What does XOR actually compute?

For each bit position, XOR (exclusive OR) produces a 1 when the two input bits differ, and a 0 when they match. It's the standard logical/bitwise XOR, applied independently across 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 XOR runs across every aligned bit position of that shared width.

Why is 1010 XOR 0110 equal to 1100?

Comparing bit by bit: 1 vs 0 differ (1), 0 vs 1 differ (1), 1 vs 1 match (0), 0 vs 0 match (0), reading left to right. So the result is 1100.

Why is XOR useful for toggling and comparing bits?

XORing a value with a mask flips exactly the bits that are 1 in the mask (useful for toggling flags), and XORing two values together highlights exactly the bit positions where they differ, which is why XOR shows up constantly in checksums and simple diffing.

Binary XOR Calculator - Bitwise XOR of Two Binary Values

Overview

Introduction

Bitwise XOR is the operation behind bit-toggling, simple diffing, and many checksum and parity schemes, since it isolates exactly the positions where two values differ.

This tool computes the bitwise XOR of two binary values, so you can see exactly which bit positions disagree between the two inputs.

What Is Binary XOR Calculator?

A calculator for the bitwise XOR of two binary values: it compares the two values bit by bit and sets a 1 wherever the corresponding bits differ.

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 XOR 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 XOR using BigInt (not JavaScript's native 32-bit-limited bitwise operators), and the result is formatted as a binary string padded to that same shared width.

When To Use Binary XOR Calculator

Use it to toggle specific bits in a value (XORing with a mask flips exactly the bits set in the mask), or to find exactly which bits differ between two values.

It's also a useful teaching tool for showing how XOR behaves on real multi-bit binary data rather than single bits.

Often used alongside Binary AND Calculator, Binary OR Calculator and Binary XNOR 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 XOR together more than two values.

Examples

XOR of two mixed bit patterns

Input

A: 1010, B: 0110

Output

1010 XOR 0110 = 1100, a 1 in every position where the two inputs disagreed.

XORing a value with itself always gives zero

Input

A: 1010, B: 1010

Output

Every bit position matches, so every position differs nowhere and the result is all zeros.

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.
Use XOR with an all-1s mask when you specifically want to invert every bit of the other operand within the shared width.

Developer Notes

Implemented with JavaScript BigInt: after zero-padding both operands to the same digit width, it computes `a ^ b` directly (no complement step), avoiding JavaScript's native 32-bit-limited bitwise operators for operands wider than 32 bits.

Binary XOR Calculator Use Cases

Toggling specific flag bits in a value by XORing with a mask
Highlighting exactly which bit positions differ between two binary values
Teaching or demonstrating the XOR logic gate using concrete multi-bit binary examples

Common Mistakes

Confusing XOR with OR; XOR excludes the case where both bits are 1 (that case yields 0), while OR would yield 1.
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

XOR a value with itself to quickly confirm the tool produces all zeros, a handy sanity check.
Compare the result with the Binary XNOR Calculator on the same inputs to see the exact inverse relationship.

Binary XOR Calculator