Number Base Converter
Convert between binary, decimal, hex and octal
About Number Base Converter
Number base conversion is essential for computer science students, programmers and network engineers. This free Number Base Converter instantly converts between Binary (base 2), Decimal (base 10), Hexadecimal (base 16) and Octal (base 8) — the four most common number systems in computing. Enter a number in any base and all other representations update in real time.
How to Use Number Base Converter
- 1Enter a number in any field: Binary (base 2), Decimal (base 10), Hex (base 16) or Octal (base 8).
- 2All other base representations update instantly.
- 3Use the bit visualization panel to see the binary breakdown.
- 4Copy any result with one click.
Common Use Cases
File permissions in Linux use octal (e.g. chmod 755 = binary 111 101 101). IP subnet masks use binary. Memory addresses use hexadecimal.
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Frequently Asked Questions
What are the four most common number bases in computing?
Binary (base 2): uses digits 0-1, used in all digital hardware. Decimal (base 10): the standard human number system, uses digits 0-9. Hexadecimal (base 16): uses digits 0-9 and A-F, common for memory addresses and color codes. Octal (base 8): uses digits 0-7, used for Unix file permissions.
How do I convert binary to decimal?
Multiply each bit by its positional power of 2 (right to left, starting at 2⁰) and sum them. For binary 1011: (1×8) + (0×4) + (1×2) + (1×1) = 8+0+2+1 = 11 decimal.
What does chmod 755 mean in binary and octal?
In Unix/Linux, file permissions use three octal digits: owner, group, others. 755 in octal = 111 101 101 in binary = rwxr-xr-x. Owner (7=111): read+write+execute. Group (5=101): read+execute. Others (5=101): read+execute.
Why does programming use hexadecimal instead of binary?
Binary is hard for humans to read — a 32-bit memory address is 32 1s and 0s. Hexadecimal compactly represents 4 binary bits with one character, so a 32-bit address becomes just 8 hex digits. This is why memory addresses, color codes and byte values are displayed in hex.