Talk:Two's complement/Archive 1

Archive 1

Requires Cleanup

This page needs to be shortened, and contain a much more consise overview of how twos complement works, on a direct practical application of which. Philcluff (talk) 02:11, 19 February 2008 (UTC)

The article is also full of typos and grammatical errors. It is also written in a tutorial-type style. —Preceding unsigned comment added by 72.140.154.188 (talk) 22:11, 27 February 2009 (UTC)

For openers... which is correct: two's or ones', both of which are used in the first paragraph? "Two's" is grammatically the possessive singular, something that "belongs to two". "Ones' " is the possessive plural, i.e. something that "belongs to ones" (plural, more than one instance of "one"). Probably "ones' complement is right - flipping every bit gives the complement with respect to a bunch of ones, one for each bit position, thus the plural of one, and the complement belonging to this plural object. In which case by analogy it should probably also be "twos' complement" or "tens' complement". And if you write it with numerals, 1s' complement and 2s' complement and 10s' complement, again a plural possessive in each case. In any case, whatever notation is used, it should at least be CONSISTENT! Including in the title of the whole article!!!!!

("For openers", "CONSISTENT!" Instead of shouting, you could read what Knuth has to say about this issue. The article is correct.)

Merge with signed number representations

Can we merge this with signed number representations? which is not too long yet and there are some overlap between that and this. -- Taku 23:23, Jul 31, 2004 (UTC)

I disagree; there may be some overlap but the pages have different purposes. Signed number representations compares different representations; this describes one of them in detail. --Rick Sidwell 03:26, 13 Apr 2005 (UTC)

Overly verbose example

In showing that -95 is congruent to 161 (mod 256), there's an example that shows "−95 + 256 = −95 + 255 + 1 = 255 − 95 + 1 = 160 + 1 = 161". What's with the verbosity? Would "-95 + 256 = 161" not work just as well?

The point of the example is to illustrate the binary subtraction. The one's complement of x

is just (255 - x). So we need the 255. Compare to the binary example immediately following.

Scottcraig 21:25, 15 July 2005 (UTC)

Re: Why it works

Ooh. All I can say is that two's complement only has to be actually implemented where the resulting numbers are actually used; a simple addition or subtraction module wouldn't care a bit (no pun intended). --Ihope127 01:49, 25 August 2005 (UTC)

I think that there is an error in 3 + (-1) calculation. 0011 + 1111=0010 not 1010 as is write in the article. —Preceding unsigned comment added by 94.37.161.40 (talk) 12:44, 2 October 2009 (UTC)

Binary notation

The article uses a strange form of binary notation:

−64 = 1100 0000₂

The subscript 2 is usually reserved for the binary numeral system, rather than any old binary represenation. As I understand it, the above binary is how to write 192 in (mathematical) binary. Is there another way we could indicate the numbers are just binary, without using the "normal" binary counting system? —Pengo 07:29, 12 September 2005 (UTC)

I agree, though I don't have a better suggestion. --63.85.132.5 13:00, 9 March 2006 (UTC)

I'm not sure I understand what Pengo means by "any old binary represenation" or "indicate that numbers are just binary" but I'm no native English speaker.

However, why not write

−64 = 1100 0000_2's

−63 = 1100 0000_1's

192 = 1100 0000₂

It wouldn't be much extra work. HenkeB 01:31, 7 June 2006 (UTC)

I think the issue, if there is one, is not in the subscript but in the '='; when I talk about this kind of thing, I like to talk about a 'value' of -64 but a 'code' of 11000000, so it just needs a note about the meaning of the equivalence; it means 'coded as'. 76.67.98.29 (talk) 21:43, 6 February 2008 (UTC)

The problem is more general, and there isn't an easy answer. Binary is, for example, commonly used to represent the opcodes in binary computers. They don't have a numerical value in the sense indicated above, but may still be represented in octal or hexadecimal. On the other hand, in the notation indicated the value is the binary representation for 192, but meaning -64 in the two's complement system. Gah4 (talk) 21:29, 14 September 2018 (UTC)

Intro changes and the concise summary

I made a few changes to the intro to try to make it more clear. The main one is the addition of the concise summary:

In an n-bit binary number, the most significant bit is usually the 2^n-1s place. But in the two's complement representation, its place value is negated; it becomes the −2^n-1s place and is called the sign bit.

When I discovered this, it instantly clarified everything about two's complement for me. I'm interested to know if it does the same for you, or if there is an easier way to present that idea.

