NOR Gate Simulator
Use the free NOR Gate Simulator to test NOR logic instantly. Switch Input A and Input B between 0 and 1 and watch the output update immediately. A NOR gate performs OR followed by NOT, so its output is 1 only when both inputs are 0.
What Is a NOR Gate?
A NOR gate is a digital logic gate that first performs an OR operation and then inverts the OR result. The name NOR comes from the words NOT OR.
For a standard two-input NOR gate, output is 1 only when Input A and Input B are both 0. If either input is 1, the OR stage becomes 1 and the final inversion changes the output to 0.
NOR Gate Truth Table
| Input A | Input B | OR | NOR Output |
|---|---|---|---|
| 0 | 0 | 0 | 1 |
| 0 | 1 | 1 | 0 |
| 1 | 0 | 1 | 0 |
| 1 | 1 | 1 | 0 |
How to Use the NOR Gate Simulator
Choose 0 or 1 for the first digital input.
Set the second signal to LOW or HIGH.
The simulator first checks whether either input is 1.
The OR result is reversed because NOR includes a NOT stage.
The result becomes 1 only when both original inputs are 0.
NOR Gate Input and Output Examples
0 NOR 0
0 OR 0 gives 0. NOT changes that value to 1.
0 NOR 1
0 OR 1 gives 1, so NOR produces 0.
1 NOR 0
1 OR 0 gives 1. Inverting the result gives 0.
1 NOR 1
1 OR 1 gives 1, which becomes 0 after inversion.
Why Does 0 NOR 0 Equal 1?
The intermediate OR result is 0 because neither input is HIGH. NOR then applies NOT to that result.
NOT 0 = 1 Therefore: 0 NOR 0 = 1
Why Does 1 NOR 0 Equal 0?
Only one HIGH input is required for OR to produce 1. The NOR inversion then changes that intermediate 1 to 0.
NOT 1 = 0 Therefore: 1 NOR 0 = 0
NOR Gate Boolean Expression
NOR can be represented as an OR expression followed by inversion.
| Notation | Expression |
|---|---|
| Word form | A NOR B |
| Expanded form | NOT(A OR B) |
| Boolean form | OR expression with an inversion bar over the complete result |
NOR Gate vs OR Gate
NOR always gives the opposite output of OR for the same input combination.
| A | B | OR | NOR |
|---|---|---|---|
| 0 | 0 | 0 | 1 |
| 0 | 1 | 1 | 0 |
| 1 | 0 | 1 | 0 |
| 1 | 1 | 1 | 0 |
Why Is NOR a Universal Gate?
NOR is a universal gate because combinations of NOR gates can reproduce NOT, OR, AND, and therefore any Boolean function.
This property is called functional completeness. It means an entire digital logic network can theoretically be constructed using only NOR gates.
Creating a NOT Gate with NOR
Connect both inputs of a NOR gate to the same signal.
Creating an OR Gate with NOR
A NOR result can be inverted using a second NOR gate whose inputs are tied together.
Creating an AND Gate with NOR
De Morgan’s law allows AND to be formed entirely with NOR gates.
Y = B NOR B Then: Q = X NOR Y Which gives: Q = A AND B
NOR and De Morgan’s Law
One of De Morgan’s laws shows how NOR relates to AND of complemented inputs:
This identity is important when simplifying Boolean expressions or converting circuits into NOR-only implementations.
NOR Gate Symbol
A NOR gate symbol resembles an OR gate with a small circle at its output. The circle is the inversion bubble.
It shows that the ordinary OR result is inverted before becoming the final output.
Three-Input NOR Gate
A NOR gate can contain more than two inputs. For three inputs, output is 1 only if all three inputs are 0.
If any one of the three inputs becomes 1, the NOR output becomes 0.
NOR Gates in Latches and Memory
Two cross-coupled NOR gates can form an SR latch, a basic circuit capable of storing one binary state.
That concept is foundational to sequential logic, where present outputs can depend on previous states as well as current inputs.
Where Are NOR Gates Used?
Digital Control
Create logic that activates only when none of several input conditions are active.
Memory Circuits
Cross-coupled NOR gates are commonly used to explain the operation of an SR latch.
Processors
NOR-based networks can implement logic functions throughout digital processors.
Logic Synthesis
Any Boolean function can theoretically be constructed using NOR gates alone.
Embedded Systems
NOR devices can combine and invert control or status signals in hardware interfaces.
Digital Education
NOR is important for learning universal gates, Boolean algebra, De Morgan’s laws, and sequential logic concepts.
NOR Gate vs NAND Gate
| A | B | NAND | NOR |
|---|---|---|---|
| 0 | 0 | 1 | 1 |
| 0 | 1 | 1 | 0 |
| 1 | 0 | 1 | 0 |
| 1 | 1 | 0 | 0 |
NAND is NOT-AND, while NOR is NOT-OR. Both are universal gates, but their truth tables are different.
Important NOR Gate Properties
| Property | Rule |
|---|---|
| Inverse of OR | NOR = NOT(OR) |
| Both inputs 0 | 0 NOR 0 = 1 |
| Any input 1 | Output becomes 0 |
| Self-input | A NOR A = NOT A |
| Universal | NOR gates alone can implement arbitrary Boolean functions |
Common NOR Gate Mistakes
NOR is the opposite of OR, so the OR output must always be inverted.
1 OR 1 equals 1, and NOT changes that value to 0.
NOR inverts OR. NAND inverts AND.
For a two-input NOR gate, 0 NOR 0 is the only combination that produces 1.
The small output circle on the gate symbol indicates that the OR result is inverted.
Related BinaryCon Tools
NOR Gate Simulator FAQs
What is a NOR gate?
What is 0 NOR 0?
0 NOR 0 = 1.
What is 0 NOR 1?
0 NOR 1 = 0.
What is 1 NOR 0?
1 NOR 0 = 0.
What is 1 NOR 1?
1 NOR 1 = 0.
When is a two-input NOR output HIGH?
What is the Boolean expression for NOR?
NOT(A OR B).
Why is NOR called NOT OR?
Why is NOR a universal gate?
How can NOR create a NOT gate?
A NOR A = NOT A.
Can an OR gate be built using NOR?
Can AND be built using NOR?
What is the difference between NOR and OR?
What is the difference between NOR and NAND?
Can a NOR gate have more than two inputs?
What does the circle on a NOR gate symbol mean?
Are NOR gates used in memory?
Does this NOR Gate Simulator require registration?
Test NOR Gate Logic Instantly
Switch both inputs between LOW and HIGH, watch the NOR output update immediately, study the complete truth table, and learn why NOR is a universal gate used throughout Boolean logic and digital circuit design.