What order are the operations applied in?

First, all values in the list are combined with bitwise OR, folded left to right. Then the bitwise NOT of that single combined result is taken at the chosen bit width.

Why does the bit width matter for NOR?

The OR step is unaffected by width, but the final NOT step flips bits within the chosen width, so the same list of values produces different final results at 8, 16, or 32 bits.

Can I NOR negative integers?

No, all values must be non-negative and must fit within the chosen bit width, since bitwise operations here are only defined in that unsigned range.

What does the NOR result actually represent?

It represents the bits that are not set in any of the input values, that is, the bits that stayed at 0 across every value in the list.

Integer NOR Calculator - OR-then-NOT at 8/16/32-bit Width

Overview

Introduction

This tool computes NOR across a whole list of non-negative integers: OR them all together, then NOT the result at a bit width you choose.

It's the combined-list version of the classic NOR logic gate, extended to fold across more than two operands.

What Is Integer NOR Calculator?

A calculator that folds a list with bitwise OR, then complements (NOTs) the single combined result at a chosen 8, 16, or 32-bit width.

Like NAND, NOR is a universal logic gate; every other logic operation can be built from NOR gates alone.

How Integer NOR Calculator Works

Each non-blank line is parsed as a non-negative integer that must fit within the selected bit width's range.

All values are combined with bitwise OR, folded left to right into a single intermediate result.

That intermediate result is then complemented at the chosen width (mask minus the OR result) to produce the final NOR value.

When To Use Integer NOR Calculator

Use it when you need to find which bits were never set across a whole list of values, in a single step.

It's also useful for digital-logic design and teaching, since NOR is a foundational universal gate.

Often used alongside Integer OR Calculator, Integer NOT Calculator and Integer NAND Calculator.

Features

Advantages

Combines the OR-fold and NOT-complement into a single calculation instead of two separate tool passes.
Supports any number of operands (2 or more), not just the classic two-input NOR gate.
Lets you choose the bit width so the complement step matches your target system size.

Limitations

Only supports non-negative integers within the chosen bit width; there's no signed mode.
Requires at least two values to OR together before the NOT step is applied.

Examples

NOR at the default 32-bit width

Input

12
10

Output

4294967281

12 | 10 = 14, then NOT 14 at 32 bits is 4294967295 - 14 = 4294967281.

NOR at an 8-bit width

Input

12
10

Output

12 | 10 = 14, then NOT 14 at 8 bits is 255 - 14 = 241.

Best Practices & Notes

Best Practices

Set the bit width to match your target system before reading the result, since it only affects the final NOT step.
Use this tool directly instead of chaining the separate OR and NOT calculators when you want the combined NOR value.

Developer Notes

The list is first folded with JavaScript's `|` operator (kept unsigned via `>>> 0`), then the single OR result is complemented as `mask - ored` where `mask = 2**width - 1`, matching the same width-aware complement approach used by the standalone NOT calculator.

Integer NOR Calculator Use Cases

Digital logic design and verification involving multi-input NOR gates
Finding bits that are never set across a group of bitmask values
Teaching how NOR is built from OR followed by NOT

Common Mistakes

Forgetting that the bit width only affects the final NOT step, not the initial OR fold.
Entering a negative or oversized value for the chosen width, which is rejected before any computation happens.
Expecting a two-input-only NOR; this tool supports folding any number of values (2 or more).

Tips

If you only need the plain OR without the complement, use the Integer OR Calculator instead.
Compare results at different bit widths to see how the same OR value complements differently depending on width.

Integer NOR Calculator