Number Base Converter

Binary, octal, decimal and hex

Pick the base your number is written in — binary (base 2), octal (base 8), decimal (base 10) or hexadecimal (base 16) — and the converter instantly shows the equivalent in every other base. Invalid digits for the chosen base are flagged so you never get a wrong answer.

Because it uses arbitrary-precision integers, even very large values convert exactly, making it reliable for programming, networking and digital electronics.

Common base conversions

• Binary to decimal and decimal to binary
• Decimal to hexadecimal and hex to decimal
• Octal conversions for file permissions

Key features at a glance

• Converts between binary, octal, decimal, and hexadecimal
• Shows all four bases at once
• Big-integer precision keeps large values exact
• Flags invalid digits for the chosen base
• Ideal for programming, networking, and digital electronics
• Runs entirely in your browser, even offline

How positional number systems work

Every number base is a positional system, meaning each digit's value depends on its place. In decimal (base 10), the digits represent powers of ten, so 254 is 2×100 + 5×10 + 4×1. Binary (base 2) uses powers of two, octal (base 8) powers of eight, and hexadecimal (base 16) powers of sixteen. The base just sets how many distinct digits exist and what each position is worth.

Hexadecimal needs sixteen digit values, so it borrows letters A through F to represent ten through fifteen. Converting between bases is really about regrouping the same underlying quantity into different-sized buckets. The converter handles this regrouping precisely, showing how one number looks in all four systems simultaneously, which makes the relationship between them tangible rather than abstract.

Why binary and hexadecimal matter in computing

Computers are built on binary because their transistors have two states, on and off, mapping naturally to 1 and 0. Everything a computer stores or processes is ultimately binary, but long strings of bits are hard for humans to read. Hexadecimal solves this neatly: because sixteen is two to the fourth power, each hex digit represents exactly four bits, so a byte is just two hex digits.

This tidy relationship is why hex appears everywhere in computing — memory addresses, color codes like #FF8800, MAC addresses, and byte dumps are all written in hexadecimal. Octal, representing three bits per digit, survives mainly in Unix file permissions. Being able to convert between these bases is a daily task for programmers and electronics engineers, and seeing them side by side builds the intuition that makes low-level work easier.

Big-integer precision and validation

Converting large numbers between bases can expose a hidden flaw in naive tools: ordinary floating-point arithmetic loses precision beyond a certain size, so a big binary or hexadecimal value can convert to a subtly wrong decimal. This converter uses arbitrary-precision (big-integer) arithmetic, so even very large values — like 64-bit addresses or long bit patterns — convert exactly, with no rounding errors.

It also validates input against the chosen base. Each base only permits certain digits: binary allows only 0 and 1, octal 0 through 7, and hexadecimal 0 through 9 plus A through F. If you enter a digit that is not valid for the selected base, the converter flags it rather than producing a misleading result, so you can trust that every conversion it shows is correct.

Tips for converting number bases

• Each hexadecimal digit represents exactly four binary bits
• A byte is two hex digits or eight binary bits
• Octal is mainly used for Unix file permissions (three bits per digit)
• Hex A–F stand for the values 10–15
• Validate input — only certain digits are legal in each base

Why choose our number base converter?

Our converter is completely free with no signup, no limits, and no subscription. It runs entirely in your browser, so conversions are instant, it works offline, and the values you enter never leave your device.

It is one of more than 200 free tools on ToopTools, and you can pin it to your My Workspace, a personalized workspace where you keep the tools you use most in a single dashboard. Beside the other converters and developer tools, it makes base conversion fast and exact.

Common use cases

Programmers use the number base converter constantly — reading memory addresses and color codes in hex, debugging bit patterns in binary, and interpreting Unix permissions in octal. It removes the mental gymnastics of converting between bases during development.

Computer science students use it to learn how number systems relate, networking professionals decode addresses and masks, and digital electronics hobbyists work with binary and hex. Because it shows all four bases at once with big-integer accuracy, it is reliable for both learning and precise professional work.

Is the number base converter free?

Yes. It is completely free with no account, no sign-up, and no usage limits. Convert as many numbers as you like at no cost.

How do I convert binary to decimal?

Add up the place values of each 1 bit, where positions represent powers of two. For example, 1011 is 8 + 0 + 2 + 1 = 11. The converter does this instantly and shows the other bases too.

Why is hexadecimal used in computing?

Because each hex digit maps to exactly four binary bits, hexadecimal is a compact, human-readable way to write binary data. A byte becomes two hex digits, which is why memory addresses and color codes use it.

Can it convert very large numbers accurately?

Yes. The converter uses arbitrary-precision integer arithmetic, so large values convert exactly without the rounding errors that floating-point math would introduce.

What do the letters A to F mean in hexadecimal?

Hexadecimal needs sixteen digit values, so after 0–9 it uses A through F to represent the values 10 through 15. So hex F is 15 and hex 10 is decimal 16.

Are my conversions kept private?

Yes. Everything is computed in your browser and nothing is uploaded, so the values you enter stay private and the tool works without an internet connection.

How do I convert decimal to binary or hexadecimal?

Enter your decimal number and the converter instantly shows it in binary, octal, and hexadecimal at the same time. You can also enter a value in any of those bases to convert it back, making it easy to move between number systems in one place.

Does the number base converter work offline?

Yes. The conversion runs entirely in your browser, so once the page has loaded the tool works without an internet connection, and nothing you enter is uploaded — it stays private on your own device.