I know of 3 other ways to 'get to' two's complement:

1. the classic 2^N-b way
2. define -1 as the bit pattern that gives you 0 when you add it to +1
3. as a nice specialization of excess notation

Perhaps someday someone can write these up in detail here.

Ken 05:41, 2 February 2006 (UTC)Ken

calculation trick

One of my teachers mentioned a trick that was pretty useful. In calculating two's compliment, one finds the least significant 1, and flips all the bits more significant that that bit (ie. find the first 1, and flip the bits above it - but don't flip the first 1). This should have a picture to go along with it, and I don't have time now. Fresheneesz 22:47, 24 May 2006 (UTC)

....so you could type all of that, but there wasn't time to type some 0's and 1's. Puzzling. — Preceding unsigned comment added by 73.213.142.170 (talk) 18:36, 19 April 2015 (UTC)

Carry Bit/OverFlow Bit

I believe this page needs to be revamped. Their are a lot of inconsitentcies regarding the MSB. First of all the (Most Significant Bit (MSB) entry says that it is the highest bit of a binary value. But then it said to be the sign bit.

But more importantly, the carry bit tells you nothing in two's compliment. The overflow bit occurs when the addition of 2 positive numbers yields a negative, or the addition of two negative numbers gets a postive.

Also there is incorrect information regarding the XOR statement, the carry bit and the sign bit to do not determine the overflow bit. I shall prove this by contradiction.

 01 1111
+10 1010
 -------
 00 1001 C=1  S= 0, but V=0

Cleary the XOR argument doesn't work --NMocho 14:49, 23 July 2006 (UTC)

The article is correct regarding the XOR statement. It isn't the carry and sign bits that determine overflow, but the carry into and out of the sign bit. In this case, they are both 1, so there is no overflow. The carry out of the sign bit goes into the carry bit, and NMocho is correct that this tells you nothing in two's complement. The carry bit is useful for multi-precision addition, when the msb is an ordinary bit in the middle of a number, not the sign bit. The carry into the sign bit is not directly accessible in typical computers; it is XOR'ed with the carry out of the sign bit and stored in the overflow bit, which itself is not useful until a multi-precision addition is complete. So after any given addition operation, either the carry bit or the overflow bit is useful depending on whether it was an intermediate or final addition, but not both.

Multi-precision arithmetic isn't covered in the article. Perhaps it should be, although it isn't specific to two's complement. --Rick Sidwell 15:33, 29 July 2006 (UTC)

I haven't thought about this recently. The carry bit and the sign bits of the two summands gives the overflow. Easier done in hardware than software, though. Gah4 (talk) 20:01, 15 February 2017 (UTC)

Explanation disorganized

It seems that at some point the text was re-arranged carelessly. In the section Explanation, reference is made to "as we did when we counted backwards", apparently referring to some preceding text that has been removed. Also there's a reference to "the aforementioned overflow checks", again apparently referring to text that has been (re)moved. At this point, I stopped reading. Ferdinand Pienaar 09:56, 31 October 2006 (UTC)

Gosper extending two's complement into infinity

Would a link to the p-adic numbers be appropiate here, considering that while meaningless in normal number space, Gosper's proof actually IS correct for the 2-adic numbers? I know I once indepently got the idea of p-adic numbers from extending two's complement, though I never did much with it. -- Milo

I came here to say something like that. The 2-adic integers in particular are exactly the set of binary expressions of the form …bbb, so it seems perverse to reinterpret such an expression as an ordinary number and then note that it no longer makes sense. I'm sure there are sources that explain …111, but I don't have one ready, so I'll just remove the paragraph in question. Melchoir 17:01, 15 February 2007 (UTC)

Melchoir, I reverted your removal. Gosper's "proof" is given in terms of the natural numbers, not the 2-adic numbers; indeed, it wouldn't be interesting if it stated a tautology about an obscure system, instead of "proving" something cute about an everyday system. Given the number of newbies who are confused by "0.9999... is the same as 1.0", I think it's very important to retain the paragraph pointing out that Gosper's "proof" is a mathematical joke, and should not be taken seriously. (Gosper's point, IMHO, was that two's complement is the best binary number representation, and I agree with that. But his conclusion that "the Universe is run on a two's complement machine" is obviously not meant to be taken literally; it's a hacker joke.) --Quuxplusone 03:06, 16 February 2007 (UTC)

