Convert between Binary, Decimal, Hexadecimal, and Octal number systems in real-time. Essential for programming and computer science.
Computers use different number systems to represent data. While humans typically use base-10 (decimal), computers natively use base-2 (binary). Programmers frequently work with hexadecimal (base-16) for its compact representation of binary data.
| System | Base | Digits | Use Case |
|---|---|---|---|
| Binary | 2 | 0, 1 | Machine code, bit manipulation |
| Octal | 8 | 0-7 | Unix permissions, legacy systems |
| Decimal | 10 | 0-9 | Human-readable numbers |
| Hexadecimal | 16 | 0-9, A-F | Memory addresses, colors, MAC addresses |
Hexadecimal is a compact way to represent binary data. Each hex digit maps to exactly 4 binary bits, so a byte (8 bits) can be represented as exactly 2 hex digits. This makes hex much easier to read than long binary strings. For example, FF is much cleaner than 11111111.
Binary uses only 0 and 1. Each position represents a power of 2, starting from the right. For example, 1011 in binary = 1×8 + 0×4 + 1×2 + 1×1 = 11 in decimal.