Free Online Number Base Converter
Working with different number systems is a daily reality for programmers, network engineers, and computer science students. Binary for bit operations, hexadecimal for memory addresses and color codes, octal for file permissions — switching between them manually is error-prone and slow. Our free number base converter handles conversions between binary (base-2), octal (base-8), decimal (base-10), and hexadecimal (base-16) instantly.
Enter a number in any base and see its equivalent in all other bases simultaneously. No more reaching for a calculator or writing conversion scripts from scratch.
How to Use the Number Base Converter
Enter a number and select its base (binary, octal, decimal, or hexadecimal). The tool instantly shows the equivalent values in all other bases. You can type in any of the input fields and the others update in real time. Copy any value with a single click and use it in your code, documentation, or calculations.
Why You Need a Base Converter
- Software developers work with hexadecimal values in memory addresses, color codes, and byte representations.
- Network engineers convert between binary and decimal for IP addressing and subnet calculations.
- Linux administrators use octal values for file permission settings (chmod 755).
- Computer science students practice number system conversions for coursework and exams.
- Embedded systems engineers work with binary bit patterns for hardware registers.
Key Features
- Converts between binary, octal, decimal, and hexadecimal
- Shows all base equivalents simultaneously
- Real-time conversion as you type
- Copy any value with one click
- Free and browser-based — no installation needed
Understanding Number Bases
Every number system uses a different set of digits. Binary uses 0 and 1. Octal uses 0–7. Decimal uses 0–9 (the one we use daily). Hexadecimal uses 0–9 and A–F (where A=10, B=11, C=12, D=13, E=14, F=15). The base tells you how many unique digits exist before you carry over to the next position. Understanding this concept makes converting between systems intuitive.
Frequently Asked Questions
Why do programmers use hexadecimal?
Hexadecimal is a compact way to represent binary data. Each hex digit maps exactly to 4 binary digits (bits), so a byte (8 bits) is always exactly 2 hex digits. This makes hex much easier to read than long strings of binary while maintaining a direct relationship to the underlying bits.
What is octal used for?
Octal is most commonly used in Unix/Linux file permissions. The command chmod 755 uses octal digits where 7 = rwx (read, write, execute), 5 = r-x (read and execute). Each octal digit represents exactly 3 binary bits, mapping directly to the permission flags.
How do I convert binary to decimal manually?
Each position in a binary number represents a power of 2, starting from the right at 2^0. To convert, multiply each digit by its position value and sum the results. For example, binary 1011 = (1x8) + (0x4) + (1x2) + (1x1) = 11 in decimal.