If any number is illegal, all numbers in such size range A xor B can be made illegal(even though A or B are both perfectly mundane, xoring them creates an illeg

If any number is illegal, all numbers in such size range A xor B can be made illegal(even though A or B are both perfectly mundane, xoring them creates an illegal number, so they're now illegal too). * Xoring the original illegal number with any random legal number A of same size creates a new (also random) number B that (A xor B) restores the original.