The Universe bit may be a joke, and that's already indicated by the "flight of fancy" language. But the mathematics is not a joke. The manipulation …110 = …111 − 1 is correct, and it is part of a valid proof of the value of …111. It's not that …111 "cannot" be considered a number in ordinary mathematics; it simply isn't considered in ordinary mathematics at all. There is no barrier to doing so, since the natural numbers are faithfully embedded in the 2-adic integers as the set of expressions with either leading 0s or leading 1s. Given all that, do you really think this is comparable to Mathematical jokes like "sex is fun" and Invalid proofs like i^2=1? Melchoir 04:42, 16 February 2007 (UTC)

I agree that Gosper's approach is sensible and somewhat logical. Two's complement numbers are always considered to have as many higher-order sign extensions as you need, out to infinity, conceptually. This is consistent with the value of ...11111 being -1 and nothing else; the value is unchanged with any finite truncation, as long as the MSB is treated as the sign. His logic makes sense for any finte length of the "...". Dicklyon 05:52, 16 February 2007 (UTC)

I do claim that Gosper's "proof" was meant to be taken humorously. For reference, we're talking about this item, which ends "therefore algebra is run on a machine (the universe) which is twos-complement." That's a joke. "Se^x = f(u_n)" might also be considered a "mathematical joke", but it's certainly on a different level, wouldn't you say? Gosper's joke is more akin in spirit to the observation that

The equation n^a+n^b=n^c has solutions in positive integers a,b,c, and n only when n=2 (and then there are infinitely many triplets a,b,c which satisfy the equation); but there are no solutions for n>2. I have discovered a truly marvelous proof of this statement, which, unfortunately, is so small that it would be well-nigh invisible if written in the margin.

— Lierre de Fourmi, in the margin of Di of Antus' Arithmetica, p. 333

Anyway, I don't really care one way or the another if you think Gosper was talking about p-adic numbers (he wasn't) or integers (he was). The clarifying paragraph certainly needs to be there in any case, so unless you want to keep trading quotations of other people's jokes, I'll move on. :) --Quuxplusone 09:18, 16 February 2007 (UTC)

I'm not disagreeing that the conclusion is meant to be taken humorously! But the mathematics isn't wrong in any meaningful way, whereas it's right in several meaningful ways. I'll try to fix the description. Melchoir 15:45, 16 February 2007 (UTC)

…Um, I appreciate that compromise is important, but this edit contains a lot of subtle problems that I tried hard to avoid. It's important to differentiate between Gosper's conclusion as a whole and the very end conclusion, since the first, mathematical part isn't a joke. Writing "see also Invalid proof" very strongly suggests that the proof in question is itself invalid, which it isn't. The phrase "can be treated as a number" is unmathematical; it is alway possible to make new definitions if necessary, or in this case to exploit old definitions that not everyone knows about. There's also no distinct "ordinary algebra", at least not in the sense that some subfield of mathematics manages to contain different results from the rest of mathematics. All one can say is that the definitions one learns in elementary school are insufficient to reason with …111. Finally, the three items in the last sentence are distinct, and they don't need to be merged. I'll expand on that last point and throw in Hardy as a source. Melchoir 02:12, 17 February 2007 (UTC)

Update: 1 + 2 + 4 + 8 + · · · now includes some of Quuxplusone's points, although it has yet to get to the 2-adic stuff. Melchoir 05:38, 17 February 2007 (UTC)

"Two's" and "ones'" complements?

A quick GBS search shows that both "twos complement" and "ones complement" are most often written without any apostrophe. This would seem preferable to the mixed way we have in this article. Or should we changes "ones'" back to "one's" or "two's" to "twos'"? Dicklyon 07:42, 19 December 2006 (UTC)

If "GBS" stands for Google Book Search, then I think what you're seeing is that Google doesn't consider the placement of apostrophes to be significant. Searching for twos complement and ones complement, with any of the three candidate punctuations, shows that the majority of the first page of results for any candidate punctuation are punctuated the way we have it: two's and ones'. My rationale is that Knuth does it that way, and has a good explanation for his choice, so let's follow the leader. But if everybody else also does it that way, that's good for us too. :) --Quuxplusone 06:09, 8 February 2007 (UTC)

Detail-oriented readers and copy editors should notice the position of the apostrophe in terms like two's complement and ones' complement: A two's complement number is complemented with respect to a single power of 2, while a ones' complement number is complemented with respect to a long sequence of 1s. (Volume 2, p. 203, according to [1])

No, I didn't rely on the search function to make the distinction; I just looked at all the occurrences to see how they were punctuated. I do agree with the logic of what you found there, I guess we're fine. Dicklyon 06:20, 8 February 2007 (UTC)

