Binary Bitwise XOR Calculator - XOR Multiple Binary Numbers

What Is Bitwise XOR on Binary Numbers?

The bitwise XOR (Exclusive OR) operation compares two or more binary values bit by bit. For two inputs, each output bit is 1 if the corresponding input bits are **different** (one is 1, and the other is 0); it is 0 if the input bits are the same. For multiple inputs, the output bit is 1 if there is an **odd number of 1s** at that bit position, and 0 if there is an even number of 1s.

How Bitwise XOR Works

Align the binary inputs by their least significant bits (padding shorter inputs with leading zeros), then apply the XOR truth table to each column:

1 XOR 1 = 0
1 XOR 0 = 1
0 XOR 1 = 1
0 XOR 0 = 0

Example: XOR of 11001100 and 10101010:

  11001100
^ 10101010
----------
  01100110

Result: 01100110 (decimal 102).

Common Uses of Bitwise XOR

Toggling bits: XORing a value with a mask of 1s flips those specific bits (0 becomes 1, and 1 becomes 0).
Simple cryptography: A basic XOR cipher encrypts data by XORing it with a secret key; repeating the same XOR operation with the key decrypts it.
Checksums & Parity: Generating parity bits and calculating error-checking values like RAID-5 parity blocks.
Swapping variables: The famous "XOR swap algorithm" swaps two variables without using a temporary variable.

Frequently Asked Questions

How does XOR behave when processing more than two binary numbers?

When multiple binary numbers are provided, the XOR operation evaluates them sequentially from top to bottom (or left to right). At each individual bit position, if the total count of 1 bits among all inputs is odd, the result bit is 1; if the count of 1 bits is even, the result is 0.

What happens if my inputs have different bit lengths?

Shorter binary inputs are automatically padded with leading zeros to align them with the longest binary input value, ensuring bit positions correspond accurately during calculation.

Why is XOR reversible?

XOR is its own self-inverse: (A ^ B) ^ B = A. This algebraic property makes it incredibly useful in simple data masking, data recovery, and symmetric key encryption algorithms.

How is XOR different from standard OR?

Standard OR (Inclusive OR) outputs 1 if any or both inputs are 1. XOR (Exclusive OR) outputs 1 only if the inputs are different (excluding the case where both are 1).