The NAND and NOR gates are called **universal gates**. That is universal gates can be used in combination to perform the AND, OR and inverter operations.

**NAND**

The term NAND implies the function of an AND gate with an inverted output. The logic symbol of NAND gate is equivalent to an **AND gate followed by an inverter**. NAND operation is represented by a bar over the AND expression.

The NAND gate produces a LOW output only when all of its inputs are HIGH. That is for a two-input NAND gate OUTPUT, X is LOW when both inputs A and B are HIGH. X is HIGH if either A or B is LOW, or when both are LOW.

This operation is described in the truth table.

INPUT (A) | INPUT (B) | OUTPUT (X) |
---|---|---|

LOW | LOW | HIGH |

LOW | HIGH | HIGH |

HIGH | LOW | HIGH |

HIGH | HIGH | LOW |

### Implementation of Logic Operations Using NAND Gate only

All logic gates can be implemented using NAND gate only.

#### NOT using NAND gate only

#### OR using NAND gate only

#### AND using NAND gate only

#### NOR using NAND gate only

**NOR**

The term NOR implies the function of an **OR gate with an inverted output**. The logic symbol of NOR gate is equivalent to an OR gate followed by an inverter. NOR operation is represented by a bar over the OR expression.

The NOR gate produces a LOW output when any of its inputs are HIGH. That is for a two-input NAND gate OUTPUT, X is LOW when either input A or B is HIGH or when both A and B is HIGH. X is HIGH only when both A and B is LOW

The operation is summarized in the following truth table.

INPUT (A) | INPUT (B) | OUTPUT(X) |
---|---|---|

LOW | LOW | HIGH |

LOW | HIGH | LOW |

HIGH | LOW | LOW |

HIGH | HIGH | LOW |

### Implementation of Logic Operations Using NOR Gate only

Since NOR gate is a universal gate, its combination can be used to implement any other logic operation.

#### NOT using NOR gate only

#### OR using NOR gate only

#### AND using NOR gate only

#### NAND using NOR gate only

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There is a small error on logic operations on nor gate

In the last portion it is NAND using NOR gate only

“Ooops! Thanks for catching that.