A NAND gate is a particular type of logic gate in a digital logic circuit that is the opposite of an AND gate. It is a combination of AND and NOT gates and is a commonly used logic gate. It is a “universal” gate in Boolean algebra because it can generate all other logic gates. That means all basic gates like AND, OR, and NOT gates can be constructed using the NAND gate.

NAND gate is a combination of a NOT-AND gate. A NAND gate output state is low only when all inputs are high. This gate returns the complement result of an AND gate. A logic or Boolean expression for a NAND gate is either a full stop or the complement of logical multiplication of inputs represented by a single dot.

(A.B)’=Y

## NAND GATE

A NAND gate has a single output and one or more inputs. The output of a NAND gate is always at logic one and goes to logic 0 only when all inputs to the NAND gate are at logic 1. The output of a NAND gate is always true for at least one of its inputs. It remained wrong. The function of a NAND gate is sometimes called the Scheffer stroke function.

**Types of AND Gate:**

### 2-input NAND Gate

A given logic or Boolean expression for a logic NAND gate is the opposite of an AND gate and operates on the complements of the inputs. Its Boolean expression is represented by a single dot or full stop symbol, ( . ) with a line or overline, ( ‾‾ ) returns a Boolean expression to describe the NOT or logical negation of the NAND gate on the expression: A.B = Pr.

**Design of 2-Input NAND Gate:**

## NAND GATE Truth Table

Input | Input | Output |

A | B | Y |

0 | 0 | 1 |

0 | 1 | 1 |

1 | 0 | 1 |

1 | 1 | 0 |

The expression for this 2-input logic NAND gate is Q = A.B

### 3-input NAND Gate:

In addition to the AND function seen earlier, the NAND function can have any number of individual inputs, and commercially available NAND gate ICs are available in standard 2, 3, or 4 input types. If additional inputs are required, for example, traditional NAND gates can be cascaded together to provide more inputs.

**Design of 3-Input NAND Gate:**

**Truth Table of 3-Input NAND Gate:**

Input | Input | Output |

A | B | Y |

0 | 0 | 1 |

0 | 1 | 1 |

1 | 0 | 1 |

1 | 1 | 1 |

1 | 0 | 1 |

1 | 0 | 1 |

1 | 1 | 1 |

1 | 1 | 0 |

The expression for this 3-input logic NAND gate is Q = A.B.C

### Multiple input NAND Gate

Similar to AND, NOT, and OR gates, we can design an n-input NAND gate. If the number of inputs is odd, any “unused” input can be kept high by connecting that to the power supply using high “matching” pull-up resistors. A 4-input NAND gate has the following expression:

The expression for this 4-input logic NAND gate is Q = A.B.C.D

The number of inputs is odd, but any “unused” inputs can be made redundant by connecting them to the power supply using suitable “pull-up” resistors.

**Why NAND gate is a universal gate?**

OR, AND, and NOT gates are the basic gates in electronic physics. We can create any logic gate or any boolean expression by combining the combination of these gates.

But NOR gates and NAND gates have the specific property that anyone can generate any logical Boolean expression if designed appropriately, so they are called universal gates.

To realize complex equations using only a NAND gate, first, simplify the equation to the simplest possible form and, if necessary, design the circuit using a NAND gate using Demorgon’s rule.

For example, you want to realize AB+CD using a NAND gate.

AB+CD=((AB)'(CD)’)’

This is easily realized using a NAND gate.

**Difference between NAND gate vs NOR gate.**

NAND | NOR |

NAND gate is the combination of NOT gate and AND gate. | NOR gate is a combination of NOT and OR gate. |

The output of a NAND gate is the complement of the product of the input. | The NOR gate output is the sum complement of the input. |

NAND gate is bubbled rather than a gate. | NOR gate bubble or gate. |

In a NAND gate, the output is high if any input is low. | Output is high when both inputs of the NOR gate are low. |

In a NAND gate, if all inputs are high, then the input is low. | In a NOR gate, the output is low if any input is high. |

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