Bitwise operations work on each pair of bits independently. XOR is used for toggling bits, simple encryption (one-time pad), checksums and parity, and swapping two variables without a temporary. Programmers meet it in C, Java, Python and JavaScript as the ^ operator.
How to use the Bitwise XOR Calculator
- Representation
- Number format
- Number 1
- Number 2
- Operation
Everything is calculated in your browser, so results appear instantly and nothing you type is sent to a server.
How it works
Choose the bit width (representation) and the input format, then enter both numbers. They are padded to the chosen width, combined bit by bit and the result is shown in every common base. With a fixed width, the signed value uses two’s complement.
Formula
a XOR b is 1 when the bits differ; truth table: 0 0 → 0, 0 1 → 1, 1 0 → 1, 1 1 → 0
Worked example
Inputs — Representation: 8-bit; Number format: Binary; Number 1: 1011; Number 2: 0110; Operation: XOR.
Results — Result (binary) = 0000 1101; Result (decimal, unsigned) = 13; Result (decimal, signed two's complement) = 13; Result (octal) = 15; Result (hexadecimal) = D; Bit by bit = 0000 1011
XOR 0000 0110
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= 0000 1101.
Key terms
- Bit
- A binary digit, 0 or 1.
- Bit mask
- A pattern of bits used to select or change other bits.
Frequently asked questions
What does bitwise XOR do?
It compares two numbers bit by bit: a XOR b is 1 when the bits differ.
Why choose a bit width?
Operations like NOT, NOR and the signed value depend on how many bits the number has.
Can I enter decimal numbers?
Yes – choose Decimal as the number format.
What is the difference between bitwise and logical XOR?
Logical operators treat whole values as true/false; bitwise ones act on every bit separately.