Talk:Power of two

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[edit] Some patterns

Some patterns I noticed that might be placed in the article: No exponent of two is divisible by and odd number, or at least 3. The other one would best be expressed square root of 2n=2(n-1) where n=or>4. Someone make that a formula for me. Can anyone check these for me? 141.156.190.218 02:22, 28 February 2007 (UTC)

The first one is almost correct, although all powers of two are divisible by one (which is odd). This property can be generalized: a power of any prime can only be divided by other powers of the same prime. (You can prove this to yourself by thinking about the prime factorization of the power of a prime, and the property of divisibility that if X is divisible by Y, then all of the elements of Y's prime factorization have to appear in X's prime factorization.) Since odd numbers are ones that can't be divided by two, then no power of two can be odd (except for 20 = 1).
Your second hypothesis isn't quite accurate, though. As a couple of counterexamples, \sqrt{2^6} = 8 = 2^3, and \sqrt{2^5} isn't a power of two at all (it's not even a whole number). You're close, though... keep working at it.
I'm glad that you're excited about finding properties of numbers. You can have a lot of fun looking for interesting patterns in numbers, like the Hardy-Ramanujan number. While it's fun and interesting to find these properties, many of them aren't notable enough to be included in an encyclopedia, so I don't think it's worth putting these in the article. --Piquan (talk) 00:48, 29 February 2008 (UTC)
Have you noticed the year in the post you replied to? It's the only post by that IP. PrimeHunter (talk) 01:13, 29 February 2008 (UTC)

It says "nonnegative integer" in the article. Now, 0 is the first nonnegative integer, 1 is the second, 2 is the third, 3 is the fourth, etc. However, 8, which corresponds to the exponent of 3, is thought of as the third power of 2, not the fourth, and 1 is thought of as the zeroth. Any modifications to the first paragraph of the article?? Georgia guy 21:05, 8 Jan 2005 (UTC)

This is kind of tricky. In common parlance we say that a is the cth power of b if a = bc, even if it is not the cth in a list of nonnegative powers of b. I've even heard people say "the one-halfth power" for the square root. It's a bit sloppy, and maybe we can rephrase it, but it's pretty common. Deco 02:54, 11 Jan 2005 (UTC)

[edit] Categories for binary number algorithms

I think rounding to nearest power of two number should be put to some algorithm/computer arithmetic category, or even some other article. Rounding to nearest power of two is often related to computer programs and it would make sense to have some article/category listing the relevant methods. Any ideas which category/article? Shd 16:01, 8 October 2006 (UTC)

[edit] First forty-one powers of 2

This phrase can be reworded as "first through forty-first", not "zeroth through fortieth". Any faulty thinking?? Georgia guy 21:06, 21 October 2006 (UTC)

[edit] Radix vs Power

This page seems to confuse radix-2 with power of 2. Radix 2 implies 2 to the n (2n), while power of 2 implies "n to the power of 2" or n2. This is a common mistake, so I have tried to fix those improper references. —The preceding unsigned comment was added by 65.242.3.72 (talk • contribs) 14:22, 16 March 2007 (UTC)

What makes you think there is a mistake? Every Google hit for "powers of two" I can find refers to 2^n. 18:51, 16 March 2007 (UTC)


What's 5 to the power of 2? 25. What's 2 to the power of 5? 32. This page is mileading simply because it forces people to look at the context "power of 2" is used in to try to guess what's really meant. As for the Google search: What's "popular" is not always right; what's right is not always popular. Why don't you look up Radix-2 and Radix-4 FFT definitions and try to figure out how they got their name? You are perpetuating a common ambiguity that only serves to add confusion to a discipline which requires precise language usage. Petersk 20:14, 18 March 2007 (UTC)