It's "ones' complement" because it's the complement with respect to multiple ones - a binary repunit. OTOH, a two's complement doesn't relate to a string of 2s, but to a single power of 2. Really, it's a (power of two)'s complement. — Smjg (talk) 21:49, 29 November 2011 (UTC)

When I learned it, a long time ago (maybe I was nine), it was two's complement because it was one more than ones' complement. Note also that you need to distinguish between the binary representation and the trinary (which might be twos' complement) representation. Gah4 (talk) 20:56, 7 May 2015 (UTC)

"howto" tag

I re-added the howto template, and also added the {{disputed}} template to open it up to wider discussion. The section does read like a how to or a receipe. Tata2007 14:36, 4 October 2007 (UTC)

I just removed the {{disputed}} template tag as it was not the correct template (it called into question the factual accuracy, which in fact is not in dispute). Tata2007 14:38, 4 October 2007 (UTC)

I think the section is fine. I would argue that the process of converting numbers to two's complement form is integral to readers' understanding on the issue. --pie4all88 19:39, 6 October 2007 (UTC)

I think it's OK, too. The tag says "This section contains instructions, advice, or how-to content," but I don't interpret it that way. It's a bit too-detailed as a description and example of the process of generating a two-complement, but it's certainly not advice, and not really instructions per se. So tune it up instead of tagging it. Dicklyon 19:44, 6 October 2007 (UTC)

If it needs a tune up (and I think it does) the tag will help attract editors to do this. Tata2007 20:13, 8 October 2007 (UTC)

ubiquitous two's-complement

I am considering adding a fact tag to the following sentence, but is also has other problems (implicit comparison to one's complement is too subtle).

“ The two's-complement system is ubiquitous today because it doesn't require that the addition and subtraction circuitry examine the signs of the operands to determine whether to add or subtract, making it both simpler to implement and capable of easily handling higher precision arithmetic. ”

The implication is that computers implement two's complement much more often than one's complement for the reason stated. E.g., it might be more precisely written:

“ The two's-complement system is ubiquitous today for a number of reasons. First, addition and subtraction circuitry is simplier than what is required for ones' complement system. Second, two's complement does not have abiguity with zero while one's complement has positive and negative zeros. ”

This, I believe, it true and verifiable; but I don't have a refernce at hand. Also, I do think the assertion that two's complement is "capable of easily handling higher precision arithmetic" should be sourced. Tata2007 14:53, 4 October 2007 (UTC)

It is a little strange. The fact that the bits are the same as unsigned arithmetic might be the reason for the comment. I suppose there is a reference for that. But a ones complement machine could also support an unsigned mode. Gah4 (talk) 02:45, 11 February 2013 (UTC)

One's complement is not the only plausible alternative. The system of sign & magnitude has also been used. Both are more complicated, and no system designed since about 1980, I think, uses anything but two's complement, for the reason given. Although, inside floating point numbers, perhaps sign and magnitude are still used. Dicklyon (talk) 17:09, 16 March 2008 (UTC)

CDC made ones complement machines for some years. It might be that the last one was designed before 1980, though they might have still built some after that. IBM machines descendent from S/360, including new designs, support sign magnitude BCD (decimal) arithmetic. It isn't so obvious why 10s complement wasn't used, though one advantage of sign-magnitude BCD, based on the BCDIC or EBCDIC code, is the way it translates to overpunched sign on punched cards. Gah4 (talk) 02:45, 11 February 2013 (UTC)

Advantages of 2's compliment

Could someone clearly state the advantages of 2's compliment. Chendy (talk) 16:57, 16 March 2008 (UTC)

First, learn the word complement and what it means, and how it differs from compliment. Then note that this representation allows addition and subtraction of signed numbers to work very easily, with uniform simple logic, and for multiplication and division to also be not bad. That's why all modern computers use it. Dicklyon (talk) 17:07, 16 March 2008 (UTC)

It's possible that Chendy is being funny. Wikipedia actually links "2's compliment" to 2's complement ! Cuddlyable3 (talk) 00:09, 6 December 2008 (UTC)

Explanation

Table "8-bit two's-complement integers" is wrong for 127 value : 127 = 1111111b. —Preceding unsigned comment added by 66.130.36.239 (talk • contribs)

I presume you mean to explain this edit. Yet your explanation is backwards. What's up with that? Dicklyon (talk) 06:04, 15 May 2008 (UTC)

1 —Preceding unsigned comment added by 99.227.31.9 (talk) 01:05, 12 February 2009 (UTC)

Subtracting 2^N?

