science

NOR logic

NOR logic is a science topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand NOR logic rather than just read about it. In short: A NOR gate or a NOT OR gate is a logic gate which gives a positive output only when both inputs are negative. Like NAND gates, NOR gates are so-called "universal gates" that can be combined to form any other kind of logic gate.

Key takeaways

NOR logic belongs to science; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect NOR logic to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of NOR logic from memory before moving on to harder problems.

Reference excerpt

A NOR gate or a NOT OR gate is a logic gate which gives a positive output only when both inputs are negative. Like NAND gates, NOR gates are so-called "universal gates" that can be combined to form any other kind of logic gate. For example, the first embedded system, the Apollo Guidance Computer, was built exclusively from NOR gates, about 5,600 in total for the later versions. Today, integrated circuits are not constructed exclusively from a single type of gate. Instead, EDA tools are used to convert the description of a logical circuit to a netlist of complex gates (standard cells) or transistors (full custom approach).

NOR

A NOR gate is logically an inverted OR gate. It has the following truth table:

Making other gates by using NOR gates A NOR gate is a universal gate, meaning that any other gate can be represented as a combination of NOR gates.

NOT

This is made by joining the inputs of a NOR gate. As a NOR gate is equivalent to an OR gate leading to NOT gate, joining the inputs makes the output of the "OR" part of the NOR gate the same as the input, eliminating it from consideration and leaving only the NOT part.

An OR gate is made by inverting the output of a NOR gate. Note that we already know that a NOT gate is equivalent to a NOR gate with its inputs joined.

AND

An AND gate gives a 1 output when both inputs are 1. Therefore, an AND gate is made by inverting the inputs of a NOR gate. Again, note that a NOR gate is equivalent to a NOT with its inputs joined.

NAND

A NAND gate is made by inverting the output of an AND gate. The word NAND means that it is not AND. As the name suggests, it will give 0 when both the inputs are 1.

XNOR

An XNOR gate is made by connecting four NOR gates as shown below. This construction entails a propagation delay three times that of a single NOR gate.

Alternatively, an XNOR gate is made by considering the conjunctive normal form ( A + B ¯ ) ⋅ ( A ¯ + B ) {\displaystyle (A+{\overline {B}})\cdot ({\overline {A}}+B)} , noting from de Morgan's Law that a NOR gate is an inverted-input AND gate. This construction uses five gates instead of four.

XOR

An XOR gate is made by considering the conjunctive normal form ( A + B ) ⋅ ( A ¯ + B ¯ ) {\displaystyle (A+B)\cdot ({\overline {A}}+{\overline {B}})} , noting from de Morgan's Law that a NOR gate is an inverted-input AND gate. This construction entails a propagation delay three times that of a single NOR gate and uses five gates.

Alternatively, the 4-gate version of the XNOR gate can be used with an inverter. This construction has a propagation delay four times (instead of three times) that of a single NOR gate.

See also NAND logic — Like NOR gates, NAND gates are also universal gates. Functional completeness

References

Illustrations

Worked examples

Example 1 — a first encounter with NOR logic

Start with the simplest possible case. Write down what NOR logic claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In science, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to NOR logic before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about NOR logic ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of NOR logic

In research: NOR logic appears in science research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses NOR logic in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: NOR logic is common in secondary-school and first-year university syllabi. It links to neighbouring topics Logic gates, so understanding it makes those chapters shorter.
In everyday life: Look for NOR logic outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study NOR logic in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what NOR logic means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain NOR logic out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is NOR logic in simple terms?

Why does NOR logic matter?

Because it connects several science ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study NOR logic?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on NOR logic.