Number Base Converter

Number Base Converter -- Binary, Octal, Decimal, Hexadecimal & Custom Bases

Number systems are the foundation of computer science and digital electronics. Every system uses a defined number of symbols -- called its base or radix -- to represent values. Get-Tools' free Number Base Converter lets you instantly convert any number between binary (base 2), octal (base 8), decimal (base 10), hexadecimal (base 16), and any custom base from 2 to 36 -- with a live visual binary display and step-by-step conversion breakdown.

The Four Main Number Systems Explained

Binary (Base 2)

The binary system uses only the digits 0 and 1. It is the fundamental language of all modern processors and digital circuits. Every bit (binary digit) represents an electrical on or off state. For example, the decimal number 13 is written as 1101 in binary. All data stored in a computer -- text, images, video, programs -- is ultimately represented in binary form. Understanding binary is essential for every IT professional and engineer, from web developers to embedded systems programmers.

Octal (Base 8)

The octal system uses digits 0 through 7. It was widespread in early computers with 12-bit and 24-bit architectures. Today it is still commonly used in Unix and Linux systems to define file permissions. For example, chmod 755 sets read, write, and execute rights. Each octal digit represents exactly 3 binary bits, making it a convenient shorthand for long binary values that is easy to convert mentally.

Decimal (Base 10)

The decimal system is the one we use every day, with digits from 0 to 9. It is the natural number system for humans, used in commerce, science, and daily life. Its adoption is believed to be related to the fact that we have ten fingers on our hands. While computers do not natively process decimal, it remains the default for human-facing interfaces.

Hexadecimal (Base 16)

The hexadecimal system uses digits 0-9 and letters A-F (where A=10, B=11, through F=15). It is extremely common in programming because each hex digit represents exactly 4 bits (one nibble), making long binary strings much more compact and readable. It is found in CSS colors, memory addresses, encryption keys, and network addresses. A single byte (8 bits) can always be represented as exactly two hex digits.

Practical Real-World Applications

• CSS & Web Colors: The notation #FF5733 means R=255, G=87, B=51 in decimal. Hexadecimal makes RGB color components easy to read and manipulate directly in modern design tools like Figma, Photoshop, and browser developer tools.
• Linux File Permissions: chmod 755 = binary 111 101 101 = owner can read/write/execute, group and others can read/execute. Understanding this conversion is critical for every system administrator.
• MAC Addresses & IPv6: Network hardware addresses and IPv6 addresses use hexadecimal to keep long binary strings concise and human-readable.
• Debugging & Assembly Programming: Memory addresses, register values, and machine code are displayed in hexadecimal in debuggers and disassemblers like GDB and Visual Studio.
• Cryptography & Hashing: Encryption keys, SHA-256 hashes, MD5 fingerprints, and other cryptographic outputs are expressed in hexadecimal.
• Network Protocol Analysis: Packet inspection tools like Wireshark display raw data in hexadecimal for human readability when analyzing network traffic.
• IoT & Embedded Systems: Programming microcontrollers such as Arduino and ESP32 requires mastery of binary and hexadecimal to work with hardware registers and I/O ports.

How Base Conversion Works

The principle is straightforward: every number conversion uses decimal as an intermediate step. The input number is first converted to decimal (base 10), then from decimal to the target base. For example, converting FF hexadecimal to binary: FF = 15 x 16 + 15 = 255 decimal, then 255 = 11111111 binary. The tool performs all these steps automatically and shows them in the "Conversion Steps" section so you can follow the math step by step and verify the result.

Privacy and Security

All conversions are performed locally in your browser using JavaScript -- no data is sent to external servers. Your numbers and data remain completely private and are neither logged nor stored anywhere. You can even use the tool offline after the initial page load, making it safe for sensitive numerical data.

Educational Use

This tool is ideal for computer science and electrical engineering students studying number systems. The binary visualization provides an intuitive understanding of how numbers are stored inside a computer. The conversion steps section clearly explains the mathematical process, helping students understand the concept rather than just obtaining a result. Support for custom bases (from 2 to 36) allows exploration of uncommon systems like ternary, quinary, and beyond.

How to Use the Converter

1. Select the source base -- the number system your input is written in (default: decimal 10)
2. Type the number in the input field -- the tool accepts negative numbers too
3. All results appear instantly: binary, octal, decimal, hexadecimal, and any custom base
4. Click any result box to copy the value to your clipboard