NAND gate is the most important logic gate in **digital electronics**. It is one of the universal logic gates. Because, other logical gates can be designed by using NAND gates only. This gate is available in IC form. IC7400 is a popular IC consists of 4 NAND gates. In other articles, **XOR gate**, **XNOR gate** and **basic logic gates **are designed by using NAND gates. A NAND gate can have infinite number of inputs and only one output. In this article, we are going to discuss the NAND gate with 2 inputs, NAND gate with 3 inputs, their symbols, Boolean equations and truth tables.

**Contents in this article:**

**What is a NAND gate?****Symbol of NAND gate****NAND gate with two inputs****NAND gate with three inputs****Truth table of NAND gate with two inputs****Truth table of NAND gate with three inputs****Use of NAND gate**

**What is a NAND gate?**

A NAND gate consists of an AND and a NOT gate in series. NAND gate is a classical logic gate which gives the output as the complement of the multiplication of the inputs. That means it gives the complement of the output of an AND gate. This can be understood from the Boolean expression and truth table which are given below.

**NAND gate Boolean equation**

A NAND gate can have infinite number of inputs and only one output. If A, B, C, D,…. be the binary inputs of a NAND gate then the expression for the Boolean output will be \small \textbf{Y=} \overline{\textbf{ABCD…}}.

For two-input NAND gate we will take up to two inputs and for three-input NAND logic we will take up to three inputs.

**NAND gate with 2 inputs**

A two input NAND gate will have two inputs and only one output. The circuit symbol and the truth table of a NAND gate with 2 inputs are shown below.

**Circuit diagram of NAND gate with 2 inputs**

The circuit symbol of a two input NAND gate is like this –

**NAND gate Truth table with 2 inputs**

Let **A** and **B** be the two inputs in a NAND gate and the output is taken at **Y**. Then the truth table for a two input NAND gate is as following –

Input (A) | Input (B) | Output \small \textbf{Y=} \overline{\textbf{AB}} |

0 | 0 | 1 |

0 | 1 | 1 |

1 | 0 | 1 |

1 | 1 | 0 |

**Truth Table for two input NAND gate**

**NAND gate with 3 inputs**

A three input NAND gate will have three inputs and only one output. The circuit symbol and truth table of NAND gate with 3 inputs are as below.

**Three inputs NAND gate circuit diagram**

Here is the circuit symbol of a NAND gate with three inputs.

**Truth table of NAND gate with 3 inputs**

Let A, B and C be the inputs in a NAND gate and corresponding output is Y. Then the truth table for three input NAND gate is as following-

Input (A) | Input (B) | Input (C) | Output \small \textbf{Y=} \overline{\textbf{ABC}} |

0 | 0 | 0 | 1 |

0 | 0 | 1 | 1 |

0 | 1 | 0 | 1 |

0 | 1 | 1 | 1 |

1 | 0 | 0 | 1 |

1 | 0 | 1 | 1 |

1 | 1 | 0 | 1 |

1 | 1 | 1 | 0 |

**Truth Table of NAND gate with 3 inputs**

**Uses of NAND gate**

- There is an integrated circuit
**IC7400**which consists of four NAND gates. This IC is used in physics and electronics practical labs to construct**basic logic gates.** - One can design Multiplexer and demultiplexer circuits using NAND gates.
**Memory units of computer**are also made of NAND gates.

This is all from this article on **NAND gate circuit diagram and truth table**. If you have any doubt on this topic you can ask me in the comment section.

Thank you!

**Related posts:**

**Basic logic gates with truth tables****Basic logic gates using NAND gate only****XOR gate****NOR gate****XNOR gate****Boolean algebra****Karnaugh map (K-map)**

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