What the mathematical XOR function is

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Discussion Overview

The discussion revolves around the mathematical XOR (exclusive OR) function, particularly its definition and behavior in the context of logic gates. Participants seek to clarify its meaning and application, especially in relation to other logical operations.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant requests an explanation of the XOR function, indicating a lack of understanding from existing resources.
  • Another participant describes the XOR gate as functioning similarly to a logical "either/or," where the output is true if either input is true, but false if both inputs are true or both are false.
  • A further contribution elaborates on the distinction between the XOR function and the regular OR function, using an analogy of switches to illustrate that in an XOR configuration, both inputs being true results in a false output.

Areas of Agreement / Disagreement

Participants appear to agree on the basic definition and behavior of the XOR function, but there is no explicit consensus on deeper implications or applications beyond the initial explanations.

Contextual Notes

The discussion does not address potential limitations or assumptions related to the definitions of logical operations or the contexts in which XOR might be applied.

qwpoi
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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
 
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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."
 
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.
 
Cool, thanks.
 

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