Introduction to DLD

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 Gate Using NOR Gate - NAND gate is unavailable, only NOR gate is available

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

NAND Gate Using NOR Gate - NAND Logic Gate

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 - NOR Logic Gate

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 - 2 Inputs

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 - 3 Inputs

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.

NAND Gate Using NOR Gate -4 Inputs