Base Converter

Programmers live in several number systems at once: decimal for humans, binary for the machine’s truth, hexadecimal for memory addresses, colours and hashes, and octal lingering in file permissions. Converting between them by hand is slow and slip-prone, especially once values grow past mental arithmetic. This converter takes a number in any of the four bases and shows all four representations simultaneously, validating digits as you type so a stray ‘2’ in a binary field is caught rather than silently misconverted. It handles large integers safely beyond the usual 32-bit limits, making it as useful for checking a Unix permission (755 in octal) as for a lesson on how computers count.

Quick Answer: Type a number in binary, decimal, hex or octal and instantly read its value in all four bases, with invalid digits flagged.

Free Online Tool

One value, four alphabets — type in any field.

Binary (base 2)

Octal (base 8)

Decimal (base 10)

Hexadecimal (base 16)

0Bits needed

How to Use the Base Converter

Type or paste your number into any one of the four fields.
The other three fields update immediately with the same value in their bases.
If a field shows an error, check for digits that do not exist in that base — like 8 or 9 in octal.
Copy whichever representation your code, lesson or documentation needs.
Use the digit-length readout to judge how many bits a value occupies.

Key Features

Four-way live conversion: binary, octal, decimal, hexadecimal.
BigInt-backed arithmetic, so large values convert exactly, not approximately.
Per-base digit validation with clear error states.
Uppercase hex output, the convention in most tooling.
Runs locally — no number you enter is sent anywhere.

Best Practices and Tips

Count digits to sanity-check: each hex digit is exactly four binary digits, so a 12-bit value is three hex digits.
File permissions decode instantly here: 755 octal is 111101101 binary — read/write/execute patterns become visible.
Colours are hex pairs per channel: #FF8800 is red 255, green 136, blue 0 in decimal.
When embedding a hex value in code, the 0x prefix is convention, not part of the number — this tool works with the bare digits.
Negative numbers are intentionally out of scope; two's-complement representation depends on bit width, which belongs to the system you are working in.

Common Mistakes to Avoid

Typing decimal digits into the binary field (any 2-9 is invalid there) and trusting a result from a tool that silently truncated.
Confusing octal and decimal for permission-like numbers — 010 is 8 in octal, 10 in decimal.
Assuming floating point converts cleanly: fractional values in binary are a different, approximate world — this converter is for integers.
Dropping leading zeros in contexts where they carry width meaning, such as fixed-size registers or colour channels.

Frequently Asked Questions

Why does hex use the letters A to F?

Hexadecimal needs sixteen distinct symbols and digits only provide ten. A to F stand for ten to fifteen, giving each hex digit exactly sixteen values — and exactly four bits — which is why hex maps so neatly onto binary.

How large a number can it convert?

Far beyond everyday needs: the converter uses arbitrary-precision integer arithmetic, so values with dozens of digits convert exactly. If you paste a hundred-digit monster, it will still give the right answer in every base.

What is octal actually used for nowadays?

Most visibly, Unix file permissions (chmod 644, 755), where each octal digit neatly encodes one permission triplet. It also appears in some legacy systems and aviation transponder codes.

Can it convert decimal fractions like 0.5?

This tool converts integers, the case that has exact representations in every base. Fractions often have no exact binary form (0.1 is infinitely repeating in binary), which is why floating-point behaviour surprises programmers — a separate, deeper topic.

What does 'invalid digit' mean in practice?

Each base has a legal digit set: binary only 0-1, octal 0-7, decimal 0-9, hex 0-9 and A-F. A character outside the set — a 'G' in hex, a '9' in octal — cannot be interpreted, so the field flags it instead of guessing.