What the mathematical XOR function is

In summary, the XOR function is a logic gate that functions as an "either/or" statement. It outputs "true" if one input is true, but not both. It differs from the OR gate in that it will output "false" if both inputs are true. This can be illustrated by imagining two switches connected to a light, where the XOR gate would only turn the light on if one switch is on, while the OR gate would turn the light on if either or both switches are on.
  • #1
qwpoi
47
0
Would someone explain to me what the mathematical XOR function is? I came across it while reading a book on cryptography, and the explanation that is in the book doesn't really help me in fully understanding the function.

Much thanks,

-Betsy
 
Last edited by a moderator:
Mathematics news on Phys.org
  • #2
One of the logic gates

AND | OR | XOR | NOT | NAND | NOR | XNOR

The XOR gate acts in the same way as the logical "either/or." The output is "true" if either, but not both, of the inputs are "true." The output is "false" if both inputs are "false" or if both inputs are "true."
 
  • #3
Let me add a bit to what Gregg has said.

The eXclusive OR function differs from the OR gate when both inputs are true.

Think of a regular OR gate as 2 switches connceted to a light in parallel, in this configuration either or both switchs will turn the light on.

If the switches could be wired as an eXclusive OR gate when both switchs are on the light will not be turned on.
 
  • #4
Cool, thanks.
 

1. What is the mathematical XOR function?

The XOR function, short for "exclusive OR", is a logical operation that compares two binary inputs and returns a 1 if the inputs are different, and a 0 if they are the same.

2. How is the XOR function represented mathematically?

In mathematical notation, the XOR function is represented with the symbol ⊕ or ⊻, and can also be written as x ⊕ y or x ⊻ y. It is often used in Boolean algebra and digital logic circuits.

3. What is the truth table for the XOR function?

The truth table for the XOR function is as follows:

x y x ⊕ y
0 0 0
0 1 1
1 0 1
1 1 0

4. How is the XOR function used in coding?

The XOR function is commonly used in coding to perform bitwise operations, such as flipping specific bits in a binary sequence or encrypting data. It is also used in error detection and correction algorithms.

5. What is the difference between the XOR function and the OR function?

The XOR function differs from the OR function in that it only returns a 1 when the inputs are different, whereas the OR function returns a 1 when at least one of the inputs is 1. In other words, the XOR function is only true when the inputs are exclusive, while the OR function is true when the inputs are inclusive.

Similar threads

  • General Math
2
Replies
61
Views
9K
  • General Math
Replies
3
Views
761
  • General Math
Replies
11
Views
1K
  • General Math
Replies
4
Views
914
Replies
4
Views
1K
Replies
14
Views
988
Replies
6
Views
1K
  • General Math
Replies
9
Views
1K
  • General Math
Replies
25
Views
3K
Replies
3
Views
1K
Back
Top