Number Base Converter
Convert numbers between binary, octal, decimal, and hexadecimal.
About Number Base Converter
Computers represent numbers in different bases. Binary (base 2) is used internally by all hardware. Octal (base 8) appears in file permissions (chmod). Hexadecimal (base 16) is everywhere in memory addresses, colors, and encoding. Type in any field to convert automatically to all other bases.
FAQ
- What is base conversion?
- Every number can be written in any positional system. Decimal uses digits 0–9, binary uses 0–1, hex uses 0–9 and A–F.
- Can I type hex letters in lowercase?
- Yes. The tool accepts both uppercase and lowercase hex digits.
- Why does hex use letters A–F?
- Hexadecimal needs 16 symbols. After using 0–9 (10 symbols), A=10, B=11, C=12, D=13, E=14, F=15.
- Is negative number conversion supported?
- Not currently. The tool handles non-negative integers only.
ABOUT THIS TOOL
Enter a number in binary, octal, decimal, or hexadecimal and instantly see it converted into the other three bases, updating as you type. Under the hood this is just repeated division and remainder tracking, or grouping bits by powers of two, but doing it by hand is slow and error-prone for anything beyond small numbers. Programmers reach for base conversion when reading memory addresses, working with bitmasks and flags, translating color codes, or debugging low-level code where hex and binary representations matter. It's also a common aid in computer science courses for building intuition about how positional number systems relate to each other.
HOW TO USE
- Type a number into any one of the four fields (binary, octal, decimal, hex).
- The other three fields update automatically with the converted value.
- Use only valid digits for each base - 0/1 for binary, 0-7 for octal, 0-9 for decimal, 0-9/A-F for hex.
- Clear a field and type a new number to start a fresh conversion.
- Copy the result you need directly from its field.
COMMON USE CASES
- A student checking manual binary-to-decimal homework conversions.
- A developer translating a hex memory address from a debugger into decimal to compare against a log entry.
- Someone decoding a hex color code's decimal RGB components for a design tool.
- A network engineer converting a subnet-related value between decimal and binary.
- An embedded systems programmer reading register values expressed as octal or hex constants in a datasheet.
TIPS & COMMON MISTAKES
- Hex letters A-F are case-insensitive here, though many codebases follow a lowercase convention for readability.
- This tool converts unsigned magnitudes only - for a negative value in a fixed-width register, apply two's complement encoding separately.
- Very large numbers can exceed the 32-bit or 64-bit ranges used in some programming languages, even though the converter itself has no such limit.
- Leading zeros are cosmetic - 0x0A and 0xA are the same hex value.
MORE QUESTIONS
- Why does the binary output look so much longer than the decimal input?
- Binary only has two digits per position, so it takes roughly 3.3 times as many digits as decimal to represent the same value - decimal 255 becomes 11111111 in binary.
- Does this tool support two's complement for negative binary numbers?
- No, it converts unsigned magnitudes only. To represent a negative number in a fixed bit width, such as an 8-bit or 32-bit signed integer, you need to apply two's complement encoding yourself.
- What's the difference between octal and hex for representing the same binary value?
- Octal groups binary digits in sets of 3 (2^3=8), while hex groups them in sets of 4 (2^4=16). Hex is more common in modern computing because it aligns cleanly with 8-bit bytes and 4-bit nibbles.
- Can I convert fractional numbers, like a decimal point value?
- No, this tool handles whole numbers only. Fractional base conversion follows a different process involving repeated multiplication and isn't supported here.