WordPress.com Stats Reports One Million Views

This site went live on November 14, 2008; that works out to an average of over 920 views per day. My decimal/binary converter (an HTML form with an accompanying article) accounts for nearly half of those views (445,700+). Not counting my converter, these are my top ten articles:

1. Java Hangs When Converting 2.2250738585072012e-308 (134,500+ views)
2. PHP Hangs On Numeric Value 2.2250738585072011e-308 (93,600+ views)
3. Binary Dates in 2010 and 2011 (45,600+ views)
4. Ten Ways to Check if an Integer Is a Power Of Two in C (37,400+ views)
5. Converting Floating-Point Numbers to Binary Strings in C (15,200+ views)
6. Why “Volatile” Fixes the 2.2250738585072011e-308 Bug (12,200+ views)
7. FPUpdater Fixes the Java 2.2250738585072012e-308 Bug (10,600+ views)
8. How I Taught Third Graders Binary Numbers (9,800+ views)
9. The Answer is One (Unless You Use Floating-Point) (9,700+ views)
10. A Closer Look at the Java 2.2250738585072012e-308 Bug (9,200+ views)

Five of my top ten articles are related to the PHP and Java floating-point conversion bugs; together they total 260,200+ views.

By Rick Regan (Copyright © 2008-2012 Exploring Binary)

Exploring Binary: One Million Views

looks like Eggland’s Best egg stamp

I don’t think there will be any confusion with the marks, unless I start writing binary numbers in eggs .

10111001: The Binary Representation of 185

By Rick Regan (Copyright © 2008-2012 Exploring Binary)

Exploring Binary or Eggland’s Best?

Partial Screenshot of Google's Home Page, July 20, 2009

This is no surprise really. I designed my header image to look like the surface of the moon, and picked the blue in the navigation bar and links to match the blue of earth as seen from space. The yellow of the lander even matches the yellow in the link to my decimal/binary converter, although I picked that to match the sun.

Here’s another screenshot from the search results page:

Partial Screenshot of Google's Search Results Page, July 20, 2009

By Rick Regan (Copyright © 2008-2012 Exploring Binary)

Google Image Matches the Imagery of Exploring Binary

This post was motivated by the article “What Are Your Internet Goals for 2009?”, by Daniel Scocco.

Since I am new to blogging (I just started this blog a month ago), my internet goals for 2009 are my goals for Exploring Binary specifically. I’d like to get this blog off the ground before I try anything else!

I’ve been maintaining a long list of things I want to accomplish with this blog, but I whittled it down to the most important goals — all challenging but realistically attainable:

1. Write 64 articles.

   My articles are technical and generally require a lot of research, and I want them to be accurate so that they will be a resource to search traffic for years to come. My current rate is about one article every 10 days. I’d like to publish one full-length article per week in 2009, plus some shorter articles that take less work.

   I wrote 36 articles in 2009. It just takes me a long time to write a good article, and I’m comfortable with that.

2. Average 512 unique visitors per day.

   This is based on some keyword research, relative to the articles I plan to write. I expect the majority of visitors to be from search engines.

   I fell way short of this goal. My average is about 50 visitors and 100 page views per day. I really had no idea what to expect, but I am happy that the numbers keep (slowly) rising. One “problem” is that I’m writing about what I find interesting, not necessarily what the masses want to read.

3. Average 256 RSS subscribers.

   I’m hoping some of my visitors are interested enough to subscribe, but from what I’ve read, only a small percentage of people use RSS.

   I fell way short on this one too. The subscriber count fluctuates daily, but it’s around 60. In fairness, I’ve done very little to promote this blog.

4. Rank #1 in Google for “binary numbers”.

   This one could be tough. I have to beat the current number one, Wikipedia, which has a page rank of six.

   I didn’t even try. I chose to write about topics that are not well covered, or covered poorly. That said, I now know that there’s no way I could have beaten a PR6 article within a year’s time!

5. Average 1 comment per day.

   Feedback is probably what I want most: to correct me, to teach me, and to guide what I publish. I would hope some feedback would follow if I meet the above goals. I am kind of in the dark on this estimate though. I’ve read that a tiny fraction of visitors make comments, and that seems to be the case on blogs I read.

   If the passive approach to getting comments doesn’t work, I may have to solicit them. Polls? Contests? Q&A? I’ll have to see.

   Factoring out trackbacks and my own comments, I got 33 (you do the math). But I got a comment from Rasmus Lerdorf, so maybe that counts for 332? The bottom line seems to be this: I need the traffic to achieve this rate.

