XNOR gate circuit diagram using NAND & NOR gate

XNOR gate is another logical gate which is available in integrated circuit (IC) form. In other articles, we have discussed that NAND gate and XOR gate are also available in IC form. Therefore, these type of logic gates are very much useful in advanced digital electronics. Basic logic gates (OR gate, AND gate and NOT gate), NAND gate, NOR gate and XOR gate are discussed in individual articles. In this article, we are going to discuss the XNOR gate circuit diagram, truth table, Boolean expression and construction of XNOR gate using NAND gates, NOR gates and basic logic gates.

Contents in this article:

  1. What is XNOR gate?
  2. Boolean expression of XNOR gate
  3. Circuit symbol of XNOR logic gate
  4. Truth table for XNOR gate
  5. 3 input XNOR gate
  6. Circuit diagram of XNOR gate with basic logic gates
  7. XNOR gate with NAND gate
  8. XNOR gate with NOR gate
  9. Uses of XNOR gate

What is XNOR gate?

Other names of XNOR logic gate are Ex-NOR gate and Exclusive NOR gate. This type of logic gate can have infinite number of inputs and only one output. XNOR gate is the inverter of XOR gate. XNOR gate gives high (1) output only if all the inputs are same ( either 0 or 1). But the output of XNOR gate is low (0) when the inputs are not equal. This can be understand in the truth table of XNOR gate. Also, one can verify this type of operation of XNOR gate practically.

Boolean expression of XNOR gate

If A and B be the two inputs of an Exclusive NOR gate then the Boolean expression for the output of XNOR gate is

\small {\color{Blue} Y = AB + \bar{A}\bar{B}}

or, \small {\color{Blue} Y=A\odot B}.

This is the input-output equation for a XNOR gate.

Circuit symbol of XNOR gate

Exclusive NOR gate is the inverter of Exclusive OR gate. It consists a XOR gate and a NOT gate in series which is shown below.

XNOR gate is the inverter of XOR gate
XNOR gate is the inverter of XOR gate

The circuit symbol for Exclusive NOR gate is shown below.

XNOR gate circuit symbol
XNOR gate circuit symbol

Truth table of XNOR gate with 2 inputs

Let a two input XNOR gate with the inputs A and B and the output of this gate is Y. Then the truth table for the Ex-NOR gate with two inputs is as following-

AB\small {\color{blue} Y=AB+\bar{A}\bar{B}}
001
010
100
111
Truth table for 2 input XNOR gate

XNOR gate with 3 inputs

Let a three input XNOR gate with inputs A, B and C. Then the Boolean expression for the XNOR gate with three inputs is \small {\color{Blue} Y=A\odot B\odot C}.

The circuit symbol of 3 input XNOR gate is same as the circuit symbol above, but the number of inputs will be three. The truth table for this gate is shown below.

Truth table of XNOR gate with 3 inputs

Let A, B and C are the inputs and Y is the output of a Ex-NOR gate. Then the truth table of three input XNOR gate will be as following. The outputs in the truth table of a three input XNOR gate are just the inverted outputs of a three input XOR gate. (Check the truth table of three input XOR gate).

ABC\small {\color{Blue} Y = A\odot B\odot C}
0001
0010
0100
0111
1000
1011
1101
1110
Truth table of XNOR gate with three inputs

Circuit diagram of XNOR gate using basic logic gates

Circuit diagram of XNOR gate using basic logic gates
Circuit diagram of XNOR gate using basic logic gates

One can design the XNOR gate by using the basic logic gates like OR gate, AND gate and NOT gate. To design the XNOR gate circuit, we need two NOT gates, two AND gates and one OR gate. Above diagram is the circuit diagram for Ex-NOR gate using the basic logic gates.

Circuit diagram of XNOR gate using NAND gate

Circuit diagram of XNOR gate using NAND gate
Circuit diagram of XNOR gate using NAND gate

The XNOR gate circuit can also be design by using universal logic gates like NAND gate. Minimum five (5) NAND gates are required to design a 2-input XNOR circuit. Above picture presents the XNOR gate circuit diagram using NAND gates only.

Circuit diagram of XNOR gate using NOR gate

Circuit diagram of XNOR gate using NOR gate
Circuit diagram of XNOR gate using NOR gate

NOR gate is another universal logic gate like the NAND gate. So, one can also design XNOR circuit by using several NOR gates only. To design a two-input XNOR gate circuit by using NOR gate we need minimum four (4) NOR gates. The XNOR gate circuit diagram using NOR gate only is shown above.

Uses of XNOR logic gate

XNOR logic gate has some uses in digital electronics.

  1. XNOR gate is available in IC form. So, it has significant uses in different ICs like CMOS IC and TTL IC families.
  2. Exclusive NOR gate also has uses in memory circuits.
  3. In two input XNOR gate we get the high output when the inputs are same. Therefore, it can be used as equality detector.

This is all from this article on XNOR logic gate or Exclusive NOR gate and its circuit diagram. If you still have any doubt on this topic, you can ask me in the comment section.

Thank you for reading this post.

Related posts:

  1. XOR gate using NAND and NOR gates
  2. Basic logic gates using NAND gates only
  3. NAND gate
  4. NOR gate
  5. Basic logic gates
  6. Karnaugh map

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