You're playing with words. Anyway, Wikipedia does not allow you to claim that the universally understood meaning of "power of two" is somehow "wrong" unless you can attribute that claim to a reliable source. Melchoir 20:28, 18 March 2007 (UTC)
OK, please, just refer to the wikipedia page on radix [1]. I make no additional claim. Both pages cannot be right, unless your page is deliberately ambiguous. Petersk 20:30, 18 March 2007 (UTC)
Although one sometimes hears the phrasing "raised to the power of" something, a "power of 2" is never something raised to the second power. A "power of 2" is 2 raised to some power. This is standard mathematical terminology and I'm afraid that it's you who are misinterpreting the term. Dcoetzee 22:18, 18 March 2007 (UTC)
I'm not even too sure where to go with this last comment... What's 5 to the power of 2? You've really never heard of that terminology before? I can show you lots of algebra/pre-calculus books that make that exact statement, so I am not sure what "standard" you're referring to. Do you have any doubt of someone's intent when they say that number is radix-2? (I am actually starting to doubt you even heard of the term radix or radius until this conversation.) Which is more clear and precise leaving no room for doubt? Just because someone in computer science got it wrong a while ago doesn't mean that this must still be perpetuated, especially in a wiki. Did you bother even looking at the radix wiki? 68.228.142.173 23:35, 18 March 2007 (UTC)
There is a difference between having a power of two and being a power of two. You are simply being confused by the multiple meanings of the word "of" in English grammar.
That's the substance of the issue; here's the procedure. There is no evidence, certainly not in our Radix article, supporting your usage of the word, and context is everything in Wikipedia policy. This website is an encyclopedia as well as a wiki; it is purely descriptive, and it does not advocate new language for any reason. You'll be happier if you stop thinking in terms of "right" and "wrong". Melchoir 23:55, 18 March 2007 (UTC)
The "new" language is using "power of" instead of "radix". Computer science came after mathematics as a discipline -- I use that term loosely when referring to computer science. Perhaps a good compromise is to allow modification of this site pointing out that radix is the historically more correct way of describing numbes that are radix-2 and refering to the radix wiki? 68.228.142.173 13:17, 23 March 2007 (UTC)
An historical claim still demands verification, and it still is not found in the Radix article. Melchoir 18:03, 23 March 2007 (UTC)
How about we start out with the US Department of Commerce? Chapter 28, p 1012, "Representation of Numbers" states the use of base or radix. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, edited by Milton Abramowitz and Irene A. Stegun, National Bureau of Standards Applied Mathematics Series 55, Issued June 1964. I'm referencing the tenth printing, Dec 1972. The American Heritage Dictionary, second College Edition, c 1982,1985, under '"power". Math. a. An exponent, b. the number of elements in a finite set.' Is two enough, considering the author only has a Master's degree and references nothing but google? 68.228.142.173 11:41, 28 March 2007 (UTC)
Those sources do not appear to support your claim. Certainly the second doesn't, and you haven't quoted the first. "Representation of Numbers" sounds like the usual usage of the word radix: indicating the base of a numeral system. For example, one would say that the number three is written 11 in radix 2. One would not go on to say that three is "radix-2", or that 11 is "radix-2". Substituting four or 100 would make no difference. Melchoir 00:28, 3 April 2007 (UTC)
I don't see how you can say that. The sources clearly delineate how numbers should be represented. I don't need to quote the first source, because a careful reading clearly shows the meaning and accepted usage, which in no way includes "power of". As for saying 4 is radix-2, that is, in fact, accepted and used -- showing your ignorance. But that's neither here nor there. Where are the sources that define "power of two" the way the author does? The first to the trough is not, by definition, removed from any burden of proof or use of references. Let's see some authoritative documentation of that definition. Petersk 16:46, 12 April 2007 (UTC)
Done. Now where's your radix-2 source? Melchoir 20:50, 12 April 2007 (UTC)
How many more do I need to provide that you'll summarily discount? I'll have to take a look at the sources you just provided and see if they meet the same "test" that you have given my two above. But... that being said, please pick up the latest "Embedded Systems Design" magazine (April 2007). There's a nice article by MIT professor Anant Agarwal (yes, the guy that's written multiple books). Surprisingly, on page 50, in his article, "Going Multicore Presents Challenges and Opportunities," he clearly uses the term "power of n" where he talks of an "n-fold" increase (implying n is in the exponent), thus validating from yet another source this wikipedia article's lack of validity. 68.228.142.173 16:17, 15 April 2007 (UTC)
Does Anant Agarwal specifically claim that a power of two is a number of the form n^2? Melchoir 19:32, 15 April 2007 (UTC)
I reiterate that the anonymous contributor is incorrect; a "power of two" is a number of the form 2n. I've seen it defined as such in many published papers and authoritative reference books. There is no room for argument here. Dcoetzee 23:34, 3 December 2007 (UTC)

[edit] Next biggest algorithm

The algorithm has unnecessary dependencies and probably suboptimal performance in modern CPUs. It relies on writing the value of n on every statement, while all ORs are independent.

And it's unnecessarily hardcoded; a loop (while n != 0) would be shorter, more general, and often faster. For that matter, why not for (j=1; ; j<<=1) { if (j>=n) break } ? —Tamfang (talk) 19:03, 31 January 2008 (UTC)

[edit] Word Size

The sentence discussing common CPU register quantities has a linked directing the reader to read the article about word size. Word size has nothing to do with the quantity of CPU registers. —Preceding unsigned comment added by 70.113.46.77 (talk) 16:16, 3 December 2007 (UTC)

[edit] Suggested merge from polite number

I have placed a tag on polite number suggesting that it be merged here. The polite numbers are exactly the non-powers-of-two, so they are not independently interesting as a number sequence. The relevant fact is that an integer N can be represented as a sum of consecutive integers, if and only if N is not a power of two; this seems worth mentioning here, with a link to the website listed on the polite number page, rather than making a whole separate article for that factoid. —David Eppstein (talk) 18:33, 5 February 2008 (UTC)

I am not sure if this merge is a good idea. If someone is looking for what a polite number is, and he will get redirected to powers of two, where will be no explanation what impolite numbers are (at least in the intro, I guess), it will just be more confusing. I think a separate, although probably always small, article, is better. Samohyl Jan (talk) 09:58, 6 February 2008 (UTC)
polite numbers are of independent interest as a set of numbers that can be investigated in an educational context. Basically they are an interesting problem that can be given to school students. Nick Connolly (talk) 22:32, 6 May 2008 (UTC)