NOR Truth Table for Beginners: Learn Logic the Easy Way

The NOR truth table is essential for analyzing the behavior of NOR logic gates, which output LOW (0) unless all inputs are LOW. As a universal gate, the NOR gate can implement any logic function, making its truth table crucial for students, engineers, and hobbyists alike.

Let’s explore how the NOR gate truth table is constructed for 2, 3, and 4-input configurations, and how this information helps in logic design.

What Is the NOR Truth Table?

The NOR truth table represents all possible input combinations and their resulting outputs for a NOR gate. A NOR gate performs the NOT operation on an OR logic function, meaning it inverts the output of an OR gate.

A second useful way to think about the NOR truth table is that it highlights the uniquely restrictive condition required to get a HIGH output. Unlike gates such as AND or OR, which may produce multiple HIGH results depending on the inputs, the NOR gate yields a HIGH only under the single scenario where every input is LOW. This makes the truth table especially important for identifying reset states, detecting inactive conditions, or designing logic that must respond only to a complete absence of active signals.

2-Input NOR Gate Truth Table

A 2-input NOR gate is often the starting point for learning NOR logic because it clearly shows how the gate behaves with the simplest non-trivial input set. Since the OR output becomes HIGH when any input is HIGH, the NOR gate flips this behavior and becomes HIGH only when both inputs are LOW. Understanding this pattern gives you a foundation for analyzing more complex multi-input versions of the gate.

For a 2-input NOR gate, the output is HIGH (1) only when both inputs are LOW (0). The following table shows the 2-input NOR gate truth table and NOR gate symbol.

Input A	Input B	Output (A NOR B)
0	0	1
0	1	0
1	0	0
1	1	0

NOR Gate Truth Table for 3 Inputs

A 3-input NOR gate follows the exact same principle as the 2-input version but accounts for an additional input, giving eight possible combinations. The output remains HIGH only when all three inputs are LOW at the same time. This extension allows designers to check multiple conditions at once using a single logic operation.

As the following 3-input NOR Gate truth table shows, a 3-input NOR gate has eight combinations of input bits. The output is HIGH only when all three inputs are LOW.

4-Input NOR Gate Truth Table

A 4-input NOR gate increases the number of input combinations to sixteen, which makes the truth table particularly useful for understanding how larger NOR gates scale. Even though the number of rows grows, the core rule remains unchanged: the output becomes HIGH only when every input is LOW. This predictable behavior makes NOR gates reliable building blocks in digital logic designs.

With four inputs, the 4 input NOR gate truth table includes 16 combinations, as can be seen in the table below. As expected, the output is HIGH only when all four inputs are LOW.

How NOR Logic Gates Work

A NOR gate works by combining OR logic with an inverting action. First, the inputs are ORed together, producing a HIGH if any input is HIGH. The NOR gate then inverts that result, forcing the output LOW whenever the OR stage detects at least one HIGH input. This two-step process, though simple, forms the basis of many larger digital systems because it allows designers to test for “all LOW” conditions efficiently.

The NOR logic gate truth table helps demonstrate the logic behavior:

• If any input is HIGH, the output is LOW.
• Only when all inputs are LOW does the output go HIGH.

This inverting behavior makes NOR gates useful in reset circuits, alarms, and digital logic combinations. They are also heavily used in integrated circuits due to their ability to implement any Boolean function when combined appropriately.

Tips for NOR Truth Table Understanding

When studying NOR logic, it’s helpful to view it as a gate that checks for the complete absence of HIGH signals. If even a single HIGH appears, the output immediately goes LOW, which simplifies reasoning about disable, idle, or fault-detection conditions in a circuit.

Here are some practical tips for working with NOR truth tables:

• Memorize the rule: The output is 1 only when all inputs are 0.
• Use truth tables when troubleshooting or designing circuits with NOR gates.
• In multi-input gates, just extend the logic — any 1 makes the output 0.
• Practice building truth tables manually to reinforce logic understanding.
• Use NOR gates in simulations (e.g., Logisim, Falstad) to test behavior.
• Consider NOR gates when designing logic that must detect “all-off” conditions.

Did You Know About the NOR Truth Table?

The NOR truth table not only describes gate behavior but also reveals why this component is so versatile in digital electronics. Because a NOR gate includes both OR logic and inversion, it naturally forms the basis for building essential operations like NOT, AND, and OR — simply by wiring NOR gates in different configurations.

• The NOR gate is one of the two universal gates (along with NAND), meaning any logic function can be created using only NOR gates.
• Early Apollo Guidance Computers used NOR gates exclusively for logic operations.
• The MOS NOR gate is fundamental in CMOS logic design due to its simplicity.
• Many early microprocessors used NOR-based designs due to efficient transistor layouts.

Frequently Asked Questions About the NOR Truth Table

This section helps clarify commonly asked questions about NOR gates and their truth tables, especially for beginners learning how multi-input logic circuits behave. These explanations expand on key concepts and give practical insights into how NOR gates are applied in real circuits.

What is the output of a NOR gate when all inputs are 0?

The output is 1. This is the only scenario where the OR stage would output 0, and after inversion, the NOR gate produces a HIGH. If even one input becomes 1, the output drops to 0.

Can NOR gates have more than two inputs?

Yes. NOR gates are available in versions with 2, 3, 4, or more inputs. Regardless of the number of inputs, the rule stays the same: if any input is HIGH, the output becomes LOW. Only an all-LOW input combination produces a HIGH output.

How does a NOR gate differ from an OR gate?

An OR gate outputs HIGH when any input is HIGH. A NOR gate inserts a NOT stage after that logic, flipping the result. So while an OR gate is HIGH for most input combinations, a NOR gate is HIGH for only one, that is all-LOW.

Why are NOR gates called universal gates?

Because you can create any logic function (AND, OR, NOT, XOR, etc.) using only NOR gates.

Are NOR gates used in real-world circuits?

Yes. NOR gates appear in microprocessors, memory circuits, timers, latch circuits, alarm systems, and custom logic networks. Because NOR can implement any Boolean function, engineers often use it as a building block for larger systems.

What’s the advantage of a NOR gate over other logic gates?

NOR gates offer versatility because they are universal. This means you can build NOT, AND, OR, or more complex logic out of NOR gates alone. They also simplify certain CMOS designs, often requiring fewer transistors than equivalent implementations using multiple different gate types.

How many rows are in a NOR truth table?

A NOR truth table contains 2ⁿ rows, where n is the number of inputs.

• 2-input NOR → 4 rows
• 3-input NOR → 8 rows
• 4-input NOR → 16 rows
  As the number of inputs increases, the truth table grows exponentially.

Conclusion on the NOR Truth Table

The NOR truth table is a foundational tool for understanding digital logic. By analyzing the outputs of 2, 3, and 4-input NOR gates, you can predict circuit behavior and design effective systems. Whether you’re learning digital logic or debugging hardware, mastering the NOR gate truth table will serve you well in logic design.