Using the LoginRadius Identity Platform, companies can offer a streamlined login process while protecting customer accounts and complying with data privacy regulations. The latest news in the world of engineering. Visit Blog. Grow your business to millions. Engage and retain your customers. Kheenvraj Lomror November 24, Let's understand how the XOR operation works with negative numbers. How XOR operation works with negative numbers?
Because in that case it is very difficult to understand what exactly satisfies the condition. To remove this ambiguity, the "exclusive" term has been added to "or" to make it more clear in meaning. The expression using an exclusive or is true if and only if one operand is true and the other is false, assuming two operands are participating in the expression. In considering a chain of operands participating in an expression with exclusive or conditional operators, for example x XOR y XOR z XOR n.
Here the output of the entire expression is true if an odd number of operands are resulting true. Conversely, the entire output of the expression is false if even numbers of operands are resulting true. In simple terms, exclusive or means that one or the other must be true, but both cannot be true and both cannot be false.
By: Justin Stoltzfus Contributor, Reviewer. By: Satish Balakrishnan. We can interpret the action of XOR in a number of different ways, and this helps to shed light on its properties.
The last, and most powerful, interpretation of XOR is in terms of parity , i. This can be proved quite easily by induction and use of associativity. It is the crucial observation that leads to many of the properties that follow, including error detection, data protection and adding. Armed with these ideas, we are ready to explore some applications of XOR. Consider the following simple code snippet:.
This will toggle between two values x and y , alternately printing one and then the other. How does it work? To prove that this is the case we will use all of the properties covered earlier:. Did you work it out? The second line comprises an expression that evaluates to a and stores it in b , just as the toggling example did.
The third line comprises an expression that evaluates to b and stores it in a. This is an example of aliasing , where two arguments to a function share the same location in memory, so altering one will affect the other. Perhaps there is some retribution for this much maligned idea, however.
This is more than just a devious trick when we consider it in the context of assembly language. A node in a singly linked list contains a value and a pointer to the next node. A node in a doubly linked list contains the same, plus a pointer to the previous node. Note that the nodes at either end store the address of their neighbours.
Then the code to traverse the list looks like Listing 1, which was adapted from Stackoverflow [ Stackoverflow ]. This uses the same idea as before, that one state is the key to getting at the other. If we know the address of any consecutive pair of nodes, we can derive the address of their neighbours. In particular, by starting from one end we can traverse the list in its entirety. A nice feature of this function is that this same code can be used to traverse either forwards or backwards.
XOR can also be used to generate pseudorandom numbers in hardware. A pseudorandom number generator whether in hardware or software e. This can be achieved very fast in hardware using a linear feedback shift register. To generate the next number in the sequence, XOR the highest 2 bits together and put the result into the lowest bit, shifting all the other bits up by one. This is a simple algorithm but more complex ones can be constructed using more XOR gates as a function of more than 2 of the lowest bits [ Yikes ].
By choosing the architecture carefully, one can construct it so that it passes through all possible states before returning to the start of the cycle again Figure 4.
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.
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