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### Course: Math for fun and glory>Unit 1

Lesson 5: Singing (and noises)

# Binary hand dance

Thanks to my bro for the music! He's at christopherhart2010@gmail.com Thanks to my other bro for hand dancin' and throwing money at me, and special thanks to my mamma and grandma for their guest appearances. Created by Vi Hart.

## Want to join the conversation?

• How high does the binary dance go? 1023? That's as far as I got but I think I got mixed up.
• I'm really not sure, I did it and reached 543. The largest binary number i reached is 32768 (in my head)!
• What's the music called?
• Soo... you’re teaching the children to do the middle finger? 😅😂
• Imagine 100 people all in a line counting in binary. What is the maximum number they can get to?
• Well, each one of the people can count as far as they want. For instance, I could count: 1,10,11,100,101,110,111,1000,1001,1010,1011,1100,1101,1110, and so on as far as I like. If you are actually saying that they are each bits, only able to say 1 or 0, then they in total could count to 1,267,650,600,228,229,401,496,703,205,375 which is 2^100 - 1. If you are saying that each of their 10 fingers are bits, like in the video, then they could count to 2^1000-1, which is 10,715,086,071,862,673,209,484,250,490,600,018,105,614,048,117,055,336,074,437,503,883,703,510,511,249,361,224,931,983,788,156,958,581,275,946,729,175,531,468,251,871,452,856,923,140,435,984,577,574,698,574,803,934,567,774,824,230,985,421,074,605,062,371,141,877,954,182,153,046,474,983,581,941,267,398,767,559,165,543,946,077,062,914,571,196,477,686,542,167,660,429,831,652,624,386,837,205,668,069,375.
• Could some one explain to me about this handy dance?
• Each finger on your hand represents a binary digit. The thumb represents the 1s digit, the forefinger represents the 2s digit, the middle finger represents the 4s digit, etc. Since each number can uniquely be represented as a sum of distinct powers of 2, you can use the arrangement of fingers on your hand to represent any number (at least until you run out of fingers at 31 or 1023, depending on whether you are using one hand or both).
• If binary is base two, what about base 3 and so on?
• Base three uses 0,1,2. Base 4 uses 0,1,2,3 and so on.
• So can I count up to 2^24 (16777216) using my fingers, toes, hands and legs.
• Yes! Have a go and time how long it takes. I'll check up on you next year, if you're not lost by then.
(1 vote)
• Is your brother really Christopher Hart, the artists who writes all those how to draw Manga books? Because if so, THAT IS SO AWESOME! :D