XOR Calculator

XOR Calculator – Bitwise Exclusive OR

Calculate the bitwise XOR of two numbers and see exactly which bits differ. Enter values in decimal, hexadecimal (0x…), binary (0b…), or octal (0o…) and the result appears instantly in all four formats, together with an aligned bit-by-bit view. For example 12 XOR 10 = 6, because 1100 XOR 1010 = 0110.

How XOR works

XOR ("exclusive or") compares two bits and returns 1 when they are different and 0 when they are the same. Applied to whole numbers, the operation is carried out on every bit position independently. In most programming languages it is written with the caret operator: a ^ b.

Useful properties of XOR

• a ^ 0 = a – XOR with zero changes nothing.
• a ^ a = 0 – any value XORed with itself is zero.
• a ^ b ^ b = a – applying the same key twice restores the original, the basis of simple XOR encryption and one-time pads.
• XOR is commutative and associative, so the order of operands does not matter.

Where XOR is used

• Toggling bits – flags ^ mask flips exactly the bits set in the mask.
• Checksums and parity – XOR of all bytes gives a simple checksum used in NMEA sentences, RAID 5 parity, and many serial protocols.
• Cryptography – stream ciphers such as ChaCha20 and AES-CTR XOR the keystream with the data.
• Finding differences – XOR two values and every 1 bit marks a difference; count them to get the Hamming distance.
• Interview puzzles – swapping two variables without a temporary variable, or finding the single non-duplicated number in a list.

Bit width and negative numbers

With Auto width the calculator picks the smallest multiple of 8 bits that holds both operands. Choose 8, 16, 32, 64, or 128 bits to work with fixed-size integers; negative inputs are then encoded in two's complement, and the result is shown both unsigned and signed. For other operations see the Bitwise Calculator.