Binary Converter
Convert numbers between binary, decimal, octal, and hexadecimal. Enter a value and select its base to see all conversions.
About Binary Converter
Our free Binary Converter lets you instantly convert numbers between the four most common numeral systems: binary (base 2), decimal (base 10), octal (base 8), and hexadecimal (base 16). These number systems are fundamental to computer science, programming, and digital electronics.
Binary is the native language of computers (0s and 1s), hexadecimal is used in programming for compact representation of binary data, octal was historically important in Unix file permissions, and decimal is our everyday number system. Understanding these conversions is essential for programming, networking (IP addresses), color codes, and debugging.
Enter any value in any supported base and the converter instantly shows all equivalents. The tool validates your input to ensure it's valid for the selected base (e.g., binary inputs can only contain 0s and 1s, hexadecimal uses 0-9 and A-F).
Frequently Asked Questions
Q What is the difference between binary and hexadecimal?
Binary uses 2 digits (0-1) and is how computers store data. Hexadecimal uses 16 digits (0-9, A-F) and is a compact way to represent binary — each hex digit represents exactly 4 binary digits. For example, the binary 11111111 equals FF in hex and 255 in decimal.
Q Why is octal still used?
Octal (base 8) is primarily used in Unix/Linux file permissions, where each permission group (read, write, execute) is represented by 3 bits, making one octal digit (0-7) per group. The chmod command uses octal notation: chmod 755 means rwxr-xr-x.
Q How do I convert binary to decimal manually?
Write out the binary digits and multiply each by 2 raised to its position (from right, starting at 0), then sum the results. For example: 1011 = 1×2³ + 0×2² + 1×2¹ + 1×2⁰ = 8 + 0 + 2 + 1 = 11 in decimal.