Convert Number to Negadecimal

Negadecimal eliminates the need for a sign bit/symbol. Every integer – positive or negative – gets a unique representation using only digits 0-9. Compare: in standard decimal, you need -15 (two characters) or a sign bit; in negadecimal, just 25. This property is studied in number theory and used as a teaching example for how positional notation works in non-standard bases. It’s also the basis for how some early Soviet computers (Setun’s negabinary cousin) avoided dedicated sign handling.

Standard remainder/quotient division, but with one twist. Compute q = n ÷ base (truncated toward zero) and r = n mod base. If r is negative, add |base| to it and increment q by 1. Push r as the next least-significant digit. Repeat with n := q until q = 0. The step panel shows every iteration.

JavaScript’s regular Number type loses integer precision above 2^53 (about 9 quadrillion). For number-theory work involving large integers, that’s not nearly enough. This tool uses native BigInt throughout, so an input like 1234567890123456789012345678901234567890 converts exactly.

It’s the safety net. If the converter outputs 195 for input 15, the verification shows: 1×(−10)² + 9×(−10)¹ + 5×(−10)⁰ = 100 − 90 + 5 = 15. The total must match your input – if not, something’s wrong. This both teaches the math and proves the conversion was correct.

Negabinary is base −2 – same idea but with digits 0 and 1 only. So 5 in negabinary is 101 (4 + 0 + 1) and −5 is 111 (4 − 2 + 1, wait that’s 3 not −5… actually -5 in negabinary is 1111: −8 + 4 − 2 + 1 = −5). It’s used in some computer architectures because you can do arithmetic without a separate sign bit. Try base −2 in the selector to see.

Yes – that’s the giveaway. In negadecimal, 0 through 9 are 1 digit (representing 0-9 positive), but to express −1 you need 19 (2 digits, because 1×−10 + 9 = −1). The parity of the digit count tells you the sign – positive numbers end up with odd length (or are zero), negative numbers with even length, after dropping the leading zero. Useful as a sanity check.

Yes – switch direction to “Negative-base → Decimal” or click Swap ⇄. The reverse parser multiplies each digit by its place value (base)^position and sums. The place-value table on the right shows exactly how that decomposition works.

Negadecimal of a negative decimal still uses only 0-9 digits – no leading minus sign. Negative input to the input field still works in decimal mode (e.g., -15 → 25); in negative-base mode the parser accepts an explicit leading - as a sign on the parsed magnitude, then negates the result. That’s slightly redundant for negadecimal but matches user expectations.

No. All BigInt arithmetic runs in your browser using vanilla JavaScript. Open DevTools → Network and confirm zero requests fire after the page loads – even when you Convert. Safe for math research, contest problems, or proprietary algorithm tests.

Yes. Total bundle is under 20 KB. Once loaded, disconnect from the internet and keep converting – useful when working through a number-theory textbook or during competitive programming practice.