Introduction to DLD

3 Input XNOR Gate

A 3-input XNOR gate is a digital logic gate with 3 inputs and 1 output.

  • The output is HIGH (1) when an even number of inputs are HIGH (1).
  • The output is LOW (0) when an odd number of inputs are HIGH (1).

Example: For three inputs, there will be 3 variables (i.e., A, B, C) that may be used, and the output is represented by the variable X. The Boolean expression for a 3-input XNOR logic gate is X = A ⊙ B ⊙ C.

XOR Logic Gate: Output is HIGH (1) when an odd number of inputs are HIGH (1).
XNOR Logic Gate: Output is HIGH (1) when an even number of inputs are HIGH (1).

Let’s explain the 3-input XNOR logic gate symbol, Boolean expression, and Truth Table.

3-Input XNOR Gate Symbol

The 3-input XNOR gate symbol has three input terminals, represented by A, B, and C. The output is represented by X.

3-Input XNOR Gate symbol

3-Input XNOR Gate Boolean Expression

The Boolean expression of a 3-input XNOR gate with inputs A, B, and C and output X is:

  • X = A ⊙ B ⊙ C

The 3-input XNOR expression can also be written using AND, OR, and NOT operations as:

  • X = A’B’C’ + A’BC + AB’C + ABC’

Here, the ⊙ symbol represents the XNOR operation. The output is HIGH when an even number of inputs are HIGH.

The following diagram shows the Boolean expression of a 3-input XNOR gate.

3-Input XNOR Gate Boolean Expression

3-Input XNOR Gate Truth Table

The 3-input XNOR gate truth table shows the output for all possible combinations of the inputs A, B, and C. The output X becomes HIGH (1) when an even number of inputs are HIGH (1). The output becomes LOW (0) when an odd number of inputs are HIGH (1).

The 3-input XNOR gate has 23 = 8 possible input combinations.

The following diagram shows the truth table of a 3-input XNOR logic gate.

XNOR Logic Gate Truth Table (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).

3-Input XNOR Gate – Timing Diagram

3-input XNOR gate timing diagram showing the relationship between inputs A, B, C, and output X in a digital logic circuit.

3-Input XNOR Gate - Timing diagram

The diagram illustrates the logic-level transitions of three inputs (A, B, and C) and one output (X) over time.

  • Input A: Initially remains at logic 0, then changes to 1 midway through the timing interval and stays high.
  • Input B: Alternates between logic 0 and 1 at longer time intervals.
  • Input C: Toggles between 0 and 1 more frequently than A and B.
  • Output X: Becomes 1 (HIGH) when an even number of inputs are 1. It becomes 0 (LOW) when an odd number of inputs are 1.

The vertical dotted lines divide the diagram into equal time intervals, making it possible to compare the input transitions with the corresponding output behavior.