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NOR Calculator

Perform the bitwise NOR (NOT OR) operation. Each output bit is 1 only when both corresponding input bits are 0.

Reviewed by Chase FloiedUpdated

This free online nor calculator provides instant results with no signup required. All calculations run directly in your browser — your data is never sent to a server. Enter your values below and see results update in real time as you type. Perfect for everyday calculations, homework, or professional use.

How to Use This Calculator

1

Enter your input values

Fill in all required input fields for the NOR Calculator. Most fields include unit selectors so you can work in your preferred unit system — metric or imperial, whichever matches your problem.

2

Review your inputs

Double-check that all values are correct and that you have selected the right units for each field. Incorrect units are the most common source of calculation errors and can produce results that are off by factors of 2, 10, or more.

3

Read the results

The NOR Calculator instantly computes the output and displays results with units clearly labeled. All calculations happen in your browser — no loading time and no data sent to a server.

4

Explore parameter sensitivity

Try adjusting individual input values to see how the output changes. This is a quick and effective way to develop intuition about how different parameters influence the result and to identify which inputs have the largest effect.

Formula Reference

NOR Calculator Formula

See calculator inputs for the governing equation

Variables: All variables and their units are labeled in the calculator interface above. Input fields accept values in multiple unit systems — select your preferred unit from the dropdown next to each field.

When to Use This Calculator

  • •Use the NOR Calculator when you need a quick mathematical result without writing out all the steps manually, saving time on repetitive calculations.
  • •Use it to verify hand calculations on tests or assignments and catch arithmetic mistakes.
  • •Use it when teaching or explaining mathematical concepts to others, demonstrating how changing inputs affects the result.
  • •Use it to explore the behavior of mathematical functions across a range of inputs.

About This Calculator

The NOR Calculator is a free mathematical calculation tool for students, educators, and professionals who need quick, reliable results. Perform the bitwise NOR (NOT OR) operation. Each output bit is 1 only when both corresponding input bits are 0. The underlying algorithms implement well-established mathematical formulas and numerical methods. Results are computed instantly in the browser. This tool is useful for learning, verification of hand calculations, and rapid exploration of mathematical relationships. All computation happens locally — no data is sent to a server.

About NOR Calculator

NOR (NOT OR) is the complement of the OR operation: it produces a 1 only when both input bits are 0. NOR is one of the two universal gates (along with NAND), meaning any Boolean function can be constructed using only NOR gates. This property made NOR gates central to early computer design — the Apollo Guidance Computer was built entirely from NOR gates. In bitwise programming, NOR can be computed as NOT(A OR B). NOR produces the inverse of OR: where OR finds positions with at least one 1, NOR finds positions where both are 0. This calculator computes the bitwise NOR of two numbers at a specified bit width.

The Math Behind It

NOR is defined as NOT(A OR B). Truth table: only the 0,0 input produces 1. NOR is functionally complete: NOT(A) = A NOR A, AND(A,B) = (A NOR A) NOR (B NOR B), OR(A,B) = (A NOR B) NOR (A NOR B). This means any digital circuit can be built using only NOR gates. The Apollo Guidance Computer used approximately 5,600 NOR gates. NOR is neither commutative nor associative in the multi-input case: (A NOR B) NOR C ≠ A NOR (B NOR C). De Morgan's law relates NOR to AND: A NOR B = NOT(A) AND NOT(B) = ~A & ~B.

Formula Reference

NOR

A NOR B = NOT(A OR B)

Variables: Output is 1 only when both inputs are 0

NOR Truth Table

0 NOR 0 = 1, 0 NOR 1 = 0, 1 NOR 0 = 0, 1 NOR 1 = 0

Variables:

Worked Examples

Example 1: 5 NOR 3 (8-bit)

Compute NOR of 5 and 3 in 8 bits.

Step 1:5 = 00000101₂, 3 = 00000011₂
Step 2:OR: 00000111₂ = 7
Step 3:NOT(7) in 8 bits: 11111000₂ = 248

5 NOR 3 = 248₁₀ = 11111000₂

Common Mistakes & Tips

  • !Forgetting to specify bit width — NOR requires NOT, which depends on the number of bits.
  • !Confusing NOR with NAND — NOR is NOT(OR), NAND is NOT(AND).
  • !Assuming NOR is associative — (A NOR B) NOR C is NOT the same as A NOR B NOR C computed left to right.

Related Concepts

OR Calculator

NOR is the complement of OR.

AND Calculator

By De Morgan's law, NOR relates to AND of complements.

Bitwise Calculator

All bitwise operations including NOR.

Used in These Calculators

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OR Calculator

Frequently Asked Questions

Why is NOR called a universal gate?

Any Boolean function (AND, OR, NOT, XOR, etc.) can be constructed using only NOR gates. This simplifies manufacturing since only one type of gate needs to be produced.

Was the Apollo computer really built with only NOR gates?

Yes. The Apollo Guidance Computer used approximately 5,600 three-input NOR gates (Fairchild Semiconductor type 9002 ICs) to implement all its logic.