6. Go social on 1 post.

   I don’t expect my content to be Dugg, but if ever there were a chance, it would be the article I plan to write about the powers of two and their relationship to the NCAA basketball tournament (Of course I plan to publish that in March Update: published 3/11/09).

   It wasn’t the NCAA article, but I wrote one that did go social — on reddit: “Print Precision of Dyadic Fractions Varies by Language”. It got about 700 views within a half day.

7. Make $128 from advertising and commissions.

   I don’t expect to make much money, especially with a tech-savvy audience. That said, I’m looking forward to hanging my first Google Adsense check on my wall (like a pizzeria hangs their first dollar bill).

   I made less than $5. I removed ads from my site halfway through the year though — it was clear they weren’t making me money, and so why cheapen my site — but maybe I would have hit $12?

(I didn’t set out to make the numbers gimmicky, but if you’re going to estimate, why not with powers of two? At least I didn’t add an eighth goal just to have 8 goals.)

I’ll let you know how I did this time next year!

By Rick Regan (Copyright © 2008-2012 Exploring Binary)

My Goals for Exploring Binary in 2009

If you want to get an idea of what this site is about, you can read the following articles:

• The Origins of This Site
• My Plan For This Site
• About The Name Exploring Binary
• About the Header Image
• My Fascination with Binary Numbers

I’ve got a big list of ideas but I’m only starting out with a few articles. My initial focus is binary numbers, but before I can get to them proper, I need to discuss the powers of two. Understanding the powers of two is key to understanding binary numbers, and just about everything binary for that matter.

I hope you stay tuned and enjoy the ride!

By Rick Regan (Copyright © 2008-2012 Exploring Binary)

Exploring Binary is Live!

The Apple II I Used in High School.

I think the desire started when I was reading my Apple II owner’s manual in 1980. It talked about bits and bytes and how software could communicate with hardware. I was more interested in how the computer worked than what it could do for me.

In 1983 and 1984, my interest was stoked anew when I took two digital logic design courses for my computer science electives. I was amazed at how all this complicated technology boiled down to just “0s and 1s.” But I had no time to ponder this philosophically; there were degrees to pursue, programs to write, jobs to tend to, ….

The Digital Logic Design Textbooks I Used in College.

After 20 some-odd years, I finally got a little time to explore — and now share — my thoughts. It turns out it’s a good thing I waited. It wouldn’t have been possible without the internet.

By Rick Regan (Copyright © 2008-2012 Exploring Binary)

The Origins of This Site

We will discuss binary as it exists both inside and outside of computers; for example, binary numbers. Binary numbers are what computers generally use to do arithmetic. There are all sorts of engineering issues related to their implementation in computers: how big to make them, how to represent negative numbers, how to approximate real numbers. etc. Binary numbers were invented long before computers were; they were just a mathematical construct. It’s enlightening to study them in this pure form, and that we’ll do.

You will see a good amount of math on this site, although nothing more complicated than elementary algebra. This math is required to understand binary, but is not limited to it. In fact, you should get a lot out of this site even if you don’t (want to) understand binary or its application to computers; you could read it just for the math.

So how much material is there related to binary? Plenty — I could post articles for years and still not cover it all. Here are just a few example topics: the powers of two, Russian peasant multiplication, Boolean algebra, binary arithmetic, digital logic, floating-point numbers, I Ching hexagrams, single-elimination tournaments, CMOS logic, Bernoulli trials, binary trees, Pascal’s triangle, the game of NIM, ASCII, logic gates, binary search, bookbinding signatures, IP addresses, etc. (The header image of this site shows some examples.)

I’m writing about these topics because they interest me. I hope they interest you too. I hope you visit often or subscribe to my RSS feed. I look forward to your feedback; if you like or don’t like what I’ve written, or if you think I could add to it or improve it in any way, please let me know!

I plan to run ads on this site, although I don’t expect to make much money. Can “two cents a click” even cover my web hosting?

By Rick Regan (Copyright © 2008-2012 Exploring Binary)

My Plan For This Site

Merriam-Webster defines binary as “something made of or based on two things or parts.” That follows from the word’s components: the prefix bi-, which means “two” (like bicycle, binocular, or biannual), and the suffix -ary, which means “relating to or connected with” (like budgetary, illusionary, or revolutionary).

