Talk:Exclusive or

• /Archive 1

This article has been renamed from exclusive disjunction to exclusive or as the result of a move request.

Proposed project

I have been working on all of the logical operators recently. I would like to see a consistent format for them. There is a wikiproject proposal for this at: Wikipedia:WikiProject_Council/Proposals#Logical_Operators. Also see Talk:Logical connective.

I would like to see the logical, grammatical, mathematical, and computer science applications of all of the operators on the single page for each of those concepts.

BTW- I am sad to see the result of the debate on naming. The primary name of the article should be "xor." In the absence of this, it should be "exclusive disjunction."

Gregbard 08:50, 28 June 2007 (UTC)

You're off to a bad start: Wikipedia:Naming_conventions#Prefer_spelled-out_phrases_to_abbreviations. Not only is "xor" an abbreviation (and not a universal one), but it conflicts with another topic. I'm not sure what you mean by "in the absense of", but if you go for the other name, you're going to bring about that fight all over again. In fact, you'll probably end up having that fight no matter what you do.

What about the logic gate page? Will you bring that in? I think I'm for that merge, because the separation seems to suggest less of a relationship than there really is. --ToobMug 10:37, 28 June 2007 (UTC)

Yes it seems like that ship has sailed for now. 'Exclusive or' it is. Thanks for the support on the logic gate page issue. I'd like to bring in anything that makes it a comprehensive page. I think there is the potential for a feature article of the day if we play our cards right. That goes for any one of the operators. Gregbard 10:54, 28 June 2007 (UTC)

One is an abstract reperesentation of a computer circuit and the other is a boolean algebra topic. Merging will cause confusion, because they are not the same thing. --Jfrascencio 00:53, 30 July 2007 (in the edit comments where the XOR gate and Exclusive or merge tags were deleted)

One is simply an electronic implementation of the other. What's to be confused about? --ToobMug 10:07, 1 August 2007 (UTC)

We don't have to delete one and merge it completely into the other. The goal here is creating a comprehensive article on xor. We can touch on it in a section. The other article can stay where it is with an appropriate link with a {{main}} Gregbard 10:44, 1 August 2007 (UTC)

I am uninitiated when it comes to general Wiki-practice and the discussion page procedure, so please bare with me...

I think it is an absolute necessity to the article to have a consistent symbol set or at least an equivalencies table. Section ==Equivalencies, elimination, and introduction== starts out using undefined operators and then defines a few terms inline of the text. Then the article proceeds to define a second (and inconsistent) set of operators in Section ==Properties==. This is confusing and could be avoided by defining a consistent set of operators in Section ==Equivalencies, elimination, and introduction== or at least explain why a different operator set is in use. I am aware that depending on your discipline (Mathematics, Philosophy, Computer Science, or Electical Engineering), the operators can vary. This is more of a reason for a clear definition of oporators. Even the Logical connective artical (among others) is not clear. For example, in Computer Science “!” is sometimes used as negation along with “¬” or “~”. Is there a reason for this article organization that I am overlooking here? --Smcreator (talk) 06:36, 23 May 2008 (UTC)

Negation of XOR input/output

The relationships between AND and OR operations as well as negations of their inputs and outputs are well explained under De Morgan's Law(s) such as an AND having all its inputs negated as well as its output makes it equivalent an OR gate. The opposite works as well with an OR gate having all its interfaces negated making it equivalent to an AND gate. Using this equivalence and the fact that NOT operations cancel each other out one can simplify and combination of AND and OR operations. I haven't found anyone stating the equivalence of negated interfaces of an XOR operation. This relation is that one negated input (either input) of a two input XOR gate is equivalent to to an XNOR, you can prove this to yourself by saying an XOR would cause two identical inputs to output a FALSE and two dissimilar inputs to output a TRUE. Let us now say that inputs A and B are both in state X if A were to pass through the negated input it would be NOT X and B would be not X so if two inputs to the equation are the same the output is TRUE and if they were different the output would be false making this equivalent to an XNOR one can use this logic again for an XOR with both inputs negated making it equivalent to a plain XOR. Why is this important? It is important because it can be used along with De Morgan's Law to simplify logic operations and logic circuits. As far as I know this relation is not stated outright even though it can be derived through De Morgan's Law and it may have benefit to beginners in logic to see this relation as it is not easy to realize that the XOR operation is not fundamental and can actually be constructed out of the more fundamental operations.MicroControl (talk) 23:10, 11 July 2008 (UTC)

Larger structures?

Come someone please tell me what this is meant to mean:

This unfortunately prevents the combination of these two systems into larger structures, such as a mathematical ring.

