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binary-to-negabinary

Negabinary is base −2 — a positional numeral system where each position's weight is (−2)^k. It can represent both positive and negative integers without a separate sign bit, making it a curiosity in computer-science theory. Position 0 = (-2)^0 = 1, position 1 = (-2)^1 = -2, position 2 = (-2)^2 = 4, position 3 = -8, ... Decimal 5 in negabinary is 101 (= 4 + 0 + 1). Decimal -1 is 11 (= -2 + 1). The ZTools Binary to Negabinary Converter handles both directions and any integer.

Use cases​

Computer-science curiosity​

Negabinary teaches positional notation generality — base doesn't have to be positive.

Algorithm exercise​

Implementing negabinary conversion is a fun coding-interview problem.

Teach number bases beyond positive​

Students see that "base" is more flexible than they think.

How it works​

  1. Paste decimal or binary — Tool detects.
  2. Convert — Repeatedly divide by −2 with a non-negative remainder. The remainder sequence is the negabinary representation.
  3. Output — Negabinary digits + verification (multiply out and check equals input).

Examples​

Input: Decimal 5

Output: Negabinary 101. Verify: 1·4 + 0·(-2) + 1·1 = 5.

Input: Decimal -1

Output: Negabinary 11. Verify: 1·(-2) + 1·1 = -1.

Input: Decimal 6

Output: Negabinary 11010. Verify: 1·16 + 1·(-8) + 0·4 + 1·(-2) + 0·1 = 6.

Frequently asked questions​

Why is this useful?

Mostly theoretical — positional notation generality. Some hardware experiments use balanced ternary or negabinary; mainstream computing uses two's complement.

Privacy?

All in browser.

Tips​

  • Pure curiosity — useful for CS theory, coding-interview problems, and teaching number bases.
  • For practical work, two's complement is the universal standard.

Try it now​

The full binary-to-negabinary runs in your browser at https://ztools.zaions.com/binary-to-negabinary — no signup, no upload, no data leaves your device.

Open the tool ↗

Last updated: 2026-05-06 · Author: Ahsan Mahmood · Edit this page on GitHub