Logic Gate

What is XOR?

exclusive or (XOR) 1 , 2

• used in cryptography because it let's us 'flip' the bits using a mask in a reversable operations

• p₁ (+) p₂ (+) ... (+) p_n is true if the number of variables with the value true (1) is odd, because the XOR is associative

• XOR is the same as addition modulo 2

  • p₁ (+) p₂ (+) ... (+) p_n == ( p₁ + p₂ + ... + p_n) % 2 - dividing mod 2 is one way to determine if a number is even or odd
  • Only the variables that have value 1 contribute to the sum, that determines how many variables have value 1

• doing parity check

  • kind of checksum: use the XOR to check whether there is the flip