How to Convert Between Number Systems (Binary, Hex, Octal)
Developers regularly work with binary, hexadecimal, and octal numbers. Learn conversion techniques and when each number system is used.
Key Takeaways
- Computers operate in binary (base-2), but humans find large binary numbers unreadable.
- Hex uses digits 0-9 and letters A-F.
- Octal (base-8) uses digits 0-7.
- It's essential for understanding bitwise operations, subnet masks, file permissions (chmod 755 = 111 101 101), and hardware-level data representation.
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Number Systems in Computing
Computers operate in binary (base-2), but humans find large binary numbers unreadable. Hexadecimal (base-16) provides a compact representation where each hex digit maps to exactly 4 binary bits.
Hexadecimal
Hex uses digits 0-9 and letters A-F. It's used for memory addresses, color codes (#FF6B35), MAC addresses (00:1A:2B:3C:4D:5E), and byte-level data representation. Two hex digits represent one byte (0x00 to 0xFF = 0 to 255).
Binary
Binary uses only 0 and 1. It's essential for understanding bitwise operations, subnet masks, file permissions (chmod 755 = 111 101 101), and hardware-level data representation.
Octal
Octal (base-8) uses digits 0-7. Its primary modern use is Unix file permissions where each digit represents read (4), write (2), and execute (1) for owner, group, and others.
Conversion Table
| Decimal | Binary | Hex | Octal |
|---|---|---|---|
| 10 | 1010 | A | 12 |
| 255 | 11111111 | FF | 377 |
| 42 | 101010 | 2A | 52 |
| 100 | 1100100 | 64 | 144 |
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