What does NOR actually compute?

NOR is NOT(A OR B): it produces a 1 only when both input bits are 0, and a 0 in every other case. It's the exact inverse of OR at every bit position.

What happens if my two values have different lengths?

The shorter value is left-padded with leading zero digits until it matches the longer value's digit count, then NOR runs across every aligned bit position of that shared width, including the complement step.

Why is 1010 NOR 0110 equal to 0001?

First OR gives 1110 (every position except the last has at least one 1). NOR then flips every bit of that within the 4-bit width, turning 1110 into 0001.

Why is NOR also considered a 'universal' logic gate?

Like NAND, every other logic gate (AND, OR, NOT, XOR, and so on) can be built entirely out of NOR gates wired together, which makes NOR another favorite building block in digital circuit design.

Binary NOR Calculator - Bitwise NOR of Two Binary Values

Overview

Introduction

NOR is the logical complement of OR, and like NAND is famous in digital logic as a 'universal gate' that every other gate can be constructed from.

This tool computes the bitwise NOR of two binary values, so you can see exactly where the OR result gets inverted.

What Is Binary NOR Calculator?

A calculator for the bitwise NOR of two binary values: it ORs the two values bit by bit, then flips every bit of that result within the shared width.

Like the other two-operand binary gate calculators in this category, it automatically left-pads the shorter operand with zero digits so both values line up bit-for-bit before combining them.

How Binary NOR Calculator Works

Both Value A and Value B are validated as binary strings, then the shorter is left-padded with leading zero digits to match the longer value's digit count.

The padded values are combined bit-by-bit with OR using BigInt, then the combined result is bitwise-inverted within that same shared width (masked so leading zero bits above the width aren't affected) to produce the final NOR output.

When To Use Binary NOR Calculator

Use it when you specifically need the NOR relationship between two values, or when studying/simulating digital circuits built from NOR gates.

It's also a useful teaching tool for showing how NOR relates to OR by simple inversion.

Often used alongside Binary OR Calculator, Binary AND Calculator and Binary XOR Calculator.

Features

Advantages

Automatically handles operands of different lengths by zero-padding, so you don't have to align widths by hand first.
Works on arbitrarily long binary values via BigInt, not limited to a fixed 8/16/32/64-bit width.
Instant, deterministic, fully client-side.

Limitations

Zero-padding the shorter operand assumes you want it treated as a smaller number within a larger field; pad manually first if your context expects different alignment.
Only combines two operands at a time; chain the tool manually if you need to NOR together more than two values.

Examples

NOR of two mixed bit patterns

Input

A: 1010, B: 0110

Output

1010 OR 0110 = 1110, then inverting within the 4-bit width gives 0001.

NORing two all-zero values gives all 1s

Input

A: 0000, B: 0000

Output

0000 OR 0000 = 0000, and inverting that within the 4-bit width gives 1111.

Best Practices & Notes

Best Practices

Confirm both values are the width you intend before relying on the auto-padding, since a short operand gets left-padded with zeros.
Remember NOR of a value with all zeros is equivalent to a plain NOT of that value, useful for sanity-checking results.

Developer Notes

Implemented with JavaScript BigInt: after zero-padding both operands to the same digit width, it computes `~(a | b)` masked to that width, avoiding JavaScript's native 32-bit-limited bitwise operators and the infinite leading 1s an unmasked BigInt NOT would otherwise produce.

Binary NOR Calculator Use Cases

Simulating digital logic circuits built from NOR gates
Teaching or demonstrating the NOR logic gate using concrete multi-bit binary examples
Cross-checking a manually-computed NOR result

Common Mistakes

Forgetting the final inversion step and reading the answer as plain OR instead of NOR.
Forgetting that a short operand gets zero-padded on the left, which can change the intended meaning if it was meant to be right-aligned instead.

Tips

NOR a value with all zeros to get a quick plain NOT of that value.
Compare the result with the Binary OR Calculator on the same inputs to see the exact bits that get inverted.

Binary NOR Calculator