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. GetTools' 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): Uses only 0 and 1 — the fundamental language of processors and digital circuits. Every bit represents an on/off electrical state. Example: decimal 13 = binary 1101. All data in a computer ultimately exists as binary.
• Octal (Base 8): Uses digits 0 through 7. Still used in Unix/Linux systems for file permissions (chmod 755). Each octal digit neatly represents exactly 3 binary bits, making it a compact shorthand for binary values.
• Decimal (Base 10): The everyday number system using digits 0–9. It is the default system humans use for counting and arithmetic.
• Hexadecimal (Base 16): Uses digits 0–9 and letters A–F (where A=10, B=11, … F=15). Extremely common in programming because each hex digit represents exactly 4 bits (one nibble), making long binary strings much shorter and easier to read.

Practical Real-World Applications

• CSS & Web Colors: #FF5733 means R=255, G=87, B=51 in decimal — hexadecimal makes RGB color components easy to read and manipulate directly
• Linux File Permissions: chmod 755 = binary 111 101 101 = owner can read/write/execute, group and others can read/execute
• MAC Addresses & IPv6: Network hardware addresses and IPv6 addresses use hexadecimal to keep long binary strings concise
• Debugging & Assembly Programming: Memory addresses, register values, and machine code are displayed in hexadecimal in debuggers and disassemblers
• Cryptography & Hashing: Encryption keys, SHA-256 hashes, and other cryptographic outputs are expressed in hexadecimal
• Network Protocol Analysis: Packet inspection tools like Wireshark display raw data in hexadecimal for human readability

How Base Conversion Works

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 → 255 decimal → 11111111 binary. The tool performs all these steps automatically and shows them in the "Conversion Steps" section so you can follow the math.

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