Number Base Converter
Convert numbers between binary, octal, decimal, and hexadecimal instantly. Type in any field and all others update in real time.
🔢 Binary (Base 2)
Uses only 0 and 1. The fundamental language of computers — every piece of data is ultimately stored as binary.
8️⃣ Octal (Base 8)
Uses digits 0–7. Common in Unix file permissions — chmod 755 means rwxr-xr-x in binary.
🔟 Decimal (Base 10)
The number system humans use. Every number you type is decimal unless prefixed with 0x (hex) or 0b (binary).
🔡 Hexadecimal (Base 16)
Uses 0–9 and A–F. Compact representation of binary — one hex digit represents exactly 4 bits. Used everywhere in computing.
⚡ Real-time
Type in any field and all other bases update instantly. No submit button needed.
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How to use the Number Base Converter
Why developers use hexadecimal
Hexadecimal (base 16) is the standard way to represent binary data compactly in code. One hex digit maps to exactly 4 bits, so a byte is always two hex digits. You'll see hex everywhere: HTML color codes like #FF5733, memory addresses like 0x7FFF5FBF, and cryptographic hashes like SHA-256 digests.
Understanding Unix file permissions with octal
Octal (base 8) is used in Unix-like systems to represent file permissions. The chmod 755 command sets permissions using three octal digits: owner (7 = rwx), group (5 = r-x), and others (5 = r-x). Each digit is the sum of read (4), write (2), and execute (1) permissions. Converting between octal and binary makes these permissions easy to reason about.
Binary and bitwise operations
Understanding binary is essential for bitwise operations in code. AND, OR, XOR, and NOT operate on individual bits. For example, 0b1010 AND 0b1100 = 0b1000. Bitwise operations are used in networking (subnet masks), graphics (color channel manipulation), embedded systems, and performance-sensitive code that avoids division with bit shifts.
Common conversions reference
Decimal 255 = hex FF = binary 11111111 — the maximum value of a single byte. Decimal 16 = hex 10. Decimal 256 = hex 100. Color #FFFFFF is decimal 16777215. IPv4 addresses in hex: 192.168.1.1 = C0.A8.01.01. ASCII character A = decimal 65 = hex 41 = binary 01000001.