All-in-One Binary/Base-Two Model

Binary/Base-Two Models, All in One

The present design is an all-in-one model for learning about binary numbers (or base-two numerals, strictly speaking). You can call it a base-two abacus if you like. It is easier to use and clean up in a classroom setting. The basic model allows the representations of base-ten numbers 0-31; with the extension, one can go all the way up to 1023.

Script if You Need One

1. Work in groups of two, say, A and B. B has the model, to begin with. Turn all the pieces on the model so that they all show 0.
2. A to B: Think of a base-ten number between 0 and 31, but do not tell me. Let N be that number. Alternatively, if you like birthdays, if you can let N be the day of your birthday.
3. A to B: Are you ready? If B says yes, move on.
4. A to B: Is N greater than or equal to 16? If yes, subtract 16 from N, turn the 16-piece to 1 on the model, and keep the leftover still in N. If no, leave the 16-piece as 0, move on.
5. A to B: Is N greater than or equal to 8? If yes, subtract 8 from N, turn the 8-piece to 1 on the model, and keep the leftover still in N. If no, leave the 8-piece as 0, move on.
6. A to B: Is N greater than or equal to 4? If yes, subtract 4 from N, turn the 4-piece to 1 on the model, and keep the leftover still in N. If no, leave the 4-piece as 0, move on.
7. A to B: Is N greater than or equal to 2? If yes, subtract 2 from N, turn the 2-piece to 1 on the model, and keep the leftover still in N. If no, leave the 2-piece as 0, move on.
8. A to B: Is N greater than or equal to 1? If yes, subtract 1 from N, turn the 1-piece to 1 on the model, and keep the leftover still in N. If no, leave the 1-piece as 0, move on.
9. Now, read the five pieces from the left to the right. That is the binary numeral for the original N. The sum of all the place values marked 1 will be the original number N.
10. For example, if the original N is 27, one would get 11011 as a binary numeral, meaning 16+8+2+1=27.
11. When using the extension, start with 512, then 256, 128, 64, 32, 16, 8, 4, 2, 1.

See Also

https://www.thingiverse.com/thing:2662334