My discrete math professor pointed out, and I have to agree, that the opening line of the article is extremely unclear in the way it represents what two's compliment is for. The two's compliment is reached by adding the negative number to the power of two. Nothing is done at all to positive numbers. Perhaps I'm getting some of the slang wrong, but this looks like it needs to be corrected. Dandaman32 (talk) 15:42, 28 September 2009 (UTC)

I believe that what the lead says is correct, about the two's complement of a (positive) number, and that what you're saying is about the two's complement representation of a negative number, which is also correct. The point is that in two's complement notation, a negative number 0-N is represented by the two's complement of N. Dicklyon (talk) 17:08, 28 September 2009 (UTC)

Calculating 2's complement

May be we should add a section to the introductory paragraphs on how to calculate 2's complement. I like the following explanation and this is the method i learned in school too. I copied this from a webpage , so dont know whether to include it or should i write it in my own words.

To calculate the 2's complement of an integer, invert the binary equivalent of the number by changing all of the ones to zeroes and all of the zeroes to ones (also called 1's complement), and then add one.

For example,

0001 0001(binary 17) 1110 1111(two's complement -17)

NOT(0001 0001) = 1110 1110 (Invert bits) 1110 1110 + 0000 0001 = 1110 1111 (Add 1)

Ursvasan, 01 Oct 2009 —Preceding undated comment added 21:52, 1 October 2009 (UTC).

'Complement of a positive number' error?

In section 'Complement of a positive number', the following formula is given:

---

  N** = (rm – N) mod (rm)

---

However, I believe this formula is incorrect/unnecessary complex: if you substract N (positive and smaller than r^m) from r^m, then the mod is not necessary, because the result will always be smaller than r^m. Right?

--Patrickdepinguin (talk) 10:54, 30 October 2009 (UTC)

I believe you are correct there. But the condition in the text allows the number to be 0, in which case the mod is needed; "positive" should chnage to "nonnegative". Dicklyon (talk) 16:56, 30 October 2009 (UTC)

Yes, you are right. I overlooked the fact that N can be 0. I agree that 'nonnegative' may be a better word in the title. --Patrickdepinguin (talk) 14:24, 4 November 2009 (UTC)

Incomprehensible to the beginner

Like most maths related articles on wikipedia this page seems incomprehensible to me. As a computer science As student who found this topic relatively simple once explained methodically this article seems to operate at a level beyond those who are kost likely to read it (such as myself).--86.138.113.101 (talk) 18:01, 17 May 2010 (UTC)

-- I used to do twos complement on a 8-bit machine, which I programmed at machine code level (hand coded from the assembly language) and I found this "explanation" if that's what it's called, beyond ludicrous. Wikipedia is moving more and more this way - becoming more esoteric and verbose even when simple subjects are involved (and twos comp. is fairly elementary). —Preceding unsigned comment added by 86.22.34.73 (talk) 15:48, 4 May 2011 (UTC)

-- Ditto on both criticisms. It is, of course, well known that much of Wikipedia is deeply flawed but I think that mathematics articles are particularly bad. Many of these are being edited by people with zero competence but the resulting errors in substance are essentially hidden from view by grammatical errors and an incoherent exposition. When an editor does possess the required background and writing ability, his or her edits will quite often be reverted by some know-nothing for some incomprehensible reason. I once corrected the grammar of a mathematical proof (you understand I have taught mathematics at a university, have published mathematical research and written a book) and my edit was reverted because the previous editor claimed that the only way to express what he wanted to express was, of necessity, ungrammatical. Will I edit the Two's complement article with a view to improving it's coherence? No because there's a good chance that any edits I make will be reverted by some guy living in his mom's basement who just read something somewhere about binary representations and wants to play professor.154.5.40.122 (talk) 06:15, 4 December 2011 (UTC)

It might be constructive to point out specific examples of what is incomprehensible. Write them here on the talk page if you don’t want to touch the article. Vadmium (talk, contribs) 04:46, 5 July 2012 (UTC).

Definition

-- It didn't help that the first sentence of the whole article contained a key error that contradicted every other example on the page ("subtract a value from n^N for an N-bit number", instead of "subtract n^N of an N-bit number from said value"). Vjofy (talk) 13:12, 5 July 2012 (UTC)

I disagree with your redefinition and think I will revert to 2^N − x. Maybe I can clarify the article a bit; I’ll have a closer look at some of “every other example on the page” to see if I can find any contradictions. Two books I quickly checked (6809 Assembly and Dictionary of Mathematics) both indicate a complement is what you have to add to a given value to get some fixed total value. For 8 bits, the total value is 256 and two’s complement of 1 would be 255. Vadmium (talk, contribs) 04:46, 5 July 2012 (UTC).

