The binary output is grouped in fours so you can line it up with the hex.
How number bases work
A number base, or radix, is how many different digits a number system uses. Everyday decimal is base 10, with digits 0–9, and each position is worth ten times the one to its right. Binary is base 2, with only 0 and 1, and each position is worth twice the one to its right. Octal (base 8) uses 0–7, and hexadecimal (base 16) uses 0–9 followed by A–F for ten to fifteen. Any base from 2 to 36 can be written with the digits 0–9 and the letters A–Z. BaseConvert converts between all of them using exact integer arithmetic, so even very long numbers convert without rounding.
Converting by hand
To convert from any base to decimal, multiply each digit by the base raised to its position, counting from zero on the right, and add the results. Binary 1011 is 1×8 + 0×4 + 1×2 + 1×1 = 11. To convert from decimal to another base, divide by the base repeatedly and keep the remainders; read them from the last to the first. 11 ÷ 2 gives remainders 1, 1, 0, 1, so the answer is 1011. Converting between binary, octal and hex is even easier because 8 and 16 are powers of two: every octal digit is three bits and every hex digit is four, so you can translate group by group.
Signed numbers and two’s complement
Computers store negative integers using two’s complement. In an n-bit number the highest bit is worth −2^(n−1) instead of +2^(n−1). To find the pattern for a negative number, write the positive value in binary, invert every bit and add one. The same bits can be read as a large unsigned number or a negative signed one, which is why a byte of 11111111 is 255 unsigned and −1 signed. The calculator shows both readings for 8, 16, 32 and 64 bits and tells you the smallest width that can hold your number.
Where you will meet each base
Binary underlies everything digital, from bit masks to network subnet calculations. Hexadecimal is used for memory addresses, colour codes like #FF8000, byte dumps and hashes. Octal survives in Unix file permissions such as 755 and 644. Base 36 is sometimes used for short IDs and URLs. All conversions happen in your browser.
Frequently asked questions
Why do programmers use hex?
It is a compact way to write binary; one byte is exactly two hex digits.
What is 0xFF?
11111111 in binary, 255 in decimal.
Can I convert long hashes?
Yes. There is no length limit.
Is BaseConvert free?
Yes, with no sign-up or ads.
Does it work offline?
Yes, once the page has loaded. Nothing you type is sent anywhere.