Binary can be used generically as a noun, as in “Exploring Binary,” or as an adjective, as in “binary number.” As an adjective it can describe many things, some of which are not of interest to us (like binary star, binary fission, or binary form). We are interested in things that relate to mathematics, computer science or computer engineering: binary numbers, binary code, binary logic, binary arithmetic, binary trees, binary search, etc.

Many things not specifically labeled as such are binary in nature. For example, coin tosses (heads or tails), single-elimination tournaments (win or lose), truth tables (true or false), etc. These also fall under our definition of binary.

The above discussion notwithstanding, it is common to use the noun binary to mean binary numbers specifically, as in the phrases “convert decimal to binary” or “5 is 101 in binary.” We will certainly be using it that way as well (that usage will be clear with context).

So in summary, we view binary as anything with “twoness” that can be studied mathematically or has an application in computers.

By Rick Regan (Copyright © 2008-2012 Exploring Binary)

About The Name Exploring Binary

This image is designed to remind you of space exploration (imagine a photo taken from the surface of the moon). The symbols “floating in space” are exemplary of the topics to be explored on this site. The black and white imagery is also symbolic of binary encoding, which is characterized by two opposing “states.”

(A reader proposed an alternate view of the image — that of a chalkboard full of mathematical symbols!)

What do the symbols mean?

Here is a brief explanation of each of the sixteen symbols in the image, from left to right:

• The eight symbols on the left side
  • 15 = 1 + 2 + 4 + 8: This is an example showing that any whole number can be written as a sum of powers of two.
  • 11001 = 25: The binary number 11001 equals

    .

  • : This is a binary search tree with seven nodes. If you were searching for the value 5, for example, you would take the right branch from node 4 to node 6 (since 5>4) and then the left branch to node 5 (since 5<6).
  • = :This is an example of a dyadic fraction (a sum of negative powers of two) written in binary.
  • ‘R’ == 0×52: Using C-language syntax, this says that capital ‘R’ has the ASCII value of hexadecimal 52.
  • : This shows the bitwise “OR” of two bytes (a bit is set to ’1′ in the answer if there is a 1-bit in the corresponding bit position in either operand).
  • : This is the first five rows of Pascal’s Triangle. Each row sums to , where n is the row number (row numbers start from 0 at the top).
  • : This shows a logic gate performing the logical AND of 1 and 0, which is 0.
• The eight symbols on the right side
  • : This is an infinite geometric series summing all the negative powers of two except for 1/2. This series converges to 1/2.
  • 101 + 101 = 1010.This is an example of binary addition. You can verify this by noting that the binary number 101 equals five and the binary number 1010 equals ten.
  • : This shows a half, quarter, eighth and sixteenth note. (They are dyadic).
  • :This is an example of how exponent arithmetic works. When you multiply two numbers with the same ‘base’ (2 in this case), the result is the base raised to the sum of their exponents. Such a computation might appear when using the binary exponentiation algorithm to computer powers of two efficiently.
  • : This is not the letter `H’, but an example of an I Ching (pronounced ‘e-ching’) hexagram. This particular hexagram signifies “clustering” or “gathering” (as in this site being a gathering place for those interested in binary). Each hexagram is made up of 6 lines — each either solid or broken — giving , or 64 hexagrams total.
  • : From De Morgan’s theorem, this states that the negation of “x ANDed with y” is equivalent to the negation of x ORed with the negation of y.
  • : This says the logarithm in base 2 of 32 is 5. This is the same as saying that = 32.
  • 07D8: The hexadecimal number 07D8 equals

    

    (Not coincidentally, this site was launched in 2008.)

If you want the details behind these explanations, stay tuned to this site!

By Rick Regan (Copyright © 2008-2012 Exploring Binary)

About the Header Image

Binary Lights

This 1970s-era light fixture adorns my bathroom: My wife sees burned out and missing bulbs; I see 10001001, or the binary representation of 137! (Update: we finally remodeled — no more binary lights .)

The binary value of 137 represented in lights.

(A reader pointed out that there are three states, not two. Technically this is correct. I view the world in black and white, so I count “bulb off” and “bulb missing” as the same state. This gives two states overall: “position lit” and “position unlit.” But for those of you who see in black, white and gray, you might see 21002112 (if you assign “bulb on” = 2, “bulb off” = 1, and “bulb missing” = 0), which is the ternary representation of 5,171.)

Binary Clock

Here’s something every computer geek needs in order to tell time:

Binary clock showing the time 9:05:53.

The time shown is 9:05:53. It is shown in BCD format, with the left two columns representing hours, the middle two columns representing minutes, and the right two columns representing seconds. (Don’t understand how to read the time? See “How to Read a Binary Clock”.)

Binary Legos

Here’s what happens when you’re daydreaming of binary numbers and you have a pile of Legos_® on hand (ever see the movie “Close Encounters of the Third Kind?” At least I didn’t break any windows or drag mud in the house to make these ):

I call this first one (yes I gave them names) the “binary wall.” It represents the number 255 with the first eight nonnegative powers of two:

Lego block representation of the number 255.

Here’s a variation of the binary wall — although since it’s mounted on a board, it’s really a “binary floor” (the green square in the upper right hand corner is not a block; it’s just the mounting board):

Another block representation of the number 255.

This following structure — the “binary towers” — also represents the number 255 with the first eight nonnegative powers of two. The wide tower represents 240 (128 + 64 + 32 + 16), and the skinny tower represents 15 (8 + 4 + 2 + 1). This is like showing a byte’s two nybbles explicitly, kind of like representing the number in hexadecimal form.

Yet another block representation of the number 255.

This last one I call the “binary city.” The heights of the “buildings” are in powers of two units:

Block "city" with building heights that are powers of two.

By Rick Regan (Copyright © 2008-2012 Exploring Binary)

My Fascination with Binary Numbers

LaTeX is a mathematical markup language used by scientists, mathematicians and engineers. Since it can’t be embedded in HTML directly, a tool such as LatexRender is required. It converts the LaTeX markup into something that can be embedded in HTML — images. Each formula is rendered as an image which is embedded in the text of its containing article.

As good as the LaTeX notation appears on this site, you may notice that it isn’t as perfectly typeset as it would be in a journal article, for instance. This is particularly true for articles delivered over RSS, which have more obvious alignment problems. That is the compromise with having to turn the notation into images — there is less control in matching the formulas to the containing text.

Can LaTeX Formulas Be Left in Comments?

No, at least not for the moment. It could be enabled, but there are some implementation issues. If there’s sufficient demand I will consider it.

By Rick Regan (Copyright © 2008-2012 Exploring Binary)

About the Math Notation

The main benefit of RSS is that you can enjoy the Web on your own schedule; you don’t have to check and recheck your favorite Web sites for new content or worry that you’ll miss something that scrolls off the main page. Whether a site adds new content ten times a day or once a month, RSS will keep you updated.

How It Works

RSS is like email, except you don’t receive deliveries in your inbox; you get them in what’s called an RSS reader. Just like you can read email either through software installed on your computer (like Outlook Express) or on a Web site (like mail.google.com), you can read Web site content through software (like FeedDemon) or on a Web site (like www.google.com/reader). There are many readers from which to choose (I use Google Reader).

In RSS parlance, you subscribe to an RSS feed. Most Web sites offer at least one feed. Many sites offer multiple feeds — one per category. A news site, for example, would have feeds for business news, sports, weather, etc.

To subscribe to an RSS feed, go to a Web site and click on the orange button (for example, ) or the letters RSS. You are usually given a choice of readers to which content can be sent — pick yours from the list. No personal information, like your name or email address, is collected. There is no fee.

When you subscribe to an RSS feed you will usually get the ten or so most recent entries delivered to you immediately. From that point on, you will be sent anything new as it’s posted to the Web site. You can subscribe to as many feeds as you like; the reader will aggregate them for you.

RSS by email

Some Web sites offer a variation on RSS where you can get content delivered by email (of course you must supply your email address in this case). There is no real standard for this, but look for a variation on the orange button (for example, ).

Other Benefits

The more Web sites you would otherwise visit, the more time you will save using RSS. You can use that time to become more widely read. (I’ve had up to 80 subscriptions at once — there’s no way I could visit 80 Web sites on a regular basis!)

You may also like the uniformity of the content as presented in your reader. This is good for sites that violate all the basic rules of typography — you know, the ones that burn your eyes with yellow text on a purple background. Your reader will present those as black text on a white background, making an otherwise unreadable site readable.

You don’t have to read the content from within your reader. In fact, sometimes you cant; some content comes in only as excerpts. You always have the option of launching the original site from your reader. You could choose to read all your content at the originating Web sites, in which case RSS is serving only as a notification mechanism. You wouldn’t be reading as efficiently, but at least you could get that yellow on purple look you so desire .

By Rick Regan (Copyright © 2008-2012 Exploring Binary)

What is RSS?