Number Base Converter — Decimal, Binary, Hex, Octal
Convert numbers between decimal, binary, octal, and hexadecimal instantly. Free online number base converter.
Number Base Systems
Computers use different number systems: binary (base 2) for machine code, octal (base 8) for Unix file permissions, decimal (base 10) for everyday math, and hexadecimal (base 16) for memory addresses and colors.
Common Conversions
Decimal 255 = Binary 11111111 = Hex FF = Octal 377. Hexadecimal is especially common in web development for CSS colors (e.g., #FF5733).
About This Tool
The Number Base Converter converts integers between binary (base 2), octal (base 8), decimal (base 10), and hexadecimal (base 16) number systems. It is an essential tool for computer science students, embedded developers, and anyone working with low-level data representations.
Key Features
- Multi-Base Conversion — Converts a number from any supported base to all other bases simultaneously, showing binary, octal, decimal, and hexadecimal results at once.
- Instant Results — Conversion happens as you type, with no button to press. Results update in real time for fast exploration.
- Input Validation — Detects invalid characters for the selected base and shows an error instead of silently producing wrong results.
- Copy Buttons — Copy any individual result to clipboard with one click for immediate use in your code or documentation.
- Free and No Signup — Convert numbers without creating an account or paying anything.
Common Use Cases
- Converting a decimal memory address to hexadecimal for use in assembly language or debugger output
- Converting binary bit patterns from CPU registers or network packets to readable decimal or hex values
- Understanding octal file permission values in Unix and Linux systems such as chmod 755
- Working with color codes that use hexadecimal notation in web development and graphic design
- Studying number systems for a computer science course or certification exam
How to Use
Select the input base (binary, octal, decimal, or hexadecimal) from the dropdown. Type or paste your number into the input field. The converted values for all other bases appear instantly below. Use the copy button next to any result to copy it to clipboard.
Frequently Asked Questions
What are the four main number bases used in computing?
Binary (base 2) uses digits 0-1 and represents data at the hardware level. Octal (base 8) uses 0-7 and is common in Unix permissions. Decimal (base 10) is everyday counting. Hexadecimal (base 16) uses 0-9 and A-F and is widely used for memory addresses, color codes, and byte values.
How do I convert a binary number to decimal by hand?
Multiply each binary digit by 2 raised to its position (counting from right, starting at 0), then add the results. For example, 1011 in binary equals 1x8 + 0x4 + 1x2 + 1x1 = 11 in decimal.
Why is hexadecimal used so often in programming?
One hexadecimal digit represents exactly four binary bits (a nibble), so two hex digits represent one byte. This makes hex far more compact and readable than binary for memory addresses, color values, and machine code.
What is the maximum integer this tool can convert accurately?
This tool uses JavaScript numbers internally, which are 64-bit floating point. Integers up to 2^53 - 1 (9007199254740991) are represented exactly. Larger integers may lose precision due to floating-point limitations.
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