Binary / Hex / Decimal Converter

What does this Base Converter do?

This tool converts a number between four common numeral systems used in computing: decimal (base 10, what we use daily), binary (base 2, what computers use internally), octal (base 8), and hexadecimal (base 16, commonly used for colors and memory addresses).

How the conversion works

Each numeral system represents the same underlying quantity using a different number of symbols per digit — binary uses only 0 and 1, decimal uses 0–9, and hexadecimal uses 0–9 plus A–F to represent values 10–15. Converting between them means re-expressing the same value using a different base, or "radix."

Step-by-step example

The decimal number 255 converts to binary as 11111111 (since 255 = 128+64+32+16+8+4+2+1, i.e. all eight bits set), to octal as 377, and to hexadecimal as FF (since 15×16 + 15 = 255).

Tips & common mistakes

• Hexadecimal digits A through F represent 10 through 15 — a common beginner mistake is treating hex digits as if they only went up to 9.
• Binary numbers get long fast — 255 in decimal is only 3 digits, but 8 digits in binary — this is exactly why hex and octal exist, as more compact shorthand for binary values.
• Leading zeros don't change a number's value in any of these systems (0011 in binary is the same as 11), though they're sometimes kept for fixed-width formatting like byte representations.

Why computers use binary — and why humans use hex as shorthand

Computers represent all data using binary (base 2) because digital circuits most naturally represent two stable states — on and off, or 1 and 0. But raw binary is unwieldy for humans to read: a modest number like 250 requires 8 binary digits. Hexadecimal (base 16) became the standard shorthand because each hex digit maps cleanly onto exactly 4 binary digits, making it much more compact while still translating losslessly back to binary — which is why you'll see hex used constantly in programming, for things like color codes (#FF5733), memory addresses, and MAC addresses.

Where octal still shows up

Octal (base 8) is less common today but still appears in specific contexts like Unix/Linux file permission notation (e.g., chmod 755), where each octal digit conveniently represents exactly 3 binary digits (read, write, execute permission bits).

More tips

• When manually converting decimal to binary, repeatedly dividing by 2 and reading the remainders from bottom to top is the standard technique — this calculator does that instantly, but it's worth understanding the manual method too.
• Every whole number has exactly one representation in each base — there's no ambiguity, just different "alphabets" for writing the same underlying quantity.

Frequently asked questions