NAND Gate Using NOR Gate

An NAND logic Gate can be made using NOR logic gates. As we know, NOR is a universal logic gate, meaning it can be used to build other logic gates such as OR, AND, NOT, XOR, and XNOR. Implementing a NAND gate using a NOR gate is useful when you need an NAND logic circuit but only have NOR gates available; an NAND logic gate is unavailable.

NAND Logic Gate

The NAND logic gate performs the NOT-AND operation.

• Output (0) only when all inputs are HIGH (1)
• Output HIGH (1) when any input is LOW (0),

The basic NAND logic gate with its truth table is given below

NOR Logic Gate

The NOR logic gate performs the NOT-OR operation.

• Output (1) only when all inputs are LOW (0)
• Output LOW (0) when any input is HIGH (1)

The basic NOR logic gate with its truth table is given below

NAND Gate Using NOR Gate – 2 Inputs

If we want to implement 2-input NAND gate using NOR gate then we need 4 NOR gates (each having 2 inputs).

• First NOR : It inverts the input (0 to 1, or 1 to 0)
• Second NOR : It also inverts the input (0 to 1, or 1 to 0)
• Third NOR : It takes the input of first two NOR gates and produces A · B as a result (by using De Morgan’s law)
• 4th NOR : It also inverts the input. The output of the third NOR gate is given as a input to 4th NOR gate at both ends.This produces the final output, which is equivalent to a 2-input NAND gate.

NAND Gate Using NOR Gate – 3 Inputs

If we want to implement 3-input NAND gate using NOR gate then we need 5 NOR gates (each having 2 inputs).

• First NOR : It inverts the input (0 to 1, or 1 to 0)
• Second NOR : It also inverts the input (0 to 1, or 1 to 0)
• Third NOR : It also inverts the input (0 to 1, or 1 to 0)
• 4th NOR : It takes the input of first three NOR gates and produces A · B. C as a result (by using De Morgan’s law)
• 5th NOR : It also inverts the input. The output of the 4th NOR gate is given as a input to 5th NOR gate at both ends.This produces the final output, which is equivalent to a 3-input NAND gate.

NAND Gate Using NOR Gate – 4 Inputs

If we want to implement 4-input NAND gate using NOR gate then we need 6 NOR gates (each having 2 inputs).

• First NOR : It inverts the input (0 to 1, or 1 to 0)
• Second NOR : It also inverts the input (0 to 1, or 1 to 0)
• Third NOR : It also inverts the input (0 to 1, or 1 to 0)
• 4th NOR : It also inverts the input (0 to 1, or 1 to 0)
• 5th NOR : It takes the input of first four NOR gates and produces A · B. C .D as a result (by using De Morgan’s law)
• 6th NOR : It also inverts the input. The output of the 5th NOR gate is given as a input to 6th NOR gate at both ends.This produces the final output, which is equivalent to a 4-input NAND gate.