Number Base Converter
Convert numbers instantly between binary, decimal, octal, hexadecimal and any base from 2 to 36. Pro Mode adds fractional conversion, bitwise operations, step-by-step working and a live custom-base slider.
Number Base Converter — Binary, Decimal, Octal, Hex and Beyond
Every number system you'll encounter in computing and mathematics — binary, decimal, octal, hexadecimal, and dozens of less common bases — represents exactly the same underlying quantities, just using a different number of digit symbols. Our free number base converter handles the conversion instantly: type a number in any base from 2 to 36, and see it represented in every other base simultaneously, with no manual calculation required.
Simple Mode covers the four bases used in virtually all real-world contexts — binary, octal, decimal and hexadecimal — updating live as you type, with clear error messages for invalid digits. Switch to Pro Mode (free) for a live custom-base slider covering any base from 2 to 36, full step-by-step working showing exactly how the conversion happens, fractional number conversion, bitwise operations, and a complete CSV export across every base.
Why "base" matters more than most people realise: the number 100 means something completely different depending on its base — it's one hundred in decimal, but only four in base 5, and 256 in hexadecimal. A "base" is simply how many distinct digit symbols a number system uses before it carries over into the next column. Base 10 (decimal) uses ten symbols (0-9) because humans evolved with ten fingers; base 2 (binary) uses only two symbols (0,1) because it maps directly onto the on/off states of a digital circuit.
Decimal to Binary — Worked Example
Quick Reference — Common Number Conversions
| Decimal | Binary | Octal | Hexadecimal |
|---|---|---|---|
| 10 | 1010 | 12 | A |
| 16 | 10000 | 20 | 10 |
| 100 | 1100100 | 144 | 64 |
| 255 | 11111111 | 377 | FF |
| 1000 | 1111101000 | 1750 | 3E8 |
Why Hexadecimal Dominates in Computing
Binary is how computers fundamentally store and process data, but raw binary is extremely difficult for humans to read and write — a single byte of data is 8 characters long, and meaningful data quickly becomes an unreadable wall of 0s and 1s. Hexadecimal solves this elegantly: because 16 is a power of 2 (2⁴), each single hex digit maps exactly onto 4 binary bits. A full byte, therefore, is always exactly 2 hex digits — making hex dramatically more compact and readable while remaining trivially convertible back to binary at any time. This is why hexadecimal appears throughout programming: memory addresses, colour codes (#FF5733), MAC addresses, and low-level debugging output.
Where Number Base Conversion Is Used
Pro Mode — Four Advanced Features
How to Use the Number Base Converter
For more number and encoding tools, use this converter alongside our Binary to Text Converter for ASCII character encoding, our Hex to Text Converter for hexadecimal text decoding, our Scientific Calculator for broader mathematical operations, and our Base64 Encoder and Decoder for a different, non-positional encoding scheme.
Frequently Asked Questions
Number bases, conversion methods and how this tool works
Repeatedly divide by 2 and record each remainder, then read the remainders bottom to top. Example: 13 → 13÷2=6 r1, 6÷2=3 r0, 3÷2=1 r1, 1÷2=0 r1 → reading bottom-up gives 1101.
Multiply each digit by 2 raised to its position (from 0 on the right) and sum the results. Example: 1101 = (1×2³)+(1×2²)+(0×2¹)+(1×2⁰) = 8+4+0+1 = 13.
Multiply each hex digit by 16 raised to its position and sum. A-F represent 10-15. Example: hex FF = (15×16¹)+(15×16⁰) = 240+15 = 255.
Base 36 is the practical limit for standard tools, using all 10 digits plus all 26 letters (A-Z). Beyond that requires extra symbols, so it's rarely used. Base64 encoding is a different, non-positional scheme.
Because 1 hex digit = exactly 4 binary bits (a nibble), so a full byte is always 2 hex digits. This makes hex far more compact and readable than long binary strings, while staying trivial to convert back.
Operations that act directly on individual bits: AND, OR, XOR, NOT, and bit shifts. Fundamental in programming for flag manipulation, encryption, graphics, and low-level optimisation — commonly taught in CS fundamentals courses.
Convert the whole part normally. For the fractional part, repeatedly multiply by 2 and record whether the result is ≥1 (write 1, subtract 1) or <1 (write 0). Example: 10.625 → whole=1010, fraction=101 → 1010.101.
Pro Mode (free) adds a custom base slider (2-36), full step-by-step working, fractional conversion for decimal-point numbers, bitwise operations between two numbers, and a complete CSV export across every base.