XORoperaatio

XORoperaatio, also known as exclusive OR, is a logical operation that outputs true only when inputs differ. It is a fundamental concept in digital electronics and computer science. The XOR operation is represented by the symbol $\oplus$. It can be understood through its truth table. For two inputs, A and B, the output of A $\oplus$ B is true if A is true and B is false, or if A is false and B is true. If both A and B are true, or both are false, the output is false.

In binary arithmetic, XOR operates on bits. When applied to two bits, 0 $\oplus$ 0 equals 0, 0 $\oplus$ 1 equals 1, 1 $\oplus$ 0 equals 1, and 1 $\oplus$ 1 equals 0. This behavior makes XOR useful for tasks such as data encryption, error detection, and arithmetic operations. For instance, adding two binary numbers without carrying can be achieved using XOR. In cryptography, XOR is often used in stream ciphers where a plaintext message is XORed with a keystream to produce ciphertext. XORing the ciphertext with the same keystream recovers the original plaintext. Its symmetric nature, where A $\oplus$ B = B $\oplus$ A, and its property that A $\oplus$ A = 0, are key to its applications.