This article describes the implementation of the NOR gate from NAND gate. NOR and NAND gates are universal logic gates that can implement any logic gate or logical expression.

## What is a NOR Gate?

**NOR Gate** is a universal logic gate that can be used to implement any other type of logic gate.

NOR is a combination of OR and NOT gates, as its output is the inversion of the OR output.

A NOR gate is a logic gate that produces a HIGH (Logic 1) output when all of its inputs are LOW (Logic 0). If any of the inputs are HIGH (Logic 1), the output will be LOW (Logic 0). The symbol used to represent a two-input NOR gate in logic circuits is illustrated in Figure 1.

### Output Equation of NOR Gate

If A and B are input variables and Y is the output variable of a NOR gate, then the output is given by:

It is read as “Y equals A plus B whole bar.

### Truth Table of NOR Gate

The truth table of a logic gate shows the relationship between inputs and output. Below is the truth table of the NOR gate.

Input | Output | |
---|---|---|

A | B | |

0 | 0 | 1 |

0 | 1 | 0 |

1 | 0 | 0 |

1 | 1 | 0 |

## What is a NAND Gate?

The NAND Gate is a universal logic gate that can be used to realize all types of logic gates.

A NAND gate combines an AND gate and a NOT gate.

A NAND gate is a logic gate that produces a LOW output (Logic 0) only when all its inputs are high. Conversely, its output is HIGH (Logic 1) when any of its inputs is LOW (Logic 0). Thus, the NAND gate performs the opposite function of an AND gate. The logic symbol for a two-input NAND gate is depicted in the figure below.

### Output Equation of NAND Gate

If A and B are the input variables and Y is the output variable of the NAND gate, then the output of the gate can be determined using the following logical expression.

It is read as Y equals A.B whole bar.

### Truth Table of NAND Gate

The truth table of the NAND gate is shown below.

Input | Output | |
---|---|---|

A | B | |

0 | 0 | 1 |

0 | 1 | 1 |

1 | 0 | 1 |

1 | 1 | 0 |

Now, let us discuss implementing a NOR gate using a NAND gate.

## Implementation of NOR Gate from NAND Gate

The NAND gate is a universal gate that can be used to implement the NOR gate. The diagram below shows how the NOR Gate is realized from the NAND gate.

The logic circuit demonstrates that we need four NAND gates to create a NOR gate using only NAND gates. The first two NAND gates complement the input variables A and B. The outputs of gates 1 and 2 are A bar and B bar, respectively. The third NAND gate produces the NAND logic output of complement variables A bar and B bar. The fourth gate inverts the output of the third gate, and the output Y is equivalent to the NOR gate output.

The third NAND gate produces the NAND output of the complemented inputs, A’ and B’. Finally, the fourth NAND gate acts as an inverter and generates the output Y, equivalent to the NOR gate output.

Output of 1^{st} gate is,

Output of 2nd gate is,

The output of the 3^{rd} gate is,

Using De Morgan’s Theorem, we can simplify the above boolean expression,

The output of the fourth gate is,

The above boolean expression is equal to the output of the NOR gate.

Thus, using NAND gates exclusively, we can construct a NOR gate.

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