Introduction to DLD

4 Input NOR Gate

A 4-input NOR gate is a digital logic gate with 4 inputs and 1 output.

  • The output is HIGH (1) when all four inputs are LOW (0).
  • The output is LOW (0) when at least one input is 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 NOR logic gate is X = (A + B + C + D)’.

Let’s explain the 4-input NOR logic gate symbol, Boolean expression, and Truth Table.

4-Input NOR Gate Symbol

The 4-input NOR logic gate symbol has four input terminals, represented by A, B, C, and D. The output is represented by X.

4-Input NOR Gate Using Three 2-Input NOR Gates

4-Input NOR Gate Using 2-Input NOR Gates

A 4-input NOR gate can be constructed using five 2-input NOR gates.

  • First NOR gate: Inputs A and B produce the output (A + B)’.
  • Second NOR gate: Inputs C and D produce the output (C + D)’.
  • Third NOR gate: The outputs of the first two NOR gates are connected to the third NOR gate, producing ((A + B)’ + (C + D)’)’.

The following diagram explains the process.

4-Input NOR Gate Using three 2-Input NOR Gates

 

4-Input NOR Gate Boolean Expression

The Boolean expression of a 4-input NOR gate with inputs A, B, C, and D and output X is:

  • X = (A + B + C + D)’

Here, the “+” symbol represents the OR operation, while the bar (‘) symbol represents the NOT operation. Therefore, a NOR gate performs the OR operation followed by NOT.

The following diagram shows the Boolean expression of a 4-input NOR gate.

4-Input NOR Gate Boolean Expression

4-Input NOR Gate Truth Table

The 4-input NOR 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) only when all four inputs are LOW (0). If any input is HIGH (1), the output becomes LOW (0).

The 4-input NOR gate has 2⁴ = 16 possible input combinations.

NOR Logic Gate Truth Table (4-Inputs)

Let’s explain the truth table of a 4-input NOR logic gate.

  • A = 0, B = 0, C = 0, D = 0: All inputs are LOW, so the output is 1 (HIGH).
  • A = 0, B = 0, C = 0, D = 1: Input D is HIGH, so the output is 0 (LOW).
  • A = 0, B = 0, C = 1, D = 0: Input C is HIGH, so the output is 0 (LOW).
  • 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: Input B is HIGH, so the output is 0 (LOW).
  • 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 0 (LOW).
  • A = 1, B = 0, C = 0, D = 0: Input A is HIGH, so the output is 0 (LOW).
  • 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 0 (LOW).
  • 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 0 (LOW).
  • A = 1, B = 1, C = 1, D = 0: Inputs A, B, and C are HIGH, so the output is 0 (LOW).
  • A = 1, B = 1, C = 1, D = 1: All inputs are HIGH, so the output is 0 (LOW).

4-Input NOR Gate – Timing Diagram

4-input NOR 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.

4-Input NOR Gate - Timing diagram

  • 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: Remains at logic 0 whenever at least one input is 1. It changes to logic 1 only when A = 0, B = 0, C = 0, and D = 0.

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