Base Converter
Convert numbers between binary, octal, decimal, and hexadecimal bases instantly with our free converter tool.
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Number Base Systems
Computers store all data as binary (base 2). Other bases — octal and hexadecimal — are shorthand notations that map cleanly to binary, making it easier for programmers to read and write binary values.
Common Bases
- Binary (base 2) — digits 0–1; one bit per digit; used in hardware and low-level programming
- Octal (base 8) — digits 0–7; one digit = 3 bits; used in Unix file permissions
- Decimal (base 10) — digits 0–9; everyday human number system
- Hexadecimal (base 16) — digits 0–9 and A–F; one digit = 4 bits; used in colors, memory addresses, hashes
Quick Reference
- Decimal 10 = Binary 1010 = Octal 12 = Hex A
- Decimal 255 = Binary 11111111 = Octal 377 = Hex FF
- Hex FF = 15×16 + 15 = 255 decimal
Why do programmers use hexadecimal?
One hex digit represents exactly 4 binary bits (a nibble), so hex is a compact, human-readable way to write binary. A byte (8 bits) is exactly two hex digits — e.g., 0xFF = 255. This maps neatly to memory addresses, color codes, and cryptographic hashes.
How do I convert binary to hex manually?
Group the binary digits into groups of 4 from the right, then convert each group: 1010 1111 → A F → AF. If the leftmost group has fewer than 4 bits, pad with leading zeros.
What are Unix file permission numbers?
Unix permissions like 755 or 644 are octal numbers. Each digit represents read/write/execute for owner, group, and others: 7 = rwx (111 binary), 5 = r-x (101 binary), 4 = r-- (100 binary).