Free Number Base Converter

1. Choose your mode. Use Number Mode to convert a single number between bases. Use ASCII Text Mode to see the binary, octal, decimal, and hex codes for each character in a string.

2. Select your input base. In Number Mode, choose whether you are entering a binary, octal, decimal, or hexadecimal number from the dropdown.

3. Type or paste your number. The converter shows results in all four bases simultaneously as you type. Invalid digits for the selected base are flagged immediately.

4. Copy your result. Click Copy next to any output to copy it to your clipboard. Use the reference table below the converter for quick lookups of common values.

Every number system uses a set of digits and a base (also called radix) that determines how values increase at each position. The decimal system you use every day has base 10 with digits 0 through 9. Computers, however, operate on binary (base 2) because transistors have two states: on and off, represented as 1 and 0.

Binary (base 2) is the foundation of all digital computing. Every piece of data in a computer, from text to images to video, is ultimately stored as a sequence of binary digits (bits). A single byte consists of 8 bits, giving it 256 possible values (0 to 255). While binary is fundamental, it is difficult for humans to read because even small numbers require long strings of digits.

Hexadecimal (base 16) solves the readability problem. Because 16 is a power of 2, each hex digit maps to exactly 4 binary digits. This makes hex a compact shorthand for binary data. A single byte can be written as two hex digits instead of eight binary digits. This is why hex is the standard format for memory addresses, color codes in CSS and design tools, MAC addresses, and byte-level data inspection.

Octal (base 8) was historically important in early computing when systems used 12-bit, 24-bit, or 36-bit words that divided evenly into 3-bit groups. Today, octal is most commonly seen in Unix and Linux file permissions, where the three permission categories (owner, group, others) each use a single octal digit to represent read, write, and execute permissions. For example, chmod 755 sets rwxr-xr-x permissions.

Understanding how to convert between these systems is essential for programming, networking, cybersecurity, and systems administration. Whether you are reading hex dumps, setting file permissions, debugging memory, or working with color values, fluency in number bases makes you a more effective developer.