In this episode: a journey into strange numbers.
Rule 5. Know your numbers
What is alternative numbering?
Normally humans use base 10, the digits 0 through 9 to represent numbers. In base 2, only uses the digits 0 and 1. This means that in base 2, the number 2 is represented by 10 and the number 4 is represented by 100. When we add 2 + 2 in base 2, we get 100, equal to 4 in base 10.
To make 2 + 2 = 5 in a different base system, we would need to use a base system with at least 6 digits. In base 6, we could represent the numbers 0 through 5 using the digits 0 through 5. When we add 2 + 2 in base 6, we get 4, which is equal to 5 in base 10.
Here is a table showing how the numbers 0 through 9 are represented in different base systems:
| Base | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
|---|---|---|---|---|---|---|---|---|---|---|
| 2 | 0 | 1 | 10 | 11 | 100 | 101 | 110 | 111 | 1000 | 1001 |
| 3 | 0 | 1 | 2 | 10 | 11 | 12 | 20 | 21 | 100 | 101 |
| 4 | 0 | 1 | 2 | 3 | 10 | 11 | 12 | 20 | 21 | 22 |
| 5 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
As you can see, the number 2 is represented by different digits in different base systems. This is because the value of a digit in a base system depends on its position. In base 10, the digit 2 in the tens place is worth 20, while the digit 2 in the ones place is worth 2. In base 2, the digit 2 in the ones place is worth 2, while the digit 2 in the twos place is worth 4.
Gibberish from a bot, or sage advice?