Counting in binary
In the decimal system we have ten digits, 0 to 9. After 9 we run out of digits, so we add a new place on the left and write 10. Binary does the same with only two digits. After 1 we run out, so we add a new place on the left: 10 means two. The places in binary are worth 1, 2, 4, 8, 16 from the right, doubling each time. So counting goes: 1, 10, 11, 100, 101, 110, 111, 1000, 1001. Read binary numbers digit by digit: 101 is ‘one-zero-one’, not ‘one hundred one’. With five places, the largest number is 11111, which is 16 + 8 + 4 + 2 + 1 = 31. On one hand, if every finger is either up (1) or down (0), you can count to 31!
| Decimal | Binary |
|---|---|
| 1 | 1 |
| 2 | 10 |
| 3 | 11 |
| 4 | 100 |
| 5 | 101 |
| 6 | 110 |
| 7 | 111 |
| 8 | 1000 |
| 9 | 1001 |
| Decimal | Binary |
|---|---|
| 10 | 1010 |
| 13 | 1101 |
| 15 | 1111 |
| 16 | 10000 |
Count to 20. Write the binary numbers for 10 to 20 on paper. Use the doubling places 16, 8, 4, 2, 1. Check each one with a partner. Then look for patterns: what happens to the last digit? What happens each time you reach 1111? What is the largest number you can write with five places? Draw five circles for fingers and colour the ones that are ‘up’ for the number 21.