Introduction to DLD

XNOR Gate Truth Table for 2, 3, 4, 5 Inputs

An XNOR gate is a digital logic gate that provides the output HIGH (1) when an even number of inputs are HIGH (1). The output will be LOW (0) when an odd number of inputs are HIGH (1).

XNOR Gate Output Rule

The output of an XNOR gate depends on whether the number of HIGH (1) inputs is even or odd:

  • Even number of 1s → Output = 1 (HIGH)
  • Odd number of 1s → Output = 0 (LOW)
For example, with 3 inputs:

  • 0 ones → Output = 1
  • 1 one → Output = 0
  • 2 ones → Output = 1
  • 3 ones → Output = 0

Truth Tables of XNOR Gate for Various Inputs

The following table shows the number of input combinations and the output behavior of XNOR gates with different numbers of inputs:

XNOR Gate Number of Inputs Possible Combinations
2-Input XNOR 2 4
3-Input XNOR 3 8
4-Input XNOR 4 16
5-Input XNOR 5 32

Let’s explain the truth tables of XNOR gates with different numbers of inputs.

XNOR Gate Truth Table for 2 Inputs

The following diagram shows the XNOR Gate Truth Table for 2 Inputs.

XNOR Gate Truth Table for 2 Inputs

Let’s explain the truth table of a 2-input XNOR logic gate.

  • A = 0, B = 0: Both inputs are LOW, so the output is 1 (HIGH).
  • A = 0, B = 1: Only input B is HIGH, so the output is 0 (LOW).
  • A = 1, B = 0: Only input A is HIGH, so the output is 0 (LOW).
  • A = 1, B = 1: Both inputs are HIGH, so the output is 1 (HIGH).

XNOR Gate Truth Table for 3 Inputs

The following diagram shows the XNOR Gate Truth Table for 3 Inputs.

XNOR Gate Truth Table for 3 Inputs

Let’s explain the truth table of a 3-input XNOR logic gate.

  • A = 0, B = 0, C = 0: No input is HIGH, so the output is 1 (HIGH).
  • A = 0, B = 0, C = 1: Only input C is HIGH, so the output is 0 (LOW).
  • A = 0, B = 1, C = 0: Only input B is HIGH, so the output is 0 (LOW).
  • A = 0, B = 1, C = 1: Two inputs are HIGH, so the output is 1 (HIGH).
  • A = 1, B = 0, C = 0: Only input A is HIGH, so the output is 0 (LOW).
  • A = 1, B = 0, C = 1: Two inputs are HIGH, so the output is 1 (HIGH).
  • A = 1, B = 1, C = 0: Two inputs are HIGH, so the output is 1 (HIGH).
  • A = 1, B = 1, C = 1: All three inputs are HIGH, so the output is 0 (LOW).

XNOR Gate Truth Table for 4 Inputs

The following diagram shows the XNOR Gate Truth Table for 4 Inputs.

XNOR Gate Truth Table for 4 Inputs

Let’s explain the truth table of a 4-input XNOR logic gate.

  • A = 0, B = 0, C = 0, D = 0: No input is HIGH, so the output is 1 (HIGH).
  • A = 0, B = 0, C = 0, D = 1: One input is HIGH, so the output is 0 (LOW).
  • A = 0, B = 0, C = 1, D = 0: One input is HIGH, so the output is 0 (LOW).
  • A = 0, B = 0, C = 1, D = 1: Two inputs are HIGH, so the output is 1 (HIGH).
  • A = 0, B = 1, C = 0, D = 0: One input is HIGH, so the output is 0 (LOW).
  • A = 0, B = 1, C = 0, D = 1: Two inputs are HIGH, so the output is 1 (HIGH).
  • A = 0, B = 1, C = 1, D = 0: Two inputs are HIGH, so the output is 1 (HIGH).
  • A = 0, B = 1, C = 1, D = 1: Three inputs are HIGH, so the output is 0 (LOW).
  • A = 1, B = 0, C = 0, D = 0: One input is HIGH, so the output is 0 (LOW).
  • A = 1, B = 0, C = 0, D = 1: Two inputs are HIGH, so the output is 1 (HIGH).
  • A = 1, B = 0, C = 1, D = 0: Two inputs are HIGH, so the output is 1 (HIGH).
  • A = 1, B = 0, C = 1, D = 1: Three inputs are HIGH, so the output is 0 (LOW).
  • A = 1, B = 1, C = 0, D = 0: Two inputs are HIGH, so the output is 1 (HIGH).
  • A = 1, B = 1, C = 0, D = 1: Three inputs are HIGH, so the output is 0 (LOW).
  • A = 1, B = 1, C = 1, D = 0: Three inputs are HIGH, so the output is 0 (LOW).
  • A = 1, B = 1, C = 1, D = 1: Four inputs are HIGH, so the output is 1 (HIGH).

