The pictures below — of items around my house — should convince you of my fascination (obsession?) with binary numbers.
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 🙁 .)
(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.)
Here’s something every computer geek needs in order to tell time:
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”.)
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:
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):
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.
This last one I call the “binary city.” The heights of the “buildings” are in powers of two units: