How high can you count on two hands? The answer is 1023, if you use binary. I made the following video to demonstrate this to my students.
True story: This is a trick that I came up with when I was 10 years old. As is common in classrooms, my teacher had had enough disruptions in class, and told us students to put our heads on our desks in silence for 15 or 20 minutes as punishment. Naturally, I was trying to think of something to do to pass the time, and I somehow came up with the idea that I could keep myself entertained by counting in binary using my fingers.
When I was a kid, I could count to 1023 in about 5 minutes. But I was a lot more dextrous then, and so it takes me about 6 or 7 minutes today.