My Fascination with Binary Numbers

The pictures below — of items around my house — should convince you of my fascination (obsession?) with binary numbers.

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.
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.
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.
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.
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.

Another block representation of the number 255.
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.
Block "city" with building heights that are powers of two.
Dingbat
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6 comments

  1. Hey Rick, Your fascination with binary numbers goes back at least to time you once told me all about a method to represent all negative and positive integers without a negative sign, using base -2. It would make a good article.
    Great website. You need a hit counter on the home page–displayed in binary naturally. Or you could have lights turning on or leggo towers getting bigger!

  2. Cool, I don’t remember that conversation, but I was talking about negabinary numbers. That is on my list of articles to write – thanks.

    BTW, if this were 1998, a binary hit counter would be a great idea. But hit counters went the way of the Dodo. Use the internet much ;)?

  3. Your LEGO walls are incomplete 😉
    They’re missing ones.

    In fact, even when you add the missing one, you will get a power of 2 less one (2^n – 1). So there would still be a bit missing, a space which could accomodate one more “1”. But it can be also filled with all the remaining negative powers of 2 up to infinitely small ones 😉 Unfortunately, there are no LEGO bricks of these sizes 😛 😉

  4. Oh, now I see it. My bad.
    I was mislead by the fact that I counted the studs as units, while you seem to use two-stud blocks as units.

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