Introduction to DLD

3 Input NOR Gate

A 3-input NOR gate is a digital logic gate with 3 inputs and 1 output.

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

Let’s explain the 3-input NOR logic gate symbol, Boolean expression, and Truth Table.

3-Input NOR Gate Symbol

The 3-input NOR logic gate symbol has three input terminals, represented by A, B, and C. The output is represented by X.

NOR Gate Symbol using 3-Inputs

3-Input NOR Gate Using 2-Input NOR Gates

A 3-input NOR gate can be constructed using three 2-input NOR gates.

  • First NOR gate: Inputs A and B produce the output (A + B)’.
  • Second NOR gate: The output of the first NOR gate and “C” connected to second NOR gate, which inverts it and produces )(A + B)’ + C’ )’.

The following diagram explains the process.

3-Input NOR Gate Using Two 2-Input OR Gates

3-Input NOR Gate Boolean Expression

The Boolean expression of a 3-input NOR gate with inputs A, B, and C and output X is:

  • X = (A + B + C)’

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 3-input NOR gate.

3-Input AND Gate Boolean Expression

3-Input NOR Gate Truth Table

The 3-input NOR logic gate truth table shows the output for all possible combinations of the inputs A, B, and C. The output X becomes HIGH (1) only when all three inputs are LOW (0). If any input is HIGH (1), the output becomes LOW (0).

The following diagram shows the truth table of a 3-input NOR logic gate.

NOR Logic Gate Truth Table (3-Inputs)

Let’s explain the truth table of a 3-input NOR logic gate.

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

3-Input NOR Gate – Timing Diagram

3-input NOR gate timing diagram showing the relationship between inputs A, B, C, and output X in a digital logic circuit.

3-Input NOR 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: Remains at logic 0 whenever at least one input is 1. It changes to logic 1 only when A = 0, B = 0, and C = 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.