“There are only 10 types of people in the world: those who understand binary, and those who don’t.”
If you’re having a hard time wrapping your head around binary, using embodied cognition can help: specifically ‘manumerical cognition’, and more specifically, counting on your fingers.
We’ve evolved to use spatial-numerical relations, and I’ve already discussed how adding a visuospatial soroban to your mental toolkit can help you with mathematics.
So naturally, why not improve your understanding of binary numbers using finger-counting?
Here's a basic explanation. Finger binary is based on the visual slotting of the 1s and 0s into powers of 2 (for more on conversion methods, see here, especially method two in each section).
You take those slots and represent them with your fingers.
Above, the raised fingers can be viewed as 1s. So in the above picture, the fingers are all added together (512 + 256, etc. all the way to 4 + 2 + 1), giving you 1,023, which in binary is 1111111111.
The unraised finger is a 0. So let’s say you lowered the finger representing 2, so the picture above would have the right index finger lowered, making it a 0. Visually that’s 1111111101. If we counted every finger but that one, we’d have 1,021, which is 1111111101 in binary.
By the way, it’s been suggested that the Incan writing system (their civilization’s not an exception to the importance of literacy, as they weren’t illiterate, unlike what phonocentrists would have you believe), the khipu, is a 7-bit 3D binary system; this interesting article describes how the Polynesians also used binary and the importance of such localized cultural evolution for insight into the diversity of numerical cognition. Binary is old school.
Keep in mind, in English-speaking countries, we tend to raise fingers to represent numbers, so the closed fist (no raised fingers) is zero, and as you can see above, that carries over into finger binary.
However, finger-counting differs by culture, even as it’s an important aspect of human embodied cognition. Here’s a paper explaining this in detail. Of course, there are other factors, e.g. situated cognition, contributing to differences, also.
At any rate, in Japan, lowered fingers represent numbers! They start with fingers extended, and count off by folding each finger. ‘To count on one’s fingers’ in Japanese, yubi-ori kazoeru (指折り数える) literally means ‘finger-folding counting’. So the open hand is zero. Thus, as you might have guessed, the raised finger is nothing, and therefore a 0 in binary (nishin [二進]), while the lowered fingers represent ones:
So the above far-left picture would be 11011, or 27 (adding the 16, 8, 2, 1) in the non-Japanese style, and is 00100, or 4 (just the middle finger, representing the 4 slot) in the Japanese style. Note we ditch the 0s to the left of the first 1, giving us 100; I left them in for the visual reference.
Here’s another Japanese finger binary diagram counting from 0 to 31 on the right hand. In the past, I half-jokingly related yubimoji (Japanese finger-spelling) to mudras while discussing meditation. The below source also muses on the correlation of finger binary with mudra and the like.
Programming is magick.
So now we know what those esoteric Japanese practitioners are really up to with the kuji-in and kuji-kiri. The ninja are using hand seals to hack the machine code of reality. All that power in 10 bits. I mean 10 values. I mean 2 values.
Of course, the Japanese have evolved to use CADs now, but as Shiba Tatsuya or Itachi Uchiha will tell you, there’s something to be said for low-level expertise.