** AIM: To Study and Verify the Truth Table of Logic Gates.**

**LEARNING OBJECTIVE**: Identify various ICs and their specification.

**COMPONENTS REQUIRED:**

- Logic gates (IC) trainer kit.
- Connecting patch chords.
- IC
- IC 7404 NOT GATE
- IC 7408 AND GATE
- IC 7432 OR GATE
- IC 7400 NAND GATE
- IC 7486 XOR GATE
- IC 7402 NOR GATE
- IC 74266 XNOR GATE

**THEORY**:

The basic logic gates are the building blocks of more complex logic circuits. These logic gates perform the basic Boolean functions, such as AND, OR, NAND, NOR, Inversion, Exclusive-OR, Exclusive-NOR. Fig. below shows the circuit symbol, Boolean function, and truth. It is seen from the Fig that each gate has one or two binary inputs, A and B, and one binary output, C. The small circle on the output of the circuit symbols designates the logic complement. The AND, OR, NAND, and NOR gates can be extended to have more than two inputs. A gate can be extended to have multiple inputs if the binary operation it represents is commutative and associative.

The different types of logic gates are:

### NOT Gate

The inverter is a logic gate which has only one input & one output. In inverter is Always opposite of input.

which means if set input LOW is output HIGH.if set input HIGH is output is LOW. the output is given below.

Logic equation is: X = X Digital IC for NOT: IC 7404.

TRUTH TABLE | |||
---|---|---|---|

INPUT | OUTPUT | ||

X | X = X | DIAGRAM | |

0 | 1 | ||

1 | 0 |

IC: 7404 NOT GATE USING UNIVERSAL GATES

NOT GATE USING NAND | NOT GATE USING NOR GATE |
---|---|

### AND Gate

AND gate is a logic gate Which can have two or more inputs.But there is only one output.

The output of AND gate is high only if all inputs are HIGH .

Even if one input is LOW the output is LOW. the output is given below.

Logic equation is: X = A . B Digital IC for AND: IC 7408.

TRUTH TABLE | |||
---|---|---|---|

INPUT | OUTPUT | ||

A | B | X = A . B | DIAGRAM |

0 | 0 | 0 | |

0 | 1 | 0 | |

1 | 0 | 0 | |

1 | 1 | 1 |

IC:7408 AND GATE USING UNIVERSAL GATES

AND GATE USING NAND | AND GATE USING NOR GATE |
---|---|

### OR Gate

OR gate is a logic gate Which can have two or more inputs.But there is only one output.

The output of OR gate is HIGH only if a one of the inputs are HIGH Even if one input is LOW, the output will HIGH. Only when both of input is zero the output will also LOW. the output is given below.

Logic equation is: X = A + B Digital IC for OR: IC 7432.

TRUTH TABLE | |||
---|---|---|---|

INPUT | OUTPUT | ||

A | B | X = A + B | DIAGRAM |

0 | 0 | 0 | |

0 | 1 | 1 | |

1 | 0 | 1 | |

1 | 1 | 1 |

IC: 7432 OR GATE USING UNIVERSAL GATES

OR GATE USING NAND | OR GATE USING NOR GATE |
---|---|

### NAND Gate

NAND gate is a logic gate Which can have two or more inputs.But there is only one output.

NAND is Compliment of AND .The output of NAND gate is HIGH only if one inputs are HIGH or both input being LOW.if both input is HIGH the output is LOW, the output is given below.

Logic equation is: X = A . B Digital IC for NAND: IC 7400.

TRUTH TABLE | |||
---|---|---|---|

INPUT | OUTPUT | ||

A | B | X = A . B | DIAGRAM |

0 | 0 | 1 | |

0 | 1 | 1 | |

1 | 0 | 1 | |

1 | 1 | 0 |

IC: 7400 NAND GATE USING UNIVERSAL GATES

NAND GATE | NAND GATE USING NOR GATE |
---|---|

### XOR Gate

XOR gate is a logic gate Which can have two or more inputs.But there is only one output.

The output of XOR gate is HIGH only if one of the inputs are HIGH.

if both input is same the output is LOW, the output will below.

Logic equation is:X = A ⊕ B Digital IC for XOR: IC 7486.

TRUTH TABLE | |||
---|---|---|---|

INPUT | OUTPUT | ||

A | B | X = A ⊕ B | DIAGRAM |

0 | 0 | 0 | |

0 | 1 | 1 | |

1 | 0 | 1 | |

1 | 1 | 0 |

IC: 7486 XOR GATE USING UNIVERSAL GATES

XOR | XOR UISNG NAND GATE | XOR GATE USING NOR GATE |
---|---|---|

### NOR Gate

NOR gate is a logic gate Which can have two or more inputs.But there is only one output.

NOR Gate is Compliment of OR. The output of NOR gate is HIGH only if both inputs are LOW.if Any input is HIGH the output is LOW, the output is given below.

Logic equation is: X = A + B Digital IC for NOR: IC 7402.

TRUTH TABLE | |||
---|---|---|---|

INPUT | OUTPUT | ||

A | B | X = A + B | DIAGRAM |

0 | 0 | 1 | |

0 | 1 | 0 | |

1 | 0 | 0 | |

1 | 1 | 0 |

IC: 7402 NOR GATE USING UNIVERSAL GATES

NOR GATE | NOR GATE USING NAND GATE |
---|---|

### XNOR Gate

XNOR gate is a logic gate. Which can have two or more inputs.But there is only one output.

XNOR Is Compliment of XOR . The output of NAND gate is HIGH only if Both inputs are same.

if both input is different the output is LOW, the output will below.

Logic equation is:X = A ⊕ B Digital IC for XNOR : IC: 74266.

TRUTH TABLE | |||
---|---|---|---|

INPUT | OUTPUT | ||

A | B | X = A ⊕ B | DIAGRAM |

0 | 0 | 1 | |

0 | 1 | 0 | |

1 | 0 | 0 | |

1 | 1 | 1 |

IC: 74266 XNOR GATE USING UNIVERSAL GATES

XNOR | XNOR GATE USING NAND GATE | XNOR GATE USING NOR GATE |
---|---|---|

Designing and Simulating Digital Logic Circuits

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