Convert Decimal to Binary

Because binary itself doesn’t have a “−” sign – computers have to pick a convention. The four common ones: sign-magnitude (first bit = sign), one’s complement (negatives are bitwise-flipped positives), two’s complement (one’s complement + 1, has a unique zero), and offset binary. Two’s complement won because addition and subtraction are the same circuit, which saves transistors.

Because two’s complement defines negative n as 2^width − n. For 8-bit: 256 − 5 = 251 = 11111011. Equivalently, take +5 (00000101), flip all bits (11111010), and add 1 (11111011). Both methods agree.

The minimum number of bits to hold the value under the chosen representation. Unsigned 10 → 4 bits (1010). Signed 10 → 5 bits (01010) so the leading 0 signals positive. Signed −10 → 5 bits (10110). Fixed widths override this and pad with leading zeros.

You get a specific error like “overflow: 128 exceeds signed 8-bit range [-128, 127]”. Unsigned 8-bit allows 0-255; signed 8-bit allows -128 to 127. The tool doesn’t silently truncate because that would hide a real bug.

Because the representation is “bitwise invert of the absolute value” – you need a width to know how many bits to invert. Without a width, -5 could be 010-inverted (101) or 0101-inverted (1010) or wider, and all are ambiguous. Two’s complement has the same issue but the auto-width heuristic (pick min bits + 1) disambiguates.

Yes – the logic uses BigInt, so 2^128 or a 200-digit decimal both encode correctly. There’s no 2^53 precision cliff that plain Number.toString(2) would hit. Stats show the actual bit count even for huge inputs.

No – this tool is integer-only. Fractional binary (e.g., 0.75 = 0.11 binary) uses a radix point and is typically stored as IEEE 754 float (sign + exponent + mantissa). For that, use a floating-point-to-bits converter.

Convenience when pasting into code. Python (0b1010), Rust (0b1010), C23, and Java 7+ all accept it. Assembly sometimes uses % instead. Turn prefix off when you just want raw bits.

Yes. Signed 64-bit max is 2^63 − 1 = 9,223,372,036,854,775,807. Signed 64-bit min is −2^63 = −9,223,372,036,854,775,808. Both encode exactly. Values outside this range return the overflow message with the exact allowed range in the error.

Yes. All arithmetic happens in your browser using native JavaScript and BigInt. No upload, no tracking, no account. Load the page once and it keeps working offline indefinitely.