Yes, I totally agree with your formula, which does accord with all the examples on the page. However, the original written definition did not accurately reflect the formula above. And although the way you re-phrased the revert is a little clearer, the current definition remains somewhat ambiguous. You reverted to: "The two's complement of a binary number is defined as the value obtained by subtracting the number from a large power of two". To me, that sounds like it could be 2^N - value = twos_complement. I know now that you mean 2^N - twos_complement = value One of the several problems with this phrasing is that when you write "obtained", that suggests that you're referring to the number on the right side of the equation. It's also not clear which number "the number" refers to in this definition. I'm going to leave your revert as is, since I suspect you're just going to revert any change I make anyway, but I'd highly suggest finding an natural language definition that better reflects the formula as given. I spent 15 minutes yesterday trying to figure out why the examples given did not match the written definition. Even if you don't change to written definition to something clearer, perhaps you could put the formula in parentheses next to the definition, so that people confused by the written definition can seek clarification from the formula..Vjofy (talk) 13:12, 5 July 2012 (UTC)

Much clearer now, thank you! That works. Vjofy (talk) 13:20, 5 July 2012 (UTC)

Sorry, I didn’t mean to completely scare you away by reverting. I see that the “value” versus the “number” in the subtraction could be confusing; I’ll try fixing it tomorrow if no one beats me to it. Also, adding a formula at the top might still be a good idea; perhaps something like

x* = 2^N − x

which is actually found amongst the mess later in the page. [Is this asterisk a recognised notation for complements, or is there any other recognised notation?] Vadmium (talk, contribs) 14:07, 5 July 2012 (UTC).

Bug in "Making the two's complement of a number"

I just noticed a bug in the section "Making the two's complement of a number". Step 2 and 3 (complement the value and add one) should only be performed if the value is negative but there is no indication of that in the current page.

(I'm sorry, but I don't have time to actually edit the page right now, but I'm noting it down here so that it is not forgotten.) —Preceding unsigned comment added by 90.228.211.236 (talk) 23:10, 16 January 2011 (UTC)

Ha ha. Thank god for anonymous users who promise to keep tabs on what's up with Wikipedia editorial requirements. This is the sort of thing that makes Wikipedia great.154.5.40.122 (talk) 17:27, 27 December 2011 (UTC)

Using a library to say the cow jumped over the moon

This article is ridiculously long for the topic. The discussion meanders and gets into signed arithmetic, endianess and who knows what, much of which has only peripheral value. If I didn't know anything about two's complement before reading this mess I surely wouldn't know any more after reading it!

38.69.12.6 (talk) 21:40, 12 September 2012 (UTC)

I agree that the article needs some overhaul; I've already removed some unneeded passages. I'd also suggest removing the section titled "Two's complement and universal algebra", since it seems too specialized for an encyclopedic article.

However, I wouldn't remove the section on arithmetic operations, since this information can't be found elsewhere on WP. Or am I mistaken? – Adrian Willenbücher (talk) 20:21, 13 September 2012 (UTC)

I'm also in the process of removing the representation of fractional numbers from the introduction, since it has no place there and only serves to confuse the novice reader. I will probably create a new section later in the article dealing with this topic. – Adrian Willenbücher (talk) 07:55, 14 September 2012 (UTC)

Two apparent degradations I had to fix after the Adrianwn’s strike: an illiterate "negative power" wording and one hyphen-minus. Also, internal redirected links like sign-and-magnitude should not be expanded. Incnis Mrsi (talk) 10:19, 14 September 2012 (UTC)

Do not <math>x*</math>

Do not use $x*$ because it is rendered as x∗ (a special vertically centered asterisk for binary operations), not x* (raised asterisk, appropriate for an unary operation). Incnis Mrsi (talk) 21:17, 14 September 2012 (UTC)

How do you get an asterisk in math-mode? Also, should we use math-mode in inline text at all? It looks strange in my browser, because it's larger than the rest of the text. – Adrian Willenbücher (talk) 06:01, 15 September 2012 (UTC)

If you insist on <math>, then use a superscript, $x^{*}$. But {{math}} is better suited for in-line text: x*. This latter does not require superscripting because ASCII asterisk is already raised. Incnis Mrsi (talk) 06:25, 15 September 2012 (UTC)