To convert between number bases means rewriting a single integer in a different numeral system — the digits change, the value stays the same. In practice, you read a number written in one base (say binary 1010) and write out the same value in another base (decimal 10), using only the legal digits of the target system. The fastest way to do this for any base from 2 to 36 is the Number Base Converter: type the value, choose the 'from base' and 'to base', and the result appears instantly alongside all four common bases — binary, octal, decimal, and hexadecimal — with no server round-trip. Every digit you type is validated against the chosen source base, letters are case-insensitive, a leading minus sign is honored, and arbitrarily large integers convert exactly because the calculation uses BigInt arithmetic rather than a fixed-size integer. Conversions happen entirely in your browser, so the numbers never leave your device.
What "Converting Between Number Bases" Actually Means
A base, or radix, is two things at once: how many distinct digits a numeral system uses, and what each position in a written number is worth. Decimal (base 10) uses the digits 0 through 9, and each position is a power of ten, so 255 in decimal means 2×100 + 5×10 + 5×1. Binary (base 2) only uses 0 and 1, with positions worth 1, 2, 4, 8, 16 and so on. Octal (base 8) uses digits 0–7, and hexadecimal (base 16) uses 0–9 followed by A–F for the values ten through fifteen. Above ten, the systems simply keep borrowing letters, all the way to base 36 which uses 0–9 plus A–Z.
The same integer can be written out in every one of these systems, and the digits will look completely different even though the value is identical. The table below shows the value 255 expressed in each of the four common bases side by side.
| Base | Name | Digits used | Same value (255 in decimal) |
|---|---|---|---|
| 2 | Binary | 0, 1 | 11111111 |
| 8 | Octal | 0–7 | 377 |
| 10 | Decimal | 0–9 | 255 |
| 16 | Hexadecimal | 0–9, A–F | FF |
The job of a converter is simply to translate one row of that table into another, in either direction.
How to Convert Between Number Bases with the Tool
For any integer and any source/target pair between base 2 and base 36, the steps are the same:
- Type the whole number you want to convert into the value field. Letters are case-insensitive (so FF and ff are treated the same), and a leading minus sign is allowed if you need a negative integer.
- Choose the 'from base' that matches the system your input is written in (Binary for something like 1010, Hexadecimal for FF, and so on), then pick the 'to base' for the system you want the answer in.
- Read the converted result instantly. The tool also shows the same value expressed in all four common bases — binary, octal, decimal, and hexadecimal — at once, so you never have to run the conversion a second time.
If you type a digit that is not legal for the chosen 'from base' — the digit 2 in a binary number, or the letter G in hex — the converter flags the exact bad character instead of silently returning a wrong answer, which is a common failure mode in lesser tools.
If your task is specifically rewriting a number into decimal, our focused guide on how to change a number to base 10 walks through the same tool with the decimal target front and center.
How Conversion Works by Hand
Understanding the two classic methods makes every automatic converter easier to trust. The first method, positional expansion, turns any base into decimal. The formula is:
value = d₀ × base⁰ + d₁ × base¹ + d₂ × base² + ...
For binary 1010, the rightmost digit is the ones place, then twos, fours, eights, and so on. Substituting the digits and positions:
(1 × 8) + (0 × 4) + (1 × 2) + (0 × 1) = 8 + 0 + 2 + 0 = 10
So 1010 in binary equals 10 in decimal.
The second method, divide-and-collect, turns a decimal integer into any other base. Repeatedly divide the decimal value by the target base, recording each remainder, then read the remainders from bottom to top. For decimal 10 into binary: 10 ÷ 2 = 5 remainder 0; 5 ÷ 2 = 2 remainder 1; 2 ÷ 2 = 1 remainder 0; 1 ÷ 2 = 0 remainder 1. Reading bottom to top gives 1010. Both methods are tedious by hand and easy to slip up on once the number has more than a handful of digits, which is exactly the workload the converter absorbs.
Where Converting Between Bases Actually Comes Up
These conversions are not abstract exercises — they are a daily task in several real areas of computing.
| Area | Base in use | Example |
|---|---|---|
| Computer hardware | Binary (base 2) | A bit is either off (0) or on (1) |
| Low-level programming | Hexadecimal (base 16) | Byte values, memory addresses, hash digests |
| Web/CSS colors | Hexadecimal | #FF8800 represents red 255, green 136, blue 0 |
| Networking | Hexadecimal | MAC addresses such as 00:1A:2B:3C:4D:5E |
| Unix file permissions | Octal (base 8) | chmod 755 sets read/write/execute on the owner |
Because every hex digit maps to exactly four binary bits, hexadecimal acts as a compact shorthand for binary that humans can read and type. That is why programmers reach for a converter whenever they need to translate between any two of these representations.
What the Number Base Converter Gets Right
A handful of design choices set a strict, accurate converter apart from a naive one:
- Strict digit validation. Every character you type is checked against the digits allowed for the chosen 'from base'. Binary only accepts 0 and 1, hex only accepts 0–9 and A–F, base 5 only accepts 0–4, and so on. An invalid character produces a clear error rather than a silently wrong number.
- Case-insensitive letters. FF, ff, and Ff are the same hex value, and the same rule applies to any base above ten that uses letters.
- Leading minus sign. Negative integers are accepted and preserved through the conversion.
- Arbitrary-precision arithmetic. The tool uses BigInt rather than a fixed-size integer, so very large numbers convert exactly with no rounding and no overflow.
- All four common bases at once. In addition to the answer in your chosen 'to base', the panel shows binary, octal, decimal, and hexadecimal side by side, which is usually what you actually need.
- Client-side only. Nothing is uploaded, so private or sensitive integers stay on your device.
For any of these cases — including arbitrary bases up to 36 and very large integers — the Number Base Converter handles the conversion the moment you finish typing.
Limits to Keep in Mind
Two constraints are worth knowing before you start.
- Whole numbers only. The converter focuses on integers and does not handle fractions or decimal points. Base conversion of fractional values is a separate, more complex operation.
- Bases 2 through 36. Any base in that range is supported. Higher bases are not, because there are no agreed-upon digits beyond 0–9 and A–Z.
Within those limits, every conversion is exact and immediate.