# Number Base Converter

> Free number base converter. Convert between binary, octal, decimal and hexadecimal instantly with digit validation. All client-side.

Convert between binary, octal, decimal and hexadecimal instantly. Enter a value in any base and see all four representations, with digit validation.

*Interactive tool: enter your values at https://toollantern.win/number-base-converter/ and results update instantly in your browser.*

## What the tool does

Computers think in binary, humans in decimal, and programmers constantly translate between those plus octal and hexadecimal. Pick the base of your input, type the value, and the tool shows all four representations at once, rejecting digits that do not belong (like 2 in binary).

## Worked example

Decimal **255** is binary 11111111, octal 377, hexadecimal FF. That is why 255 shows up everywhere in computing: it is the largest value in one byte.

## Where you meet these

Hex in color codes (#FF0000) and memory addresses, binary in bit flags and subnet masks, octal in Unix file permissions (see the [chmod calculator](/chmod-calculator/)).

## Frequently asked questions
### What is hexadecimal?

Base 16: digits 0-9 then A-F for values 10-15. One hex digit maps exactly to four binary digits, which is why programmers use it as shorthand for binary.

### Why do programmers use hex?

It is compact and aligns with bytes: two hex digits make one byte. Memory addresses, color codes and hash digests are all conventionally written in hex.

### What is octal used for?

Mostly Unix file permissions (chmod numbers like 755 are octal). Otherwise it has largely been replaced by hex.

### Does it handle negative numbers?

Yes for decimal input with a leading minus. Binary and hex outputs show the magnitude conversion, not two's complement encoding.

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Interactive version: https://toollantern.win/number-base-converter/