And the bit about failing a more generalizable structure as well. For instance, the system $({0, 1}, \times)$ is isomorphic to $({F, T}, \and)$, and the former system can be extended to a ring, namely the integers modulo 2. Or am I misinterpreting the way it has been written, in which case can somebody rewrite it in a clearer way? Jason A. Recliner (talk) 12:44, 28 July 2008 (UTC)

Unicode values for symbols

The circle with a cross should be mentioned.
—Preceding unsigned comment added by 41.241.196.250 (talk) 06:05, 7 August 2008 (UTC)

Unicode for circle cross

name    Circle-plus 
decimal 8853 
symbol  ⊕ (may not appear correctly on your system)
hex     2295    
html    ⊕

Unicode for XOR

name        XOR
decimal 8891    
symbol  ⊻ (may not appear correctly on your system)
hex     22BB

—Preceding unsigned comment added by 198.54.202.70 (talk) 06:19, 7 August 2008 (UTC)

More than two inputs

If you attach multiple XOR gates after each other to create a component with more than two inputs, you get an odd-parity gate that will output 1 if an odd number of inputs is 1, 0 if an even number of inputs is 1. This is contrary to the meaning of the word "exclusive or". A true multiple input exclusive or gate would output 1 only if exactly 1 input is 1 and all other inputs are 0. Such a component however isn't as easy to create as an odd parity gate using multiple XORs. 193.190.253.144 (talk) 20:23, 4 October 2008 (UTC)

That used to be discussed on the XOR gate page, but it boiled off over successive edits. --ToobMug (talk) 22:47, 1 November 2008 (UTC)

Exclusive or in natural language

The article currently reads

"There are also good general reasons to suppose that no word in any natural language could be adequately represented by the binary exclusive “or” of formal logic. First, any binary or other n-ary exclusive “or” is true if and only if it has an odd number of true inputs. But it seems as though no word in any natural language that can conjoin a list of two or more options has this general property."

In Stuart Russel and Peter Norvig's textbook "Artificial Intelligence: A Modern Approach 2nd Ed.", page 207, footnote 9: "Latin has a separate word, aut, for exclusive or." This seems to contradict the wording currently in the article, but I'm not familiar enough with Latin to rewrite that paragraph intelligently. —Preceding unsigned comment added by 152.14.68.254 (talk) 20:12, 18 June 2009 (UTC)

aut has been claimed to mean 'exclusive or', as opposed to vel 'inclusive or'. But as I recall Latin experts say there is no evidence for this distinction in extant Latin literature -- it's a modern myth. I think this is why you see it claimed by those in logic and math as opposed to those in the classics. CRGreathouse (t | c) 03:44, 3 August 2009 (UTC)

"Either or" currently redirects here. It should probably redirect to Logical_disjunction as that is more in line with its meaning in language. Disjunction at Stanford's philosophy dictionary 74.198.151.77 (talk) 02:36, 8 February 2011 (UTC)

This now redirects to a better spot -R. S. Shaw (talk) 04:49, 9 February 2011 (UTC)

Pronunciation

Is it EX-or or zor? I know there's no established way since you don't normally say it out loud, but I'm going to start using it in everyday language as a replacement for and/or and I can't make up my mind as to which is better.. I personally am leaning towards zor. It flows better. Hopefully, I can do my part in helping to make this a legit (slang) word. It should be much easier than trying to get a gender neutral pronoun accepted. 75.4.145.158 (talk) 01:24, 3 August 2009 (UTC)

The first, I believe. I once pronounced it like 'zor' but was corrected, though I can't remember where (or even if in a book or by a person). But if you're trying to start a trend there's no reason to use the accepted pronunciation. CRGreathouse (t | c) 03:45, 3 August 2009 (UTC)

I pronounce it ECKsor but I don't know that this is standard. —David Eppstein (talk) 04:06, 3 August 2009 (UTC)

It is. David Spector 02:32, 27 February 2010 (UTC)

Properties of XOR Operation (in the Computer Science section)

I think the computer science section should mention some of the common properties of the XOR operation as it applies to binary calculations.

e.g., where A and B are two arbitrary binary digits (0 or 1)

   if XOR(A,B) = C, then XOR(B,A) = C; commutativity
   if XOR( XOR(A,B), C ) = D, then XOR( A, XOR(B, C) ) = D; associativity    
   and XOR(A,A) = 0 and if XOR(A,B) = C, then XOR(A,C) = B and XOR(C,B) = A; a binary string is its own inverse (logic)

That is to say, the XOR operation is commutative (it doesn't matter what order the operands are passed to the function), is associative (it doesn't matter how multiple operands are grouped), and binary strings passed to it are their own inverses with respect to XOR.

I'll add this into the page sometime in the next week or two, unless someone objects. Let me know of any flaws/improvements! Jthechemist (talk) 23:21, 13 May 2010 (UTC)

Proof unhelpful

I propose dropping the proof of ¬(p^q) ^ (pvq) because it is easy to prove it exhaustively using the truth table. Much easier than to follow the first step of the provided proof.

Sweavo (talk) 12:35, 7 January 2011 (UTC)

XOR Swap

The page for XOR Swap does not indicate the following sentence: "using the XOR swap algorithm; however this is regarded as more of a curiosity and not encouraged in practice." "In practice" seems to be an opinion of the author of that statement and doesn't follow from the body of knowledge (nor it is cited). Revenge by someone couldn't answer it on an interview question? :) Freakdog (talk) 02:45, 10 September 2011 (UTC)

Distributivity over Exclusive Or

xor is communicative and associative. false xor p is p, for any formula p. p xor p is false for any formula p. Thus (if xor is distributive over itself):

p xor (q xor r)
is (p xor q) xor (p xor r)
is (p xor q xor p xor r)
is (p xor p xor q xor r)
is (false xor (q xor r))
is (q xor r).

p xor (q xor r) is NOT (q xor r).
Proof by Counter Example:

p := true
q := false
r := true

p xor (q xor r) is true xor (false xor true) is true xor true is false.
q xor r is true.

xor is NOT distributive over itself. --Xor logician (talk) 04:45, 14 September 2011 (UTC)