Need to convert a number from one number base to another? Our free Number Base Converter makes it easy to change numbers between different numeral systems. Enter a number, choose the base you are converting from and the base you want, then click Convert to get the result instantly. It supports bases from 2 to 36, including binary, decimal, hexadecimal, and other commonly used number systems.
How to Use the Number Base Converter
The Number Base Converter is easy to use. You only need to enter the number and select the two bases.
- Enter the number you want to convert.
- Select the base of the number from From Base.
- Select the base you want to convert it to from To Base.
- Click Convert.
- The converted number will appear in the result box.
For example, if you enter 1010, select Base 2 (Binary) as the starting base and Base 10 (Decimal) as the target base, the result will be 10.
What Is a Number Base?
A number base determines how numbers are represented using a particular set of digits or symbols.
The decimal system that we use in everyday life is Base 10. It uses the digits 0 through 9.
Computers commonly use Base 2, also known as binary. Binary uses only 0 and 1.
Other number systems are also used in mathematics, programming, computing, and electronics.
Common Number Bases
Here are some of the most common bases you may come across:
| Base | Name | Digits or Symbols |
|---|---|---|
| 2 | Binary | 0–1 |
| 8 | Octal | 0–7 |
| 10 | Decimal | 0–9 |
| 16 | Hexadecimal | 0–9, A–F |
| 36 | Base 36 | 0–9, A–Z |
The converter also supports every integer base from 2 through 36.
What Is Binary?
Binary is the Base 2 number system. It uses only two digits: 0 and 1.
Computers use binary because digital electronic systems can represent two basic states.
For example:
1010₂ = 10₁₀
So the binary number 1010 has the same value as the decimal number 10.
What Is Decimal?
Decimal is the Base 10 number system used for most everyday counting and calculations.
It uses ten digits:
0, 1, 2, 3, 4, 5, 6, 7, 8, 9
For example, the number 255 is written in decimal as 255.
What Is Hexadecimal?
Hexadecimal is the Base 16 number system. It is widely used in computing and programming.
It uses the digits 0 through 9 and the letters A through F.
| Hexadecimal | Decimal |
|---|---|
| A | 10 |
| B | 11 |
| C | 12 |
| D | 13 |
| E | 14 |
| F | 15 |
For example:
FF₁₆ = 255₁₀
Hexadecimal is especially useful because each hexadecimal digit represents four binary digits.
What Is Octal?
Octal is the Base 8 number system. It uses the digits from 0 through 7.
For example:
77₈ = 63₁₀
Octal has been used in computing and programming, although hexadecimal and binary are more common in many modern applications.
Number Base Conversion Example
Suppose you want to convert 25 from decimal to binary.
The conversion is:
25₁₀ = 11001₂
You can enter 25, select Base 10 (Decimal) as the starting base, and select Base 2 (Binary) as the target base.
The converter will calculate the result for you.
Another Example: Decimal to Hexadecimal
To convert 255 from decimal to hexadecimal:
255₁₀ = FF₁₆
Enter 255, choose Base 10 as the starting base and Base 16 as the target base.
The result will show:
255 (Base 10) = FF (Base 16)
How Digits Work in Bases Above 10
Bases above 10 need additional symbols because there are more than ten possible digit values.
This converter uses the letters A through Z for values from 10 through 35.
For example:
- A = 10
- B = 11
- C = 12
- D = 13
- E = 14
- F = 15
- Z = 35
This allows the converter to support bases up to 36.
Supported Bases
The converter supports all integer bases from 2 to 36, including:
- Base 2
- Base 3
- Base 4
- Base 5
- Base 6
- Base 7
- Base 8
- Base 9
- Base 10
- Base 11
- Base 12
- Base 13
- Base 14
- Base 15
- Base 16
- Base 17
- Base 18
- Base 19
- Base 20
- Base 21
- Base 22
- Base 23
- Base 24
- Base 25
- Base 26
- Base 27
- Base 28
- Base 29
- Base 30
- Base 31
- Base 32
- Base 33
- Base 34
- Base 35
- Base 36
Where Is Number Base Conversion Used?
Number systems are useful in several areas of technology and mathematics.
Common uses include:
- Computer programming
- Software development
- Digital electronics
- Computer science
- Binary calculations
- Hexadecimal calculations
- Data representation
- Mathematics and education
- Debugging and technical work
You may need to convert between bases when working with binary data, hexadecimal values, programming exercises, or computer-related calculations.
Binary, Decimal and Hexadecimal
Binary, decimal and hexadecimal are often used together.
For example, the decimal number 255 can be represented as:
255₁₀ = 11111111₂ = FF₁₆
All three representations have the same numerical value.
The only difference is the number system used to write the value.
Why Use a Number Base Converter?
Converting numbers manually between different bases can take time, especially when working with larger values.
A number base converter can help you quickly check conversions and avoid mistakes when working with different numeral systems.
It can be useful for students, programmers, developers, electronics enthusiasts, and anyone working with number systems.
Frequently Asked Questions
What is a number base?
A number base is the number of unique digits or symbols used in a numeral system. For example, decimal is Base 10 and binary is Base 2.
What is Base 2?
Base 2 is the binary number system. It uses only 0 and 1.
What is Base 10?
Base 10 is the decimal number system used for everyday numbers. It uses the digits 0 through 9.
What is Base 16?
Base 16 is hexadecimal. It uses 0–9 and A–F.
What is the largest base supported by this converter?
The converter supports bases from 2 through 36.
Can I convert hexadecimal to binary?
Yes. Select Base 16 (Hexadecimal) as the From Base and Base 2 (Binary) as the To Base.
Can I convert binary to decimal?
Yes. Select Base 2 (Binary) as the From Base and Base 10 (Decimal) as the To Base.
Can I use letters in the converter?
Yes. Letters are used for bases above 10. For example, hexadecimal uses A–F, while Base 36 can use A–Z.
Can I convert large numbers?
Yes. The converter uses JavaScript BigInt for integer conversions, allowing it to handle very large whole-number values without relying on the normal JavaScript number limit.
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