Hello Guys, Today we are going to discuss another important topic of basic electronics, i.e., Boolean algebra and logic circuits. This is part two of the number system article which is mentioned here. In today’s article we’ll be going to discuss Logic Gates and the Truth Table for each gate which eases the answer determining value of the problem. We’ll also see some basic examples for easy discussion and problem-solving. So, without distracting, let’s begin.

## BOOLEAN ALGEBRA

So Now it’s time to discuss some boolean algebra, Boolean Algebra is nothing but 2 constants either **True** or **False**. All the logic circuits and gates, give output in either **0** or **1** which is **True** or **False**, **High** or **Low**. Now to understand the Boolean algebra you need to learn first some of its symbol to rear and write logic circuits.

### Boolean Operators

#### NOT

This Operator is symbolized by in many ways like If we take **A** as input then not A is symbolized by **!A ,** **~A**, **A’**, **Ā**. Its use is very simple, it is used to reverse the input given at the output like for 0 it will be 1 and vice versa. This operator is used with single input.

##### TRUTH TABLE

A | Ā |
---|---|

0 | 1 |

1 | 0 |

#### AND

This operator is symbolized by **^**, **.** , **&** operators. This operators give output true if both input are true means in simple words it multiplies the both inputs and then give the product as output. This operators works between two inputs.

##### TRUTH TABLE

A | B | A.B |
---|---|---|

0 | 0 | 0 |

0 | 1 | 0 |

1 | 0 | 0 |

1 | 1 | 1 |

#### OR

This operator is symbolized by **∨**, **+** , **||** operators. This operator gives output true if any one of the input is true. Like, and it works between two operators.

##### TRUTH TABLE

A | B | A+B |
---|---|---|

0 | 0 | 0 |

0 | 1 | 1 |

1 | 0 | 1 |

1 | 1 | 1 |

## Gates & Truth Tables

### NOT GATE

This Logic gate is also called an Inverter Gate, which takes only a single input. The output is the negation or compliment of the input.

#### TRUTH TABLE

X | X̅ |
---|---|

0 | 1 |

1 | 0 |

#### SYMBOL

#### SIMULATION

### AND GATE

This Logic gate works with the two input. This gate gives input true or high if both input are true.

#### TRUTH TABLE

X | Y | X.Y |
---|---|---|

0 | 0 | 0 |

0 | 1 | 0 |

1 | 0 | 0 |

1 | 1 | 1 |

#### SYMBOL

#### SIMULATION

### OR GATE

This Logic gate also works with two input. It gives output true or high if any one of the input is true.

#### TRUTH TABLE

X | Y | X+Y |
---|---|---|

0 | 0 | 0 |

0 | 1 | 1 |

1 | 0 | 1 |

1 | 1 | 1 |

#### SYMBOL

#### SIMULATION

### NOR GATE

This Logic gate is the combination of OR gate followed by an Inverter (NOT) Gate. The output of this gate are reversed as of OR gate so in this case the output will be true only if both input are false or low else it will be false.

#### TRUTH TABLE

X | Y | X+Y | (X+Y)’ |
---|---|---|---|

0 | 0 | 0 | 1 |

0 | 1 | 1 | 0 |

1 | 0 | 1 | 0 |

1 | 1 | 1 | 0 |

#### SYMBOL

#### SIMULATION

### NAND GATE

This Logic Gate is the combination of an AND Gate and an Inverter (NOT) Gate. Also, output are reversed as, if any of the one input is true output will be true else it will be false if both input are false.

#### TRUTH TABLE

X | Y | X.Y | (X.Y)’ |
---|---|---|---|

0 | 0 | 0 | 1 |

0 | 1 | 0 | 1 |

1 | 0 | 0 | 1 |

1 | 1 | 1 | 0 |

#### SYMBOL

#### SIMULATION

### XOR GATE

This Logic Gate works the same as the OR Gate, but the only difference is in the output. The output will be true only if one input is true, else it will be false.

#### TRUTH TABLE

X | Y | X⊕Y |
---|---|---|

0 | 0 | 0 |

0 | 1 | 1 |

1 | 0 | 1 |

1 | 1 | 0 |