A number base converter changes a number from one base, or radix, into another, such as turning the decimal value 255 into the binary 11111111 or the hex FF. The tool below parses your value in the base you choose, computes its true numeric size, and rewrites it in any base from 2 to 36, all inside your browser.
What a Number Base or Radix Is
A base, also called a radix, is the count of unique digit symbols a number system uses before it has to add another place. Decimal is base 10 because it uses ten digits, 0 through 9. Binary is base 2 with just 0 and 1. Hexadecimal is base 16, so it borrows the letters A through F to stand for the values 10 through 15. Each place in a number is worth the base raised to a power, which is why moving one column to the left multiplies a digit’s worth by the base.
How to Use It
- Type the number you want to convert into the value field.
- Set the from base to match the system your number is already written in.
- Set the to base to the system you want the result in.
- Read the converted value at the top of the result.
- Check the reference list below it for the same number in binary, octal, decimal, and hex.
How Base Conversion Works
Conversion happens in two steps. First the tool reads each digit of the source number, multiplies it by the base raised to its column position, and adds the results to get the number’s value as a plain decimal integer. Second it divides that value by the target base over and over, collecting the remainders, which become the digits of the answer from right to left. The middle value never changes, so any base can convert to any other through that shared decimal step.
The First Sixteen Numbers in Four Bases
| Decimal | Binary | Octal | Hex |
|---|---|---|---|
| 0 | 0 | 0 | 0 |
| 1 | 1 | 1 | 1 |
| 2 | 10 | 2 | 2 |
| 3 | 11 | 3 | 3 |
| 4 | 100 | 4 | 4 |
| 5 | 101 | 5 | 5 |
| 6 | 110 | 6 | 6 |
| 7 | 111 | 7 | 7 |
| 8 | 1000 | 10 | 8 |
| 9 | 1001 | 11 | 9 |
| 10 | 1010 | 12 | A |
| 11 | 1011 | 13 | B |
| 12 | 1100 | 14 | C |
| 13 | 1101 | 15 | D |
| 14 | 1110 | 16 | E |
| 15 | 1111 | 17 | F |
Why Bases 2, 8, and 16 Matter in Computing
Computers store everything as bits, which are base 2 by nature, so binary is the language hardware actually runs on. Binary numbers get long fast, so programmers group bits to read them more easily. Three bits map to one octal digit, and four bits map to one hex digit, which is why a byte is two hex characters. Hex shows up in color codes, memory addresses, and error codes because it packs binary into a short, readable form without losing any detail.
When to Use It
Reach for a base converter when you are reading a hex color and want its decimal channels, decoding a memory address, checking a permission value, working through a computer science exercise, or translating a binary mask into something you can read at a glance. Because the tool covers every base from 2 to 36, it also handles less common systems used in encoding and puzzles where letters extend the digit set past base 16.
Last Thoughts on Converting Number Bases
Switching a number between bases looks like a trick at first, but it is one idea repeated: read the value, then rewrite it. The value is fixed; only its clothing changes. Once you see decimal as just one base among many, binary and hex stop being mysterious and become two more ways of writing the same counts you already know.
Convert your next value above, and when you need to work with specific systems try our hex calculator and binary calculator. Browse the rest of our free online tools for more.
Key Takeaways:
- A base, or radix, is the number of distinct digits a counting system uses; base 10 uses 0 to 9, base 16 adds A to F.
- Conversion reads the source number into a single decimal value, then rewrites that value using the target base’s digits.
- A digit must always be smaller than its base, so 2 cannot appear in a binary number.
- Binary, octal, and hex matter because computers run on bits and these bases group bits into shorter, readable forms.
- This converter supports every base from 2 to 36 and runs entirely in your browser.
- The result also lists the same value in binary, octal, decimal, and hex for quick reference.
Frequently Asked Questions (FAQs)
What is a number base or radix?
A base, or radix, is how many distinct digit symbols a number system uses before it needs another place column. Decimal is base 10 with the digits 0 through 9. Binary is base 2 with only 0 and 1. The base sets what each column is worth, since each place is the base raised to a power.
How do you convert a number from one base to another?
First read the source number to find its actual value, by multiplying each digit by the base raised to its column position and adding the results. Then divide that value by the target base repeatedly, and the remainders, read in reverse, become the digits of the converted number. The value stays the same; only its written form changes.
What does base 16 or hexadecimal mean?
Hexadecimal is base 16, so it uses sixteen digits. The first ten are 0 through 9, and the letters A through F stand for the values 10 through 15. Hex is popular in computing because each hex digit maps exactly to four bits, which makes long binary values short and easy to read.
Why did the converter say my number is invalid?
Every digit must be smaller than the from base you selected. If you enter a value with a digit that does not belong, such as the digit 2 in a binary number or the letter G in hex, the converter flags it. Check that your value matches the base you chose, then try again.
What is the highest base this tool supports?
This converter handles any base from 2 up to 36. Base 36 uses all ten digits and all twenty-six letters of the alphabet, A through Z, as its digit set. That covers binary, octal, decimal, and hex along with the extended bases used in some encoding and puzzle systems.
Does this base converter send my data anywhere?
No. The conversion runs entirely in your browser using local arithmetic, and nothing you type is uploaded, logged, or stored on any server. You can confirm this by disconnecting from the internet and watching the converter keep working.
