# Half Adder / Full Adder / Half Subtractor / Full Subtractor:

AIM: To realize

## LEARNING OBJECTIVE:

- To realize the adder and subtractor circuits using basic gates and universal gates
- To realize full adder using two half adders
- To realize a full subtractor using two half subtractors

## COMPONENTS REQUIRED:

- IC 7400
- IC 7408
- IC 7486
- IC 7432
- Patch Cords & IC Trainer Kit

**THEORY:**

### Half-Adder:

A combinational logic circuit that performs the addition of two data bits, A and B, is called a half-adder. Addition will result in two output bits; one of which is the sum bit,

S, and the other is the carry bit, C.

TURTH TABLE | |||
---|---|---|---|

INPUT | OUTPUT | ||

A | B | S = A ⊕ B | C = AB |

0 | 0 | 0 | 0 |

0 | 1 | 1 | 0 |

1 | 0 | 1 | 0 |

1 | 1 | 0 | 1 |

**BASIC GATE**

**OUTPUT**

**HALF ADDER USING NAND**

**HALF ADDER USING NOR**

### Full-Adder:

The half-adder does not take the carry bit from its previous stage into account.

This carry bit from its previous stage is called carry-in bit. A combinational logic circuit that

adds two data bits, A and B, and a carry-in bit, Cin , is called a full-adder.

TURTH TABLE | ||||
---|---|---|---|---|

INPUT | OUTPUT | |||

A | B | C | S =A ⊕ B | C = AB + BC + AC |

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 |

**BASIC GATE**

**OUTPUT**

**FULL ADDER USING NAND**

**FULL ADDER USING NOR**

### Half Subtractor:

Subtracting a single-bit binary value B from another A (i.e. A -B ) produces

a difference bit D and a borrow out bit B-out. This operation is called half subtraction and the

circuit to realize it is called a half subtractor.

TURTH TABLE | |||
---|---|---|---|

INPUT | OUTPUT | ||

A | B | D = A ⊕ B | B = AB |

0 | 0 | 0 | 0 |

0 | 1 | 1 | 1 |

1 | 0 | 1 | 0 |

1 | 1 | 0 | 0 |

**BASIC GATE**

**OUTPUT**

**HALF SUBTRACTOR USING NAND**

**HALF SUBTRACTOR USING NOR**

### Full Subtractor:

Subtracting two single-bit binary values, B, Cin from a single-bit value A

produces a difference bit D and a borrow out Br bit. This is called full subtraction.

TURTH TABLE | ||||
---|---|---|---|---|

INPUT | OUTPUT | |||

A | B | C | D =A ⊕ B ⊕ C | B = AB + BC + AC |

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 |

**BASIC GATE**

**OUTPUT**

**FULL SUBTRACTOR USING NAND**

**FULL SUBTRACTOR USING NOR**

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