XOR (eXclusive OR):
XORing is same to ORing with one exception. An OR may also be called an inclusive OR. It means that a 1 in either number or both will result in a 1. An eXclusive OR says that if either number has a 1 in it, however not both, a 1 will result. A seemingly little difference, but crucial. By using the similar two numbers, the result would be 1100b. The first two bits contain a 1 in either the first or the second number but not both. The third bit contains a 1 in both of the numbers, which results in a 0. The fourth has no 1's at all, hence the result is 0. The difference may seem small, even though the OR and XOR result in different answers. The major use of an XOR is to test two numbers against each other. If they are the same, the result will be all 0's, or else the answer will have 1's where there are differences.
Complementing a number results in the opposite state of all the 1's and 0's. Take the number 1111b. Complementing results in 0000b. It is the simplest operator of all and the easiest to understand. Its uses are varied, but compulsory.