# Talk:Logical equality

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Logic

## I've never seen this before

I've never seen XNOR, XAND (or xand), "Exclusive nor", "Exclusive and", or the symbols ("", or ) before. I have seen iff (and the corresponding arrows and symbols), biconditional, and if and only if -- and occasionally an NXOR, EQV, EQIV for the gate or for inline textual representations. For a symbol, a slashed circled + (̸⊕) or an equal sign ("=") is often used, as well as the symbols listed under iff. I don't dispute that Google finds more XNORs than NXORs, but they may all be echos of MathWorld. -- Arthur Rubin (talk) 23:27, 8 November 2005 (UTC)

The SNES uses XNOR to combine two areas in a scanline. 84.182.91.73 13:26, 12 August 2007 (UTC)

XNOR is "equal" or equivalent (for two valued logics). I have trouble imagining a reason anybody would devote a page to it. XNOR is the not of exclusive or... so I'd actually expect it to be called NXOR. There are 16 logical functions of two variables in two valued logic. And, Or, and Not are popular, and complete (The others can be built out of these.) Nand and Nor are popular in circuit design, and complete. "True" and "False" (for all inputs) have at least some sort of name. That leaves about nine others we could name and make pages about. Seems rather pointless. Nahaj 03:45, 10 November 2005 (UTC)

Given the choice of the two, I would choose "not XOR" (NXOR), which actually makes sense, while "exclusive NOR" (XNOR) doesn't seem to make any sense at all. I would still need to use a truth table to figure out what NXOR means, though. If it is true only on the same inputs (both true or both false), wouldn't the simplest and most logical name be SAME ? StuRat 11:46, 10 November 2005 (UTC)
SAME 965,000,000 Logical SAME 1,190
XNOR 104,000 Logical XNOR 250
NXOR 9,720 Logical NXOR 34
Here's my Google hits research on the various terms and phrases:

As you can see, the term "logical SAME" is used 35 times more than "logical NXOR" and almost 5 times more than "logical XNOR". The ratios are much higher if the word "logical" is omitted, but I don't think this is a fair comparison, since SAME is a common English word. "Logical SAME", however, is not a common English phrase (although "logically the same" would be). 14:52, 10 November 2005 (UTC) StuRat 12:33, 10 November 2005 (UTC)

"Simplest and most logical name" is irrelevant. We should document what is, not what we would like to be. xnor is the name for this gate in Verilog and in VHDL. Uncle G 15:27, 10 November 2005 (UTC)
I disagree that using terms which are "simplest and most logical" should not be our goal. I also have shown that the term is used, see the Google hits table. StuRat 16:39, 10 November 2005 (UTC)
Then please refresh your memory of our no original research policy. We aren't here to make up new names for this gate that you think are the simplest and most logical. Your Google searches, which (as has already been pointed out) pick up all sorts of arbitrary and completely irrelevant stuff, are not anywhere near as convincing as looking at the specifications for Verilog and VHDL and seeing what the gate is actually called in languages that describe gates. Uncle G 19:48, 10 November 2005 (UTC)
StuRat, I find your interpretation of the google statistics misleading. there may be no hits for "logical xnor", but no one uses that phrase, since it's redundant (it suffices to say xnor). xnor has far more hits than anything except "same", which is of course a common word outside of logic/CS. I have always known this operator as XNOR, and can provide textbook references if you like. That's its name. -Lethe | Talk 16:19, 10 November 2005 (UTC)
Well, as I had noted, there is the problem that "SAME" can either mean "logical SAME" or the common meaning of the English word "same". Both "NXOR" and "XNOR" seem to be about 300-400 times more prevalent than "logical NXOR" and "logical XNOR", respectively. If we assume a similar ratio for SAME, that would mean about 400,000 of the 965 million usages of the word "same" are the "logical SAME" meaning. This would still make it, by far, the most common of the three. StuRat 16:28, 10 November 2005 (UTC)
I disagree with this analysis. -Lethe | Talk 17:20, 10 November 2005 (UTC)
I also disagree with this analysis. The relationship of "same" to "logical same" has nothing to do with the relationship of "xnor" to "logical xnor". Some uses of "logical xnor" are an obscure different operation from "xnor" -- a distinction similar to the difference between the C language operators & and &&. --A D Monroe III 18:39, 10 November 2005 (UTC)
SAME 1,050,000,00 Logical SAME 1,190
XNOR 104,000 Logical XNOR 250
NXOR 9,720 Logical NXOR 34
EQV 319,000 Logical EQV 323
EQIV 16,100 Logical EQIV 77
Updated google research, including some of the other choices I made. That justifies EQV (which I gave as an alternate) as a better choice. Furthermore, even if the name of the gate is XNOR, the name of the logical operation could still be EQV. Arthur Rubin (talk) 01:01, 11 November 2005 (UTC)
I'm gonna need something other than google counts (many of which seem spurious) before I'm convinced. -Lethe | Talk 01:18, 11 November 2005 (UTC)
The first page of google results on "Logical EQV" are all from descriptions of computer languages, for example, Visual Basic, Fortran-90 extensions, Bitwise classes, LISP, etc., etc. The corresponding first page of "Logical XNOR" show that it's used, but only by idiots, for the most part; and in some SPARC upgrades. Comparing those pages for usefulness, I'd go with EQV. Arthur Rubin (talk) 01:31, 11 November 2005 (UTC)
Seriously, knock it off with the google hits. I've got an (idiot) CS textbook and two (idiot) calculators that use XNOR. Yeah, you can find some (nonidiot) google hits that use EQV and some that use SAME. Now please stop throwing google hits at the us idiots. -Lethe | Talk 02:07, 11 November 2005 (UTC)
Google hits are really the only way to defend against the charge that "the term isn't used". I also think simplicity should be considered. EQV, or EQUIVALENCE, sounds like a good term to me, both for the logic gate and the logical operation. I've also seen it used in computer programming. The Google hits seems to show it is the most widely used term, if SAME is discounted. So, it sounds like a winner to me. StuRat 18:02, 11 November 2005 (UTC)
Fallacy 5,670,000 Logical Fallacy 281,000
XNOR 104,000 Logical XNOR 250
NXOR 9,720 Logical NXOR 34

