Introduction to DLD

NOR Gate Truth Table

In Logic Gates, a truth table shows all possible combinations of binary input values (0 and 1) and their corresponding binary outputs. NOR Logic Gate is a very basic digital logic gate that produces an output of 1 (HIGH) when all inputs are 0 (LOW or inactive). The output becomes 0 (LOW) in only the case, when any input is 1 (HIGH or active).

Note:

A NOR gate is made by connecting an OR gate followed by a NOT gate (inverter). So, the OR gate produces the result first, and the NOT gate reverses it.

The following diagram shows the very basic Boolean Expression, NOR Gate Symbol, and NOR Gate Truth Table.

NOR Gate Truth Table

NOR Gate Truth Table

Truth tables show all possible input combinations and their corresponding outputs for a logic gate. NOR Gate truth tables for various numbers of inputs are explained below

The total possible input combinations in a truth table are calculated using 2ⁿ, where n is the number of inputs.

For example:

  • For 2 inputs, combinations will be 22 = 4
  • For 3 inputs, combinations will be 23 = 8
  • For 4 inputs, combinations will be 24 = 16
  • For 5 inputs, combinations will be 25 = 32
  • For 6 inputs, combinations will be 26 = 64

and so on…

Let’s explain various truth tables of NOR Logic gate for different numbers of inputs

NOR Gate Truth Table – 2 Inputs

For 2-input NOR Gate, there are 22=4 possible input combinations, explained below.

  • Input A Column: First 2 bits = 0, next 2 bits = 1
  • Input B Column: Alternates 0 and 1

The truth table of 2 inputs NOR Gate with their output is given below

NOR Gate Truth Table - 2 Inputs

In the above NOR gate truth table of 2 inputs

  • For A=0 and B = 0, the output (X) will be 1 because neither input is active.
  • For A=0 and B = 1, the output (X) will be 0 because the B input is active.
  • For A=1 and B = 0, the output (X) will be 0 because the A input is active.
  • For A=1 and B =1, the output (X) will be 0 because both inputs are active.

NOR Gate Truth Table – 3 Inputs

For 3-input NOR Gate, there are 23=8 possible input combinations, explained below.

  • Input A Column: First 4 bits = 0, next 4 bits = 1
  • Input B Column: First 2 bits = 0, next 2 = 1, next 2 = 0, next 2 = 1
  • Input C Column: Alternates 0 and 1

The truth table of 3 inputs NOR Gate with their output is given below

NOR Gate Truth Table - 3 Inputs

In the above NOR gate truth table of 3 inputs

  • For A = 0, B = 0, and C = 0, the output (X) will be 1 because no input is active.
  • For A=0, B = 0, and C = 1, the output (X) will be 0 because the C input is active.
  • For A=0, B = 1, and C = 0, the output (X) will be 0 because the B input is active.
  • For A=0, B = 1, and C = 1, the output (X) will be 0 because the B and C inputs are active.
  • For A=1, B = 0, and C = 0, the output (X) will be 0 because the A input is active.
  • For A=1, B = 0, and C = 1, the output (X) will be 0 because A and C inputs are active.
  • For A=1, B = 1, and C = 0, the output (X) will be 0 because A and B inputs are active.
  • For A=1, B =1, and C = 1, the output (X) will be 0 because all inputs (A, B, C) is active.

NOR Gate Truth Table – 4 Inputs

For 4-input NOR Gate, there are 24=16 possible input combinations, explained below.

  • Input A Column: First 8 bits = 0, next 8 bits = 1
  • Input B Column: First 4 bits = 0, next 4 = 1, next 4 = 0, next 4 = 1
  • Input C Column: 2 zeros, 2 ones, repeated
  • Input D Column: Alternates 0 and 1

The truth table of 4 inputs NOR Gate with its output is given below

NOR Gate Truth Table - 4 Inputs

In the above NOR gate truth table of 4 inputs

  • For A = 0, B = 0, C = 0, and D = 0, the output (X) will be 1 because no input is active.
  • For A=0, B = 0, C = 0, and D = 1, the output (X) will be 0 because the D input is active.
  • For A=0, B = 0, C = 1, and D = 0, the output (X) will be 0 because the C input is active.
  • For A=0, B = 0, C = 1, and D = 1, the output (X) will be 0 because the C and D inputs are active.
  • For A=0, B = 1, C = 0, and D = 0, the output (X) will be 0 because the B input is active.
  • For A=0, B = 1, C = 0, and D = 1, the output (X) will be 0 because B and D inputs are active.
  • For A=0, B = 1, C = 1, and D = 0, the output (X) will be 0 because B and C inputs are active.
  • For A=0, B =1, C = 1, and D = 1, the output (X) will be 0 because B, C, and D inputs are active.
  • For A = 1, B = 0, C = 0, and D = 0, the output (X) will be 0 because A input is active.
  • For A=1, B = 0, C = 0, and D = 1, the output (X) will be 0 because A and D inputs are active.
  • For A=1, B = 0, C = 1, and D = 0, the output (X) will be 0 because the A and C inputs are active.
  • For A=1, B = 0, C = 1, and D = 1, the output (X) will be 0 because the A, C, and D inputs are active.
  • For A=1, B = 1, C = 0, and D = 0, the output (X) will be 0 because the A and B inputs are active.
  • For A=1, B = 1, C = 0, and D = 1, the output (X) will be 0 because A, B, and D inputs are active.
  • For A=1, B = 1, C = 1, and D = 0, the output (X) will be 0 because A, B, and C inputs are active.
  • For A=1, B =1, C = 1, and D = 1, the output (X) will be 0 because all inputs (A, B, C, and D) are active.

