Number Base Converter

What is a number base converter?

A number base converter translates a value between binary (base 2), octal (base 8), decimal (base 10), and hexadecimal (base 16). It’s an essential tool for programming, networking, and digital logic work where the same number appears in several bases.

How this converter works

• Type a value and choose its base — the tool detects the rest.
• It parses the input with that base’s allowed digits (binary only 0/1, octal 0–7, hex 0–9/A–F).
• All four representations are shown side by side.
• Invalid digits for the selected base are rejected with a clear message.

How to use the result

1. Use hex to read memory addresses and colour codes — each hex digit is four bits, so it compresses binary perfectly.
2. Use binary for bit masks and logic operations — seeing the bits makes AND/OR/shift behaviour obvious.
3. Use octal mainly for legacy Unix file permissions and older systems.
4. Verify a hex value by checking the binary column — FF, 11111111, and 255 are the same number.

Why do computers use binary and hex?

Computers work in binary because transistors are on/off switches — two states, base 2. Hex is a human-friendly shorthand because every hex digit maps cleanly to four bits, so a byte (8 bits) is exactly two hex digits. Octal covers three bits at a time and survives in some legacy tools.

Common mistakes

• Treating hex letters as decimal. A = 10 through F = 15, not numbers in their own right.
• Reading a hex number as decimal. FF is 255, not “fifteen f”.
• Forgetting prefixes. Code often marks bases explicitly — 0x for hex, 0b for binary, 0o for octal — so “10” is ambiguous without context.

Base conversion is the language of the unit converter’s digital-storage category — bytes, KB, and GB are all powers of two under the hood. For the decimal side of everyday numbers, the percentage calculator stays in base 10.