All Tools VerseNegabinary is base -2: a number system that uses only 0 and 1 like binary, but with place values that are powers of negative two. That single twist lets it store both positive and negative numbers without a separate sign bit, so the negabinary 110 is decimal 2 and 111 is decimal 3. This guide explains how base -2 works, how to read and convert it, and a free converter for the job.
In this guide
What negabinary is
Standard binary uses place values of 1, 2, 4, 8, and so on, all positive powers of two. Negabinary uses powers of negative two instead: 1, -2, 4, -8, 16, and so on. The digits are still only 0 and 1, but because every other place value is negative, the same string of bits can land on a negative total. It is a real positional system, just with an unusual base. Our number systems guide covers the positive bases this builds on.
The place values
From the right, negabinary places are 1, -2, 4, -8, 16, -32. Each is the previous one multiplied by -2. So a 1 in the second position from the right contributes -2, and a 1 in the fourth contributes -8. The alternating sign is the whole mechanism: