A number base converter translates values between different numeral systems used in computing and mathematics. Decimal (base 10) is the system we use daily, while binary (base 2), hexadecimal (base 16), and octal (base 8) are essential in programming, networking, and digital electronics. Enter a number in any base below to see all four representations instantly.
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Common Values Quick Reference
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How to Use This Binary / Hex / Decimal / Octal Converter
Working with different number bases is a fundamental skill in programming, networking, and computer science. Whether you are debugging memory addresses in hexadecimal, setting Unix file permissions in octal, or analyzing bit patterns in binary, this free number base converter lets you translate between all four systems instantly without any manual math.
Step 1: Choose Your Input Base
Use the dropdown menu next to the input field to select the number system you are entering. Choose from Decimal (base 10), Binary (base 2), Hexadecimal (base 16), or Octal (base 8). The tool validates your input in real time, so it will only accept digits that are valid for the selected base. For example, if you select Binary, only 0 and 1 are accepted.
Step 2: Enter Your Number
Type or paste your number into the input field. The converter updates all four output panels in real time as you type. You can also use common prefixes like 0x for hex, 0b for binary, or 0o for octal. The tool handles arbitrarily large numbers using BigInt, so there is no size limit on your conversions.
Step 3: Read the Results
All four number representations appear simultaneously in clearly labeled output panels. Binary output is grouped into nibbles (groups of 4 bits) for easy reading, and hexadecimal output is grouped into pairs of digits representing individual bytes. The stats section below shows the bit count, byte count, and digit counts in hex and octal. These metrics are useful for understanding data sizes when working with registers, memory, or network protocols.
Step 4: Copy the Result
Click the Copy button on any output panel to copy that representation to your clipboard. The button confirms the copy with a brief "Copied!" label. This makes it easy to convert a decimal IP address component to hex for a network configuration file, or translate an octal permission code into binary to understand the individual permission bits.
Quick Reference Table
The table at the bottom of the page shows commonly used values from 0 to 255, including powers of two and byte boundaries. These are the numbers programmers encounter most often when working with colors, ASCII codes, file permissions, and memory addresses. Click any row to load that value into the converter for further exploration.
FAQ
Is this binary converter free to use?
Yes, this number base converter is completely free with no usage limits. Everything runs locally in your browser using JavaScript. There is no signup, no account, and no data sent to any server.
Is my data safe when using this tool?
Absolutely. All conversions happen entirely in your browser. No numbers or data are ever transmitted to a server. You can verify this by disconnecting from the internet and using the tool offline.
What is binary (base 2)?
Binary is a number system that uses only two digits: 0 and 1. It is the fundamental language of computers because digital circuits have two states: on (1) and off (0). Every piece of data in a computer, from text to images, is ultimately stored and processed as binary numbers.
What is hexadecimal (base 16)?
Hexadecimal uses 16 symbols: 0-9 for values zero to nine, and A-F for values ten to fifteen. Programmers use hex because it provides a compact way to represent binary data. Each hex digit maps to exactly four binary digits, so a byte (8 bits) can be written as just two hex characters instead of eight binary digits.
What is the difference between decimal, binary, hex, and octal?
Each system uses a different base. Decimal (base 10) uses digits 0-9 and is the system we use daily. Binary (base 2) uses only 0 and 1. Hexadecimal (base 16) uses 0-9 and A-F. Octal (base 8) uses digits 0-7. They all represent the same values but in different notations.
How large of a number can I convert?
This tool uses JavaScript BigInt for conversions, so it can handle arbitrarily large integers. There is no practical limit on the number of digits. You can convert numbers with hundreds of digits in any base without losing precision.
Why do programmers use hexadecimal instead of binary?
Hexadecimal is more compact and easier to read than binary. Since each hex digit maps to exactly four bits, converting between hex and binary is trivial. For example, the byte 11111111 in binary is simply FF in hex. This makes hex ideal for memory addresses, color codes, and debugging.
What are common uses of octal (base 8)?
Octal is most commonly used in Unix and Linux file permissions, where each permission set (read, write, execute) maps to three bits or one octal digit. For example, chmod 755 sets permissions using octal notation. Octal was also historically used in older computer systems that used 12-bit or 36-bit words.