFF | BORR | |

1. | 0 | 0 | 0 | 0 | 0 |

2. | 0 | 0 | 1 | 1 | 1 |

3. | 0 | 1 | 0 | 1 | 1 |

4. | 0 | 1 | 1 | 0 | 1 |

5. | 1 | 0 | 0 | 1 | 0 |

6. | 1 | 0 | 1 | 0 | 0 |

7. | 1 | 1 | 0 | 0 | 0 |

8. | 1 | 1 | 1 | 1 | 1 |

**DESIGN:**

**From the truth table the expression for difference and borrow bits of the output can be obtained as,**

**Difference, DIFF= A’B’C + A’BC’ + AB’C’ + ABC**

**Borrow, BORR = A’BC + AB’C + ABC’ +ABC**

**Using Karnaugh maps the reduced expression for the output bits can be obtained as,**

__DIFFERENCE__

**DIFF = A’B’C + A’BC’ + AB’C’ + ABC = A**

**B**

**C**

__BORROW__**BORR = A’B + A’C + BC**

**CIRCUIT DIAGRAM:**

**PROCEDURE:**

**Connections are given as per the circuit diagrams.****For all the ICs 7**^{th }pin is grounded and 14^{th}pin is given +5 V supply.**Apply the inputs and verify the truth table for the half subtractor and full subtractor circuits.**

**RESULT:**

**The design of the half subtractor and full subtractor circuits was done and their truth tables were verified.**

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