Number Base Converter

Convert numbers between binary, octal, decimal, and hexadecimal free online. Enter a value in any base and see all four representations simultaneously.

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How to Use This Tool

Choose the input baseDecimal, binary, octal, or hexadecimal

Enter your valueUsing valid digits for that base

See all four representationsCalculated simultaneously from one input

One Value, Four Ways to Write It

Every number base represents the exact same underlying quantity, just using a different counting system -- base 10 for everyday human use, base 2 for how computers fundamentally store data, base 16 for compact human-readable representation of binary data, and base 8 as a historical computing convention that still appears occasionally.

Hexadecimal's Clean Mapping to Binary

Each hexadecimal digit corresponds to exactly 4 binary bits, which is precisely why programmers reach for hex constantly -- it compresses binary's verbosity into a much shorter, still precisely structured representation, showing up everywhere from color codes to memory addresses to debugging output.

Decimal as the Universal Intermediate Step

Regardless of which base you enter a value in, this calculator converts it to decimal first as a common reference point, then calculates the other three bases from that decimal value -- a clean, reliable conversion path that works consistently regardless of which specific base pairing you're actually interested in.

Frequently Asked Questions

Decimal (base 10) is what humans use daily. Binary (base 2) is how computers represent data at the hardware level. Octal (base 8) was historically used in some early computing contexts. Hexadecimal (base 16) is favored by programmers because it maps cleanly to binary -- each hex digit represents exactly 4 bits.

A byte in binary is 8 characters (like 11010110), while the same value in hex is just 2 characters (D6) -- hex preserves the clean mapping to binary bits while being far more compact and readable for humans, which is why it shows up constantly in programming contexts like color codes and memory addresses.

Internally, any input value first converts to decimal regardless of its original base, then that decimal value converts into each of the other three target bases -- decimal serves as the common intermediate representation for all conversions.

This handles non-negative integer values across all four bases. Negative number representation in different bases (especially binary) involves additional conventions like two's complement that go beyond simple base conversion.

Unix file permission notation (like chmod 755) is one of the few places octal still commonly appears in everyday computing, a holdover from earlier computing conventions even though hex has largely replaced octal elsewhere.