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Number Base Converter

Convert between Binary, Octal, Decimal, Hexadecimal and custom bases (2-36)

Enter Number

Results

Binary (Base 2)
11111111
Octal (Base 8)
377
Decimal (Base 10)
255
Hexadecimal (Base 16)
FF

Base Systems Explained

Binary (Base 2): Uses 0, 1. Each digit is a power of 2. Used by computers.
Octal (Base 8): Uses 0-7. Used in Unix file permissions (e.g., chmod 755).
Decimal (Base 10): Uses 0-9. The everyday number system.
Hexadecimal (Base 16): Uses 0-9, A-F. Used for colors (#FF0000), memory addresses.
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How Number Base Conversion Works

A number base (or radix) determines how many unique digits are used to represent numbers. To convert between bases, first convert to decimal (base 10), then to the target base.

Converting to Decimal

Multiply each digit by its positional power of the base and sum. E.g., binary 1101 = 1x8 + 1x4 + 0x2 + 1x1 = 13.

Converting from Decimal

Repeatedly divide by the target base and collect remainders in reverse order. E.g., 13 in binary: 13/2=6 R1, 6/2=3 R0, 3/2=1 R1, 1/2=0 R1 → 1101.

Frequently Asked Questions

What is binary?
Binary (base-2) uses only 0 and 1. Computers use it because circuits have two states: on and off.
What is hexadecimal?
Hexadecimal (base-16) uses 0-9 and A-F. 1 hex digit = 4 binary digits, making it compact for representing binary data.
How do you convert decimal to binary?
Divide by 2 repeatedly and record remainders in reverse. Example: 13 → 1101.
What is octal used for?
Octal is used in Unix/Linux file permissions (chmod 755) and some legacy computing contexts.