Base Converter
Convert numbers between binary, decimal, hexadecimal and octal instantly. Enter a value, pick the bases, get the result. No signup. Ideal for programmers and students.
Result
| Result | ||
|---|---|---|
| Decimal value |
Share on Social Media:
This base converter changes numbers between binary, decimal, hexadecimal and octal instantly, directly in your browser. Enter a value, choose its base and the base you want, and read the converted result. No account, no install, so programmers, students and anyone working with number systems can convert between bases on any device in seconds.
How to Convert Between Number Bases Step by Step
- Enter your number. Type the value you want to convert into the input field. Make sure it uses only the digits valid for its base, so a binary number uses only zeros and ones.
- Select the source base. Choose the base your number is currently in: base two for binary, base ten for decimal, base sixteen for hexadecimal, or base eight for octal.
- Select the target base. Choose the base you want the number converted into. The tool can convert between any of the supported bases in either direction.
- Read the converted value. The result appears instantly in the target base, correctly translated so it represents the same underlying quantity in the new number system.
- Convert again as needed. Change the input or the bases to convert another value or the same value into a different base, with the result updating each time.
What Number Bases Are and Why They Exist
A number base, or radix, is the number of distinct digits a counting system uses. The decimal system we use daily is base ten, with digits zero through nine, because we have ten fingers. But base ten is just one choice. Computers work in base two, binary, using only zero and one, because electronic circuits naturally represent two states, on and off. Understanding that the same quantity can be written in different bases is the foundation of digital computing.
Binary is the native language of computers, but it is unwieldy for humans because numbers become very long strings of ones and zeros. Hexadecimal, base sixteen, solves this: each hex digit represents exactly four binary digits, so hex is a compact, human friendly way to write binary values. This is why colours, memory addresses and many low level values are written in hex. Octal, base eight, plays a similar compacting role in some contexts, where each octal digit is three binary digits.
Hexadecimal needs sixteen digits, but we only have ten numeric symbols, so it borrows letters. The digits run zero through nine, then A, B, C, D, E and F for the values ten through fifteen. This is why hex numbers contain letters, which surprises people new to them. A hex value like FF represents two hundred and fifty five in decimal, and understanding the letter digits is essential to reading hex correctly.
Converting between bases does not change the quantity, only how it is written. The decimal number ten is the same quantity whether written as ten in decimal, one zero one zero in binary, A in hexadecimal, or one two in octal. Each representation points to the identical underlying value. Conversion is translation between notations, and doing it by hand involves repeated division or multiplication that is easy to slip up on, which is why a converter is invaluable for accuracy.
This Converter Versus Manual Base Conversion
| Base | Name | Digits used | Common use |
|---|---|---|---|
| 2 | Binary | 0 and 1 | The native language of computers |
| 8 | Octal | 0 to 7 | Some legacy and Unix permission contexts |
| 10 | Decimal | 0 to 9 | Everyday human counting |
| 16 | Hexadecimal | 0 to 9 and A to F | Colours, memory addresses, low level values |
Who Uses a Base Converter
Pro Tips for Working Across Number Bases
Common Base Conversion Mistakes to Avoid
Related Tools You May Need Next
For specific conversions, our Binary to Decimal and Decimal to Hex tools target those pairs directly. For colour values, the Color Converter translates hex colours into RGB, and the Hex to Binary tool handles that specific step.
Frequently Asked Questions
How do I convert a number between bases?
Enter your number, select the base it is currently in, binary, decimal, hexadecimal or octal, choose the base you want it converted to, and the result appears instantly. The converter translates the number between notations while preserving the same underlying value. Make sure your input uses only the digits valid for its source base, or the conversion cannot be performed correctly.
Why does hexadecimal use letters?
Hexadecimal is base sixteen, so it needs sixteen distinct digits, but there are only ten numeric symbols, zero through nine. To represent the remaining six values, ten through fifteen, hex borrows the letters A, B, C, D, E and F. So a hex number can contain both digits and these letters, and each letter is a numeric digit, with F representing fifteen and FF representing two hundred and fifty five in decimal.
What is the difference between binary, decimal and hexadecimal?
They are number systems using different numbers of digits. Binary is base two, using only zero and one, and is how computers store data. Decimal is base ten, using zero through nine, and is how humans normally count. Hexadecimal is base sixteen, using zero through nine and A through F, and provides a compact, human friendly way to write binary values. All three can represent the same quantities.
Does converting a number change its value?
No. Converting between bases changes only how the number is written, not the quantity it represents. The value ten is the same whether written as ten in decimal, one zero one zero in binary, A in hexadecimal, or one two in octal. Conversion is simply translation between different notations for the identical underlying value, much like writing the same word in different alphabets.
Why do programmers use hexadecimal?
Because each hexadecimal digit represents exactly four binary digits, hex is a compact and readable way to write the long binary values computers use. This makes hex ideal for colours, memory addresses, bit flags and other low level data, where writing everything in binary would produce unwieldy strings of ones and zeros. Hex lets programmers work with binary values in a far more manageable form.
What is octal used for?
Octal is base eight, using digits zero through seven, and each octal digit represents exactly three binary digits. It was more common in older computing and still appears in some contexts, notably Unix file permissions, which are often expressed in octal. While hexadecimal has largely replaced octal for most compacting of binary, understanding octal remains useful when working with systems that use it.
How do I know what base a number is in?
You often need context, but there are clues. A number containing the letters A to F is hexadecimal. A number using only zeros and ones might be binary, though it could also be decimal. Many systems mark the base with a prefix, and documentation usually states it. When using this converter, you specify the source base explicitly, which removes any ambiguity about how to interpret the number.
Is the base converter free?
Yes, it is completely free with no account and no usage limit. You can convert as many numbers between as many bases as you like, as often as you like, at no cost. It runs entirely in your browser on any device, so there is nothing to download or install, and the converted value appears instantly whenever you enter a number and choose the bases.