Lesson 1 of 7
Numbers in five holes
Show on a big screenA card has five holes in a row. Each hole is open or shut.
Step 1 of 4
- Five holes. Each place has a value.
- Open the 8 hole. The card shows 8.
- Open the 2 hole too. Now 8 + 2.
- Open the 1 hole. 8 + 2 + 1 = 11.
The rule
In binary, each place is worth twice the place on its right. Add the places that have a 1.
Binary counts with only 0 and 1. An open hole is 1. A shut hole is 0. A place is the spot of one hole. On our card the places are 16, 8, 4, 2 and 1.
| Card | Open places | Number |
|---|---|---|
| 01101 | 8 + 4 + 1 | 13 |
| 10110 | 16 + 4 + 2 | 22 |
| 11111 | 16 + 8 + 4 + 2 + 1 | 31 |
Five holes stop at 31, because 16 + 8 + 4 + 2 + 1 = 31.
To make a number, start with the biggest place. Use it only if it is not more than the number. Then do the same with what is left. For 13, 16 is too big, so its hole stays shut. Then 8 fits: 13 − 8 = 5. Next 4 fits: 5 − 4 = 1. Then 1 fits: 1 − 1 = 0. The open holes are 8, 4 and 1.
Open the holes. Make the number.
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Try the lab to finish this lesson.