Number Base Converter
Convert numbers between binary, decimal, hexadecimal, and octal bases
Base Converter
Enter a number and select its base to convert it to other bases
Conversion Results
Binary (Base 2)
Decimal (Base 10)
Octal (Base 8)
Hexadecimal (Base 16)
What are Number Bases?
Number bases are different ways to represent numbers. The base of a number system tells us how many digits are available for representing values. Most people use decimal (base 10) in everyday life, but computers use binary (base 2), and programmers often use hexadecimal (base 16) and octal (base 8).
Our converter helps you translate numbers between these different systems. This is super helpful for computer science students, programmers, and anyone curious about how numbers work in different systems.
Common Number Bases
Binary (Base 2)
Uses only 0 and 1. This is the language computers understand at their most basic level.
Decimal (Base 10)
Uses digits 0-9. This is the everyday number system used by people around the world.
Octal (Base 8)
Uses digits 0-7. Sometimes used in computing as a more compact representation than binary.
Hexadecimal (Base 16)
Uses digits 0-9 and letters A-F. Widely used in programming and digital systems.
How to Use the Base Converter
Enter Your Number
Type the number you want to convert in the input field
Select Its Base
Choose whether your number is binary, decimal, octal, or hexadecimal
Click Convert
Press the convert button to see your number in all the different bases
Review Results
See your number converted to binary, decimal, octal, and hexadecimal all at once
Base Converter Examples
Here are some common examples to help you understand how number conversion works:
Decimal to Other Bases
Binary: 11111111
Octal: 377
Hex: FF
Binary to Other Bases
Decimal: 10
Octal: 12
Hex: A
Hex to Other Bases
Decimal: 47
Binary: 101111
Octal: 57
Frequently Asked Questions
Number base conversion is essential in computer programming and digital electronics. Programmers often need to work with memory addresses, color codes, and bitwise operations that use hexadecimal. Understanding binary helps with understanding how computers process information at the fundamental level.
Decimal uses 10 digits (0-9) and is based on powers of 10. Hexadecimal uses 16 symbols (0-9 and A-F) and is based on powers of 16. Hexadecimal is more compact than binary for representing large numbers, which is why it’s often used in programming.
Binary is a base-2 system that uses only two digits: 0 and 1. Each digit represents a power of 2. The rightmost digit represents 2^0 (1), the next represents 2^1 (2), then 2^2 (4), and so on. So the binary number 1010 represents (1×8) + (0×4) + (1×2) + (0×1) = 10 in decimal.
Hexadecimal is popular in programming because it’s more compact than binary but still easily converts to binary. Since 16 is a power of 2 (2^4), each hexadecimal digit corresponds to exactly 4 binary digits (bits). This makes it perfect for representing binary data in a more human-readable form.
Octal (base-8) was more commonly used in older computer systems. Today, it’s less common than hexadecimal but still appears in some specialized applications like Unix file permissions where each digit represents three bits, making it convenient for representing groups of permissions.