The binary XOR operation is identical to nonequivalence. Simpson , where denotes NAND. The binary XOR operator has the following truth table.
For multiple arguments, XOR is defined to be true if an odd number of its arguments are true, and false otherwise. This definition is quite common in computer science, where XOR is usually thought of as addition modulo 2. In this context, it arises in polynomial algebra modulo 2, arithmetic circuits with a full adder, and in parity generating or checking.
While this means that the multiargument "XOR" can no longer be thought of as "the exclusive OR" operation, this form is rarely used in mathematical logic and so does not cause very much confusion.
The XOR operation is associative, so is the same as. Computation of the multiargument XOR requires evaluation of all its arguments to determine the truth value, and hence there is no "lazy" special evaluation form as there is for AND and OR.
A bitwise version of XOR can also be defined that performs a bitwise XOR on the binary digits of two numbers and and then converts the resulting binary number back to decimal.
Portions of this entry contributed by Roger Germundsson. Rangel-Mondragon, J. Simpson, R. Boston, MA: Allyn and Bacon, pp. Stewart, I. The essence of encryption is to apply some key to an input message in order to output a new message.
The encryption is only useful if it is very hard to reverse the process. We can achieve this by applying our key over the message using XOR see Listing 2. The choice of key here is crucial to the strength of the encryption.
If it is short, then the code could easily be cracked using the centuries-old technique of frequency analysis. As an extreme example, if the key is just 1 byte then all we have is a substitution cipher that consistently maps each letter of the alphabet to another one.
This is known as a stream cipher , and in a real-worl situation this would also be combined with a secure hash function such as md5 or SHA Another type of cipher is the block cipher which operates on the message in blocks of fixed size with an unvarying transformation. The best-known encryption method is the RSA algorithm. Even when the above algorithm is made unbreakable, it has one crucial disadvantage: it is not a public key system like RSA.
Using RSA, I can publish the key others need to send me encrypted messages, but keep secret my private key used to decrypt them. On the other hand, in XOR encryption the same key is used to encrypt and decrypt again we see an example of toggling. Before you can send me encrypted messages I must find a way to secretly tell you the key to use. If an adversary intercepts that attempt, my code is compromised because they will be able to decrypt all the messages you send me. Now we will see the first application of XOR with respect to parity.
There are many ways to defend against data corruption when sending digital information. One of the simplest is to use XOR to combine all the bits together into a single parity bit which gets appended to the end of the message. By comparing the received parity bit with the calculated one, we can reliably determine when a single bit has been corrupted or indeed any odd number of bits.
But if 2 bits have been corrupted or indeed any even number of bits this check will not help us. Checksums and cyclic redundancy checks CRC extend the concept to longer check values and reducing the likelihood of collisions and are widely used. It was invented in the s as a way to recover from hard drive corruption.
If we have n hard drives, we can create an additional one which contains the XOR value of all the others:. This introduces redundancy : if a failure occurs on one drive, say A1, we can restore it from the others since:. This is the same reasoning used to explain toggling earlier, but applied to n inputs rather than just 2. In the highly unlikely event that 2 drives fail simultaneously, the above would not be applicable so there would be no way to recover the data.
Computers are built from logic gates, which are in turn built from transistors. A transistor is simply a switch that can be turned on or off using an electrical signal as opposed to a mechanical switch that requires a human being to operate it.
So for example, the AND gate can be built from two transistors in series, since both switches must be closed to allow current to flow, whereas the OR gate can be built from two transistors in parallel, since closing either switch will allow the current to flow.
Most binary logical operations can be constructed from two or fewer transistors; of all 16 possible operations, the only exception is XOR and its complement, XNOR, which shares its properties. Until recently, the simplest known way to construct XOR required six transistors [ Hindawi ]: the simplest way to see this is in the diagram below, which comprises three gates, each of which requires two transistors.
In , Bui et al came up with a design using only four transistors [ Bui00 ] — see Figure 5. Another way in which XOR stands apart from other such operations is to do with linear separability.
This is a concept from Artificial Intelligence relating to classification tasks. Suppose we have a set of data that fall into two categories. Our task is to define a single boundary line or, extending the notion to higher dimensions, a hyperplane that neatly partitions the data into its two categories.
This is very useful because it gives us the predictive power required to correctly classify new unseen examples. For example, we might want to identify whether or not someone will default on their mortgage payments using only two clues: their annual income and the size of their property.
But I can't get him to show up again. How do I get him to show up again? Who is Xor. User Info: faulknerbobby. Wait a while, finish up any sub quests, swoop racing, and item buying on the other worlds before heading for the final planet, otherwise you are screwed.
He usually shows up for the second time on either Manaan or Korriban. It took him a while to show up for me too, and he finally showed up the third time I played the game. I went to the Star Forge planet too quickly :. User Info: SparrowSilver. All's I did was encounter him and then I used the transit to ship system.
The same exact thing happened to me on my last two runs, so i'm pretty sure that the easiest way to get him to show up is the transit back to ship option specifically on Manaan or Korriban
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