NOR Gate Truth Table – 5 Inputs

For 5-input NOR Gate, there are 25=32 possible input combinations, explained below.

  • Input A Column: First 16 bits = 0, next 16 bits = 1
  • Input B Column: First 8 bits = 0, next 8 = 1, next 8 = 0, next 8 = 1
  • Input C Column: 4 zeros, 4 ones, repeated
  • Input D Column: 2 zeros, 2 ones, repeated
  • Input E Column: Alternates 0 and 1

The truth table of 5 inputs NOR Gate with its output is given below

NOR Gate Truth Table - 5 Inputs

In the above NOR gate truth table of 5 inputs

  • For A = 0, B = 0, C = 0, D = 0, and E = 0, the output (X) will be 1 because no input is active.
  • For A=0, B = 0, C = 0, D = 0, and E = 1, the output (X) will be 0 because one or more inputs are active.
  • For A=0, B = 0, C = 0, D = 1, and E = 0, the output (X) will be 0 because one or more inputs are active.
  • For A=0, B = 0, C = 0, D = 1, and E = 1, the output (X) will be 0 because one or more inputs are active.
  • For A=0, B = 0, C = 1, D = 0, and E = 0, the output (X) will be 0 because one or more inputs are active.
  • For A=0, B = 0, C = 1, D = 0, and E = 1, the output (X) will be 0 because one or more inputs are active.
  • For A=0, B = 0, C = 1, D = 1, and E = 0, the output (X) will be 0 because one or more inputs are active.
  • For A=0, B =0, C = 1, D = 1, and E = 1, the output (X) will be 0 because one or more inputs are active.
  • For A =0, B = 1, C = 0, D = 0, and E = 0, the output (X) will be 0 because one or more inputs are active.
  • For A=0, B = 1, C = 0, D = 0, and E = 1, the output (X) will be 0 because one or more inputs are active.
  • For A=0, B = 1, C = 0, D = 1, and E = 0, the output (X) will be 0 because one or more inputs are active.
  • For A=0, B = 1, C = 0, D = 1, and E = 1, the output (X) will be 0 because one or more inputs are active.
  • For A=0, B = 1, C = 1, D = 0, and E = 0, the output (X) will be 0 because one or more inputs are active.
  • For A=0, B = 1, C = 1, D = 0, and E = 1, the output (X) will be 0 because one or more inputs are active.
  • For A=0, B = 1, C = 1, D = 1, and E = 0, the output (X) will be 0 because one or more inputs are active.
  • For A=0, B =1, C = 1, D = 1, and E = 1, the output (X) will be 0 because one or more inputs are active.
  • For A = 1, B = 0, C = 0, D = 0, and E = 0, the output (X) will be 0 because one or more inputs are active.
  • For A=1, B = 0, C = 0, D = 0, and E = 1, the output (X) will be 0 because one or more inputs are active.
  • For A=1, B = 0, C = 0, D = 1, and E = 0, the output (X) will be 0 because one or more inputs are active.
  • For A=1, B = 0, C = 0, D = 1, and E = 1, the output (X) will be 0 because one or more inputs are active.
  • For A=1, B = 0, C = 1, D = 0, and E = 0, the output (X) will be 0 because one or more inputs are active.
  • For A=1, B = 0, C = 1, D = 0, and E = 1, the output (X) will be 0 because one or more inputs are active.
  • For A=1, B = 0, C = 1, D = 1, and E = 0, the output (X) will be 0 because one or more inputs are active.
  • For A=1, B =0, C = 1, D = 1, and E = 1, the output (X) will be 0 because one or more inputs are active.
  • For A = 1, B = 1, C = 0, D = 0, and E = 0, the output (X) will be 0 because one or more inputs are active.
  • For A=1, B = 1, C = 0, D = 0, and E = 1, the output (X) will be 0 because one or more inputs are active.
  • For A=1, B = 1, C = 0, D = 1, and E = 0, the output (X) will be 0 because one or more inputs are active.
  • For A=1, B = 1, C = 0, D = 1, and E = 1, the output (X) will be 0 because one or more inputs are active.
  • For A=1, B = 1, C = 1, D = 0, and E = 0, the output (X) will be 0 because one or more inputs are active.
  • For A=1, B = 1, C = 1, D = 0, and E = 1, the output (X) will be 0 because one or more inputs are active.
  • For A=1, B = 1, C = 1, D = 1, and E = 0, the output (X) will be 0 because one or more inputs are active.
  • For A=1, B =1, C = 1, D = 1, and E = 1, the output (X) will be 0 because all inputs (A, B, C, and D) are active.