Number Systems
Before diving into Bitcoin private keys, it’s important to understand how different number systems work.
note
If you’re already familiar with binary, decimal, and hexadecimal, feel free to skip ahead.
Decimal (Base 10):
- Each digit has 10 possible values (0-9).
- For example, in the number 4.25, the first digit is 4, the second is 2, and the third is 5.
- We count: 0, 1, 2, ..., 9. When we reach 9, we add a new digit to the left and reset the rightmost digit to 0 (e.g., 10).
Binary (Base 2):
- Each digit has only 2 possible values (0 or 1).
- Counting in binary looks like this: 0, 1, 10, 11, 100, 101, 110, 111, 1000, 1001, 1010, 1011, etc.
- It may seem like a big jump, but that’s because we’re used to decimal counting.
Hexadecimal (Base 16):
- Each digit has 16 possible values (0-9 and a-f, where a=10, b=11, ..., f=15).
- Just like playing cards where the Jack, Queen, and King represent specific numbers, letters can be used to represent numbers in hex.
- Hex numbers are more compact. For example, the decimal number 2047 is 11111111111 in binary (11 digits) but just 7FF in hex.
| Decimal | Binary | HEX |
|---|---|---|
| 0 | 0000 | 0 |
| 1 | 0001 | 1 |
| 2 | 0010 | 2 |
| 3 | 0011 | 3 |
| 4 | 0100 | 4 |
| 5 | 0101 | 5 |
| 6 | 0110 | 6 |
| 7 | 0111 | 7 |
| 8 | 1000 | 8 |
| 9 | 1001 | 9 |
| 10 | 1010 | a |
| 11 | 1011 | b |
| 12 | 1100 | c |
| 13 | 1101 | d |
| 14 | 1110 | e |
| 15 | 1111 | f |