Powers of 2 and 10

Our number system is built around 10. We have 10 digits — zero through nine — and everything we count is based on powers of 10. Tens, hundreds, thousands. It makes sense — we have 10 fingers. But computers don’t have fingers. Inside every computer chip, there are billions of tiny circuits, and each circuit is either on or off. Current flowing, or not. One, or zero. That’s it. That’s base 2.

And because computers think in base 2, all their specs are powers of 2. A kilobyte is 1024 bytes — that’s 2 to the 10. Your phone might have 512 gigs of storage — 2 to the 9. A 64-bit processor? That’s 2 to the 6. Powers of 2 are everywhere in technology.

Here’s something to think about. We built our entire number system around the number 10 — almost certainly because we have 10 fingers. It’s not that our brains need base 10 — it’s just the system our culture settled on, thousands of years ago. But computers had no such choice. They’re built from circuits that are either on or off — so they’re locked into base 2. A human tradition, meets a machine reality. And right now, both are being used to try to build a new kind of intelligence.

Now let’s see powers of 2 somewhere you might not expect — your family tree. You have 2 parents. Each of your parents has 2 parents, so that’s 4 grandparents. Each grandparent has 2 parents — that’s 8 great-grandparents. See the pattern? Every generation doubles.

Parents — that’s 2 to the 1. Grandparents — 2 to the 2, which is 4. Great-grandparents — 2 to the 3, which is 8. Great-great-grandparents — 2 to the 4, which is 16. The power tells you how many generations back you’re looking.

Here’s one more cool thing. Add up all the people in your family tree — including yourself. 1, plus 2 parents, plus 4 grandparents, plus 8 great-grandparents. That’s 1 plus 2 plus 4 plus 8, which equals 15. Notice anything? 15 is one less than 16, which is 2 to the 4. That’s not a coincidence. When you add up powers of 2 like this, the total always equals the next power of 2, minus 1.