Introduction to DLD

3 Input XOR Gate

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

  • The output is HIGH (1) when an odd number of inputs are HIGH (1).
  • The output is LOW (0) when an even 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 XOR logic gate is X = A ⊕ B ⊕ C.

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

3-Input XOR Gate Symbol

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

 

3-Input XOR Gate Using 2-Input XOR Gates

A 3-input XOR gate can be constructed using two 2-input XOR gates.

  • First XOR gate: Inputs A and B produce the output A ⊕ B.
  • Second XOR gate: The output A ⊕ B from the first XOR gate and input C are connected to the second XOR gate, producing (A ⊕ B) ⊕ C.

Therefore:

X = (A ⊕ B) ⊕ C

which can also be written as:

X = A ⊕ B ⊕ C

The following diagram explains the process.

 

3-Input XOR Gate Boolean Expression

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

  • X = A ⊕ B ⊕ C

The 3-input XOR 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 XOR operation. The output is HIGH when an odd number of inputs are HIGH.

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

 

3-Input XOR Gate Truth Table

The 3-input XOR logic 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 odd number of inputs are HIGH (1). The output becomes LOW (0) when an even number of inputs are HIGH (1).

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

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

 

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

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

3-Input XOR Gate – Timing Diagram

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

 

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 odd number of inputs are 1. It becomes 0 (LOW) when an even 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.