Introduction to DLD

4 Input XOR Gate

A 4-input XOR gate is a digital logic gate with 4 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 four inputs, there will be 4 variables (i.e., A, B, C, and D) and the output is represented by the variable X. The Boolean expression for a 4-input XOR logic gate is X = A ⊕ B ⊕ C ⊕ D.

Let’s explain the 4-input XOR logic gate symbol, Boolean expression, and Truth Table.

4-Input XOR Gate Symbol

The 4-input XOR logic gate symbol has four input terminals, represented by A, B, C, and D. The output is represented by X.

 

4-Input XOR Gate Boolean Expression

The Boolean expression of a 4-input XOR gate with inputs A, B, C, and D and output X is:

  • X = A ⊕ B ⊕ C ⊕ D

The 4-input XOR expression can also be written using AND, OR, and NOT operations as:

  • X = A’B’C’D + A’B’CD’ + A’BC’D’ + AB’C’D’ + ABCD

Here, the ⊕ symbol represents the XOR operation. Therefore, the output is HIGH when an odd number of inputs are HIGH.

The following diagram shows the Boolean expression of a 4-input XOR gate.

 

4-Input XOR Gate Truth Table

The 4-input XOR logic gate truth table shows the output for all possible combinations of the inputs A, B, C, and D. 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 4-input XOR gate has 2⁴ = 16 possible input combinations.

 

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

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

4-Input XOR Gate – Timing Diagram

4-input XOR gate timing diagram showing the relationship between inputs A, B, C, D, and output X in a digital logic circuit. The diagram illustrates the logic-level transitions of four inputs (A, B, C, and D) 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.
  • Input D: Alternates between logic 0 and 1 at a different timing pattern.
  • Output X: Becomes 1 (HIGH) when an odd number of inputs are 1. It remains 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.