**What Is Boolean Logic & Basic Logic Gates? Symbols & Truth table.**

Table of Contents

**What Is Boolean Logic?**

* Boolean logic* refers to the form of algebra where the variables have only 2 unique values i.e. TRUE or FALSE. These values are often used as

**1**or

**0**in binary language.

**Boolean function**

A **Boolean function** is a logical operation of one or more than one variables whose resultant is a single binary bit. It can only be either TRUE or FALSE. Boolean functions are based on** boolean logic**.

**Digital Logic Gate**

A **digital logic gate** is a device which implements any Boolean function. Some of these basic logic gates are given below:

**NOT Gate**

**NOT gate** is a basic digital logic gate. This digital logic gate **inverts** its input into output. It is also known as **Inverter**. It is also sometimes referred to as **negation buffer**. NOT gate is a **single input single output gate**.

The logical operator for NOT is **‘!’** and it inverts its operand’s value.

The **Truth table** for NOT gate is:

Input | Output |

1 | 0 |

0 | 1 |

**AND Gate**

This digital logic gate implements the logical **AND function**, which is the **Boolean product** of **two** or more than two variables. AND operation is also known as a **logical conjunction**. In other words, **the output of AND gate is TRUE when all of its inputs are TRUE**.

AND function’s operator, the logical conjunction is denoted by ‘**Λ’** or ‘**.’**.

**AND gate** has minimum two inputs and a **single output**. The truth table for AND gate is:

Input 1 | Input 2 | Output |

0 | 0 | 0 |

0 | 1 | 0 |

1 | 0 | 0 |

1 | 1 | 1 |

**OR Gate:**

Digital logic **OR Gate** implements the logical **OR function**. Logical OR function gives TRUE output if any of its operands are **TRUE**. Thus, *the output of OR gate is True if any of its Input is TRUE.*

OR logic function is also known as **inclusive disjunction**. And its operator is **‘∨’** or **‘+’**.

**OR gate** has a minimum of two inputs and a **single output**. The truth table for OR gate is:

Input 1 | Input 2 | Output |

0 | 0 | 0 |

0 | 1 | 1 |

1 | 0 | 1 |

1 | 1 | 1 |

**NAND Gate:**

**NAND Gate** is a digital logic gate which performs **negative AND function**. As its name suggests, NAND (NOT of AND) operation **inverts** the output of **AND operation**. In other words, *the output of NAND gate is False only when all of its inputs are high.*

**NAND gate** has minimum two inputs and a single output.

**NAND gate’s** truth table is

Input 1 | Input 2 | Output |

0 | 0 | 1 |

0 | 1 | 1 |

1 | 0 | 1 |

1 | 1 | 0 |

**NOR Gate:**

The digital **NOR **gate is a **Negative-OR** gate. The operation of NOR is **negation** or NOT of **logical OR** gate. In other words, the output of NOR gate is **LOW** when any of its input is **HIGH**.

It has minimum two inputs and a single output.

The truth table of NOR gate is

Input 1 | Input 2 | Output |

0 | 0 | 1 |

0 | 1 | 0 |

1 | 0 | 0 |

1 | 1 | 0 |

**XOR GATE:**

**Exclusive-OR** or **XOR gate** is a digital gate used as a **parity checker**. XOR gate gives output **TRUE** when the **numbers** of TRUE inputs are **odd**. For a **two-input** XOR gate, the output is **TRUE** if the **inputs** are **different**. Otherwise, the gate will produce **FALSE** output.

The truth table of XOR gate is following

Input 1 | Input 2 | Output |

0 | 0 | 0 |

0 | 1 | 1 |

1 | 0 | 1 |

1 | 1 | 0 |

**XNOR GATE:**

**XNOR gate** or **Exclusive NOR** gate is the negative or **inverse of XOR** gate. Generally, XNOR gate give **output TRUE** if it has **EVEN number** of TRUE inputs. The output of **two-input** XNOR gate is **TRUE** if the inputs are **same**. When the inputs are different, the 2-input XNOR gate produces FALSE output.

The following is the Truth table for XNOR gate

Input 1 | Input 2 | Output |

0 | 0 | 1 |

0 | 1 | 0 |

1 | 0 | 0 |

1 | 1 | 1 |

you may also read: