Last Updated on May 1, 2023 by Electricalvolt

In this article, we will discuss the definition, symbol, truth table, and equivalent circuit diagram of a logic NOR gate. So let’s get started with the basic definition of NOR Gate.

**What is a NOR Gate?**

In digital logic circuits, the NOR gate is a type of universal logic gate that combines the operation of two basic logic gates namely, OR gate and NOT gate. Therefore, it is also specified as a **NOTed OR Gate**.

The NOR gate has a high output or logic 1 if all its inputs are low or logic 0. If one or all inputs of the NOR gate be high or logic 1, then it produces a low or logic 0 at the output.

Therefore, NOR gate basically performs the negation of the OR gate.

The NOR gate is considered a **universal logic gate** because it can perform all three basic logic operations, i.e.**, OR, AND, and NOT.**

The logic symbols of** two-input and three-input NOR gates** are represented in the following figure.

**Logic NOR Gate Equivalent**

NOR gate can be formed by an OR Gate and NOT gate.

The output of the OR gate is the sum of the input. When the sum of the OR gate is inverted using a NOT gate, we get output that is equivalent to the output of the NOR Gate.

**Logic Expression of NOR Gate**

The **logic expression of a two-input NOR gate** is given by the following equation:

Where, Y is the output of the NOR gate, and A and B are the input variables of the NOR gate.

For the **three-input NOR gate**, the logical expression is given by the following equation:

**Operation of NOR Gate**

The following points explain the **operation of a two-input NOR gate** for different input combinations:

- When A = 0 and B = 0, then the output Y is equal to 1 (as per the logical expression given above).
- When A = 0 and B = 1, then the output Y is equal to 0.
- When A = 1 and B = 0, then the output Y is equal to 0.
- When A = 1 and B = 1, then the output Y is equal to 0.

The **operation of a three-input NOR gate** is explained below:

- When A = 0, B = 0, and C = 0, the output Y is equal to 1, refer above logical expression of the three-input NOR gate.
- When A = 0, B = 0, and C = 1, the output Y is equal to 0.
- When A = 0, B = 1, and C = 0, the output Y is equal to 0.
- When A = 0, B = 1, and C = 1, the output Y is equal to 0.
- When A = 1, B = 0, and C = 0, the output Y is equal to 0.
- When A = 1, B = 0, and C = 1, the output Y is equal to 0.
- When A = 1, B = 1, and C = 0, the output Y is equal to 0.
- When A = 1, B = 1, and C = 1, the output Y is equal to 0.

**Truth Table of NOR Gate**

The truth table is a table that represents the operation of a logic gate for different input combinations.

The **truth table of a two-input NOR gate** is given below:

**2-input Logic NOR Gate**

Inputs | Output | |

A | B | Y |

0 | 0 | 1 |

0 | 1 | 0 |

1 | 0 | 0 |

1 | 1 | 0 |

**3-input Logic NOR Gate**

For the **three-input NOR gate**, the truth table is given below:

Inputs | Output | ||

A | B | C | Y |

0 | 0 | 0 | 1 |

0 | 0 | 1 | 0 |

0 | 1 | 0 | 0 |

0 | 1 | 1 | 0 |

1 | 0 | 0 | 0 |

1 | 0 | 1 | 0 |

1 | 1 | 0 | 0 |

1 | 1 | 1 | 0 |

**4-input NOR Function**

For the 4-input NOR gate, five NOR Gates of 2-inputs are required. For the 6-input NOR Gate, three NOR Gates of 2-input are required. Now, if there are 5 inputs, then we need Nine NOR Gates of 2 inputs, and one unused input is held LOW by connecting the unused input to the ground.

Thus, If the required number of inputs is an odd number of inputs, then “unused” inputs should be directly connected to the ground with a suitable pull-down resistor.

The **Logic NOR Gate** function is also called the **Pierce Function** and it is denoted by a downwards arrow operator as A↓B.

**Equivalent Circuit Diagram of NOR Gate**

The equivalent circuit diagram or switching circuit diagram of a NOR gate is represented in the following figure.

Here, when both switches A and B are open, the bulb will glow, while when switch, either A or B is closed, the bulb will not glow.

Hence, this is all about the NOR logic gate, its operation, truth table, and logical expression in digital electronics.

**Logic NOR Gate using Transistors**

Logic Nor Gate can be constructed using a transistor and resistor circuit. The circuit diagram of NOR gate using a combination of resistors and transistors is given below.

- When input A and input B is zero, transistor Q
_{1}and Q_{2}will remain in the off state and no collector current flow through the transistor. Therefore, the drop across resistance RE is zero and Vout=5 Volts, thus we get output 1 when A=0 and B=0 - When A=0 and B=1, the transistor Q
_{2}conducts and V_{out}=0 - When A=1 and B=0, the transistor Q
_{1 }conducts and V_{out}=0 - When A=1 and B=1, the transistor Q
_{1}and Q_{2}conducts and V_{out}=0

**Other Logic Gates using only NOR Gates**

**OR Gate**

**NOR Gate Integrated Circuits**

The following are the NOR Gate integrated circuits widely used in digital circuits.

TTL Logic NOR Gates | CMOS Logic NOR Gates |

74LS02 Quad 2-input | CD4001 Quad 2-input |

74LS27 Triple 3-input | CD4025 Triple 3-input |

74LS260 Dual 5-input | CD4002 Dual 4-input |

**7402 Quad 2-input Logic NOR Gate**

Pinout diagram of 7402 IC is;

**74LS27 Triple 3-input**

It contains three inputs NOR gates.

**74LS260 Dual 5-input**

It has five inputs NOR gates.

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