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XOR Calculator

Perform the bitwise XOR (exclusive OR) operation. Each output bit is 1 when the corresponding input bits are different.

Reviewed by Chase FloiedUpdated

This free online xor 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.

Results

A XOR B (Decimal)

1e+23

How to Use This Calculator

1

Enter your input values

Fill in all required input fields for the XOR 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 XOR 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

XOR 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 XOR 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 XOR Calculator is a free mathematical calculation tool for students, educators, and professionals who need quick, reliable results. Perform the bitwise XOR (exclusive OR) operation. Each output bit is 1 when the corresponding input bits are different. 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 XOR Calculator

XOR (exclusive OR) produces a 1 when the two input bits are different and a 0 when they are the same. XOR is one of the most versatile bitwise operations in computer science. It is its own inverse: A XOR B XOR B = A, which means XOR can be used for encryption/decryption (one-time pad cipher), error detection (parity bits), swapping variables without a temporary (a^=b; b^=a; a^=b), and detecting changes between two values. XOR is also the addition operation in GF(2) (binary Galois field), making it central to coding theory and CRC checksums. This calculator computes the bitwise XOR of two numbers.

The Math Behind It

XOR properties: A ^ 0 = A (identity), A ^ A = 0 (self-inverse), A ^ ~0 = ~A (complement), commutative, associative. XOR is its own inverse: (A ^ B) ^ B = A. This makes it ideal for: simple encryption (ciphertext = plaintext ^ key, plaintext = ciphertext ^ key), detecting differences (A ^ B is nonzero iff A ≠ B), computing parity (XOR all bits: result is 1 if odd number of 1s), swapping without temp (a^=b; b^=a; a^=b), and finding unique elements (XOR all elements: pairs cancel, unique remains). In arithmetic, XOR computes the sum bits of binary addition without carry.

Formula Reference

XOR Truth Table

0^0=0, 0^1=1, 1^0=1, 1^1=0

Variables: Output is 1 when inputs differ

Worked Examples

Example 1: 60 XOR 13

Compute bitwise XOR of 60 and 13.

Step 1:60 = 111100₂
Step 2:13 = 001101₂
Step 3:XOR: 110001₂

60 XOR 13 = 49₁₀ = 110001₂

Common Mistakes & Tips

  • !Confusing XOR with OR — XOR gives 0 when both inputs are 1, while OR gives 1.
  • !Forgetting that XOR is its own inverse — applying it twice restores the original value.

Related Concepts

AND Calculator

AND checks where both bits are 1.

OR Calculator

OR checks where at least one bit is 1.

Binary Addition

XOR computes the sum bit in binary addition.

Used in These Calculators

Calculators that build on or apply the concepts from this page:

Binary Addition Calculator

Bitwise Calculator

Frequently Asked Questions

How can XOR be used for encryption?

In a one-time pad, plaintext XOR key = ciphertext, and ciphertext XOR key = plaintext. If the key is truly random and as long as the message, this encryption is theoretically unbreakable.

How does the XOR swap trick work?

a ^= b sets a to a^b. Then b ^= a sets b to b^(a^b) = a. Then a ^= b sets a to (a^b)^a = b. The values are swapped without a temporary variable.