XNOR Gate Truth Table for 5 Inputs

The following diagram shows the XNOR Gate Truth Table for 5 Inputs.

XNOR Gate Truth Table for 5 Inputs

Let’s explain the truth table of a 5-input XNOR logic gate.

  • A = 0, B = 0, C = 0, D = 0, E = 0: No input is HIGH, so the output is 1 (HIGH).
  • A = 0, B = 0, C = 0, D = 0, E = 1: One input is HIGH, so the output is 0 (LOW).
  • A = 0, B = 0, C = 0, D = 1, E = 0: One input is HIGH, so the output is 0 (LOW).
  • A = 0, B = 0, C = 0, D = 1, E = 1: Two inputs are HIGH, so the output is 1 (HIGH).
  • A = 0, B = 0, C = 1, D = 0, E = 0: One input is HIGH, so the output is 0 (LOW).
  • A = 0, B = 0, C = 1, D = 0, E = 1: Two inputs are HIGH, so the output is 1 (HIGH).
  • A = 0, B = 0, C = 1, D = 1, E = 0: Two inputs are HIGH, so the output is 1 (HIGH).
  • A = 0, B = 0, C = 1, D = 1, E = 1: Three inputs are HIGH, so the output is 0 (LOW).
  • A = 0, B = 1, C = 0, D = 0, E = 0: One input is HIGH, so the output is 0 (LOW).
  • A = 0, B = 1, C = 0, D = 0, E = 1: Two inputs are HIGH, so the output is 1 (HIGH).
  • A = 0, B = 1, C = 0, D = 1, E = 0: Two inputs are HIGH, so the output is 1 (HIGH).
  • A = 0, B = 1, C = 0, D = 1, E = 1: Three inputs are HIGH, so the output is 0 (LOW).
  • A = 0, B = 1, C = 1, D = 0, E = 0: Two inputs are HIGH, so the output is 1 (HIGH).
  • A = 0, B = 1, C = 1, D = 0, E = 1: Three inputs are HIGH, so the output is 0 (LOW).
  • A = 0, B = 1, C = 1, D = 1, E = 0: Three inputs are HIGH, so the output is 0 (LOW).
  • A = 0, B = 1, C = 1, D = 1, E = 1: Four inputs are HIGH, so the output is 1 (HIGH).
  • A = 1, B = 0, C = 0, D = 0, E = 0: One input is HIGH, so the output is 0 (LOW).
  • A = 1, B = 0, C = 0, D = 0, E = 1: Two inputs are HIGH, so the output is 1 (HIGH).
  • A = 1, B = 0, C = 0, D = 1, E = 0: Two inputs are HIGH, so the output is 1 (HIGH).
  • A = 1, B = 0, C = 0, D = 1, E = 1: Three inputs are HIGH, so the output is 0 (LOW).
  • A = 1, B = 0, C = 1, D = 0, E = 0: Two inputs are HIGH, so the output is 1 (HIGH).
  • A = 1, B = 0, C = 1, D = 0, E = 1: Three inputs are HIGH, so the output is 0 (LOW).
  • A = 1, B = 0, C = 1, D = 1, E = 0: Three inputs are HIGH, so the output is 0 (LOW).
  • A = 1, B = 0, C = 1, D = 1, E = 1: Four inputs are HIGH, so the output is 1 (HIGH).
  • A = 1, B = 1, C = 0, D = 0, E = 0: Two inputs are HIGH, so the output is 1 (HIGH).
  • A = 1, B = 1, C = 0, D = 0, E = 1: Three inputs are HIGH, so the output is 0 (LOW).
  • A = 1, B = 1, C = 0, D = 1, E = 0: Three inputs are HIGH, so the output is 0 (LOW).
  • A = 1, B = 1, C = 0, D = 1, E = 1: Four inputs are HIGH, so the output is 1 (HIGH).
  • A = 1, B = 1, C = 1, D = 0, E = 0: Three inputs are HIGH, so the output is 0 (LOW).
  • A = 1, B = 1, C = 1, D = 0, E = 1: Four inputs are HIGH, so the output is 1 (HIGH).
  • A = 1, B = 1, C = 1, D = 1, E = 0: Four inputs are HIGH, so the output is 1 (HIGH).
  • A = 1, B = 1, C = 1, D = 1, E = 1: All five inputs are HIGH, so the output is 0 (LOW).