Does this table prove that the name of this article should be logical fallacy?  ;) --A D Monroe III 21:07, 11 November 2005 (UTC)

Only if you can also show that it's a simple and logical name for this type of logic operation/gate. StuRat 23:23, 11 November 2005 (UTC)
I haven't seen any serious objections to Arthur Rubin's suggestion of changing the name to "Logical EQV", so would like to change it to that. StuRat 04:21, 20 November 2005 (UTC)
I object. I think you should leave it at XNOR. -lethe talk 14:39, 20 November 2005 (UTC)
Leave as XNOR. Maybe we can decide on a "better" name, but that wouldn't change what people call it. If you want to create "Logical EQV" as a redirect, or even a new article, go for it; but this article is about XNOR. --A D Monroe III 15:04, 20 November 2005 (UTC)
I have added redirects, but it seems that Arthur Rubin has proven that Logical EQV is the most common term for this logic gate. StuRat 19:05, 20 November 2005 (UTC)
No. You've misinterpreted the google results. -lethe talk 19:34, 20 November 2005 (UTC)
Lethe, since your interpretation of the Google results is different from ours, could you please explain it to us ? StuRat 04:46, 22 November 2005 (UTC)
Your google count for "logical same" should not be compared, because it counts unrelated uses. "logical xnor" is a strawman; no one uses that redundant phrase. Going by google hits, with "logical same" ruled out, xnor is the clear winner. Furthermore, I and Uncle G have provided sources which use xnor. I and Uncle G and AD Monroe seem to agree that xnor is the right name, I'm not sure why you and Arthur are so determined to replace it. You said that you would provide a source not from google but have failed to do so. I've made a redirect from EQV, as far as I can tell there's nothing more to say on the matter. -lethe talk 08:19, 22 November 2005 (UTC)
Apparently you missed my comment: "I haven't seen any serious objections to Arthur Rubin's suggestion of changing the name to 'Logical EQV', so would like to change it to that." This means I withdrew my recommendation of changing it to "logical same" and now support changing it the "logical EQV". Are you suggesting that "logical EQV" also counts unrelated uses ? I doubt this, since EQV is not a common English word, unlike "same". Here is the Google hits chart with "logical same" removed, so please let's stop any more discussion of that dead issue, the current issue is whether to change the name to "logical EQV":
EQV 319,000 Logical EQV 323
XNOR 104,000 Logical XNOR 250
EQIV 16,100 Logical EQIV 77
NXOR 9,720 Logical NXOR 34
StuRat 15:39, 22 November 2005 (UTC)
So you want to change it to the one with 323 google hits? I know I said that google hits weren't a good criterion, but come on .... lethe talk 17:47, 22 November 2005 (UTC)
Are you really that incapable of reading a simple chart ? It says 323 hits on "Logical EQV" vs 250 for "Logical XNOR", which is MORE. It also says 319,000 hits for "EQV" vs 104,000 for "XNOR", which is also MORE ! StuRat 22:01, 22 November 2005 (UTC)
• Sigh*. "Logical XNOR" is a straw man. No one ever put that forth as a correct term. "XNOR" is the correct name of this article. "EQV" suffers the same fate as "Logical Same": some of its google hits are not related to the operator (at least 5 from the top 10 hits). XNOR wins in google hits, but really I want XNOR because of other sources than google. And why are you accusing me of misreading your ridiculous chart? I said I want XNOR, and you said you want "logical eqv". 104000 vs 323. Yeah, maybe some other things which are wrong have more hits than either, like "sex fetish". If you want to rename the article "EQV", then say so. -lethe talk 00:04, 23 November 2005 (UTC)
Even if 5 of the top 10 hits for "EQV" were "not related to the operator", that would mean that 50% are. And 50% of 319,000 is still far more than 104,000 hits for "XNOR", even if we assume all 104,000 hits there are related to the operator. I accuse you of misreading the chart because you keep comparing apples and oranges, namely "logical EQV" with "XNOR". It only makes sense to compare "logical EQV" with "logical XNOR" and "EQV" with "XNOR". Obviously an exact two word search term will find fewer matches than a one word search. I can't really believe you needed to have all this explained to you, so must conclude you are intentionally trying to misinterpret the chart so it supports your claim. I could just as well misinterpret it the same way and say "319,000 hits for 'EQV' and only 250 hits for 'Logical XNOR' !" StuRat 00:47, 23 November 2005 (UTC)
I still disagree. -lethe talk 01:24, 23 November 2005 (UTC)
Can't you be any more specific about what part of my statement you disagree with ? StuRat 02:35, 23 November 2005 (UTC)
I'm sure you know what I disagree with you on. I've said it many times, and I'm tired of saying it. I oppose the move. Call for others to comment if you want a move, because it doesn't look like either of us is going to convince the other. -lethe talk 03:04, 23 November 2005 (UTC)
I know you oppose the move, but what I don't know is why. You've said many times that you've opposed it, but I don't recall seeing a list of your reasons. StuRat 05:00, 23 November 2005 (UTC)
Seems almost willful. -lethe talk 05:48, 23 November 2005 (UTC)
Possibly -- but I doubt it. As for A D Monroe III's comment, "Logical EQV" is exactly the same gate and logical operation as is used in this article. I'm willing to defer to to experts on the name of the gate being XNOR, but the name of the logical operation, both in logic and in computer languages, is EQV. I hate splitting the article into XNOR for the gate and EQV for the operation, but, if it must be done, it must be done. Arthur Rubin | (talk) 22:22, 21 November 2005 (UTC)
No need to split, the other names are well covered. See logical equivalence. logical biconditional and if and only if. In fact, there is possibly a need for a merger. I've made EQV a redirect to logical biconditional. -lethe talk 00:03, 22 November 2005 (UTC)
This (redirecting EQV) borders on vandalism, although I'm not going to revert it. As a logician, I can assert that the name of the logical operator in mathematical logic (or boolean algebra) is NOT "XNOR". In that context the name could be "EQV", "EQUIV", or an overdefined "=". I would have to defer to others on the name of the gate or the name of the operation in computer languages. Arthur Rubin | (talk) 00:32, 30 November 2005 (UTC)

Whoa, Arthur! Vandalism? Creating a new redirect that points to a related topic? Let's keep our shirts on. Also, are you under the impression that I redirected EQV to XNOR? If you reread what I wrote more carefully, you'll see that I redirected EQV to logical biconditional. Do you find logical biconditional equally as offensive as XNOR? If so, feel free to change it, nominate it for deletion, whatever. I only created the redirect to appease you, so if you don't like it, then by all means, get rid of it. And I do apologize if you took it the wrong way (I swear, it wasn't vandalism. It was meant to help!). -lethe talk 01:19, 30 November 2005 (UTC)

I would have stated that EQV is the most commonly used form as an associative (or n-ary) logical operation, more so than the other forms I consider acceptable as a logical operation (iff, SAME, "="). I probably would have moved the logical operation to EQV, leaving the non-logical context in iff and logical biconditional (which, by the way, should probably be merged. They seem to have almost identical content and refer to each other.) None the less, I overreacted.

It occurs to me, though, that we may have a reason for having separate articles on xnor and eqv, even so...

• A xor B xor ... xor T is true if an odd number of A, B, ..., T is true.
• A xnor B xnor ... xnor T (as an n-ary operation or an n-input gate, rather than as an associative binary operation) is true if an even number of A, B, ..., T is true.
• A EQV B EQV ... EQV T is true if an even number of A, B, ..., T is false.
-- Arthur Rubin | (talk) 02:23, 30 November 2005 (UTC)

## Logical Equality

JA: I have restored the name to the rightful moniker of Logical equality. This is what it's called in logic, and also in programming languages going back to Fortran. Hardware folks may seek their own salvation, and I'm sure that the equanimity of logicians will eventually be equal to the task of curing souls among those Philistines, but in the meantime we have to do our level best to call an equality and equality. Jon Awbrey 12:02, 3 May 2006 (UTC)

## Truth Tables

Do we really need both truth tables? — Arthur Rubin | (talk) 16:03, 23 May 2006 (UTC)

## Three Way Light Switch?

Is a properly functioning three-way light switch an xnor gate? I began thinking this because I have an improperly wired three-way light switch in my kitchen that operates as an "and" gate, instead of an "xnor" gate. —Preceding unsigned comment added by 71.238.34.102 (talkcontribs) 20:25 (UTC), 5 February 2007