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Universal Logic Gates (NAND, NOR)

Universal Logic Gates: In this tutorial, we are going to learn about the Universal Logic Gates which are NAND Gate and NOR Gate.
Submitted by Saurabh Gupta, on November 13, 2019

NAND and NOR Gates are known as Universal Logic Gates, because we can realize any logic circuit or gate only by using NAND or NOR gates single-handedly.

Although the logic circuit of any complexity can be realized using three basic gates i.e., AND, OR, NOT Gates, but they can also be realized using only a single type of gate, that is why sometimes NAND and NOR gates are called "universal building blocks". Thus, AOI logic can be converted into NAND or NOR logic.

1) NAND Gate

NAND Gate is a combination of two gates. It is an AND Gate followed by a NOT Gate where the output of AND Gate is inverted using a NOT Gate to get the final output. The logic operation for the NAND gate can be written as Y= A.B

Symbol and Truth Table for a two-input NAND Gate is:

NAND Gate

2) NOR Gate

NOR Gate is also a combination of two gates namely, OR Gate followed by a NOT Gate where the output of OR Gate is inverted using a NOT Gate to get the final output. The logic operation of NOR Gate can be written as Y = A+B

NOR Gate

Question 1: Realize the following gates by only using NAND Gates.

  1. AND
  2. OR
  3. NOT
  4. NOR
  5. XOR
  6. XNOR

Answer:

  1. AND Gate can be implemented using NAND Gate as:

    Universal Logic Gate | Question 1 (i)

  2. OR Gate can be implemented using NAND Gate as:

    Universal Logic Gate | Question 1 (ii)

  3. NOT Gate can be implemented using NAND Gate as:

    Universal Logic Gate | Question 1 (iii)

  4. NOR Gate can be implemented using NAND Gate as:

    Universal Logic Gate | Question 1 (iv)

  5. XOR Gate can be implemented using NAND Gate as:

    Universal Logic Gate | Question 1 (v)

  6. XNOR Gate can be implemented using NAND Gate as:

    Universal Logic Gate | Question 1 (vi)

Question 2: Realize the following gates by only using NOR Gates.

  1. AND
  2. OR
  3. NOT
  4. NOR
  5. XOR
  6. XNOR

Answer:

  1. AND Gate can be implemented using NOR Gate as:

    Universal Logic Gate | Question 2 (i)

  2. OR Gate can be implemented using NOR Gate as:

    Universal Logic Gate | Question 2 (ii)

  3. NOT Gate can be implemented using NOR Gate as:

    Universal Logic Gate | Question 2 (iii)

  4. NAND Gate can be implemented using NOR Gate as:

    Universal Logic Gate | Question 2 (iv)

  5. XOR Gate can be implemented using NOR Gate as:

    Universal Logic Gate | Question 2 (v)

  6. XNOR Gate can be implemented using NOR Gate as:

    Universal Logic Gate | Question 2 (vi)






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