Decimal to Binary Converter

Repeatedly divide the number by 2 and record each remainder, either 0 or 1. Reading the remainders from the last division back to the first spells out the binary digits. This tool performs every division for you and shows the finished string instantly.

Yes. The conversion runs on arbitrary-precision integers rather than 64-bit floats, so values well beyond 2 to the 53rd power convert exactly. No digits are dropped and nothing is rounded, which is why a 40 digit number still returns an exact bit string.

No. This converter accepts non-negative whole numbers only. A minus sign, a decimal point, or any non-digit character triggers an Invalid number message rather than a guess. For signed values, see a two's complement tool instead.

No. Commas and whitespace are removed before the number is parsed, so 1,024 and 1 024 both convert cleanly to 10000000000. Any other symbol, including letters or currency signs, is still rejected as invalid.

Binary is base 2, so each digit is a power of two that doubles from right to left: 1, 2, 4, 8, 16 and so on. The string 1010 therefore means 8 plus 0 plus 2 plus 0, which equals 10 in decimal.

Zero has no bits set, so its shortest representation is a single 0. The converter also drops leading zeros from every other result, so you always get the minimal length bit string with no padding.

The bit count grows slowly: roughly the base-2 logarithm of the number, rounded up. As a rule of thumb every three decimal digits add about ten bits, so a million, which has 7 decimal digits, needs 20 bits and returns 11110100001001000000.

No. The conversion runs entirely in your browser using local JavaScript, so the number you type is never uploaded or logged. You can even use the tool with your connection switched off once the page has loaded.

Use the binary to decimal tool to go the other way, or the decimal to hex tool when you want base 16 instead. All three share the same arbitrary-precision engine, so large values stay exact across each conversion.