Binary Converter

Write the binary number with place values that double from right to left (1, 2, 4, 8, 16, 32, 64, 128…), then add the place values where the bit is 1. For 1010: 8 + 0 + 2 + 0 = 10. For 1101: 8 + 4 + 0 + 1 = 13. This tool does the math instantly for values of any size, including numbers far too large for a calculator.

Repeatedly divide the decimal number by 2 and record the remainders from the last to the first. For 13: 13÷2=6 r1, 6÷2=3 r0, 3÷2=1 r1, 1÷2=0 r1, so reading remainders backwards gives 1101. An easier shortcut is to subtract the largest powers of 2 (8, 4, 2, 1) that fit.

They are all ways of writing the same number with different bases. Binary uses only 0 and 1 (base 2, used by every computer). Decimal uses 0-9 (base 10, everyday math). Hexadecimal uses 0-9 and A-F (base 16, used for colors and memory addresses). Octal uses 0-7 (base 8, used in Unix file permissions). 255, 11111111, 0xFF, and 0o377 all represent the same value.

Digital electronics have only two reliable states — on and off, or high and low voltage — which map perfectly to 1 and 0. Every piece of data in a computer (text, images, video, programs) is ultimately a sequence of bits. Grouping 8 bits into a byte, 16 bits into a word, and so on lets hardware manipulate larger numbers efficiently.

Most calculators overflow above 2^53 (about 9 quadrillion), but this tool uses arbitrary-precision BigInt arithmetic internally, so it converts values with dozens of digits without rounding. The result is exact no matter how large the input.

If a number is made of 8-bit chunks that all map to printable characters (like 72 101 108 108 111), the tool shows the text interpretation. 72 = "H", 101 = "e", 108 = "l", 111 = "o", so 0x48656C6C6F reads "Hello". It is a handy way to spot encoded text while converting.

Yes — completely free, no registration, and 100% private. All conversion runs locally in your browser; your numbers are never sent to any server. The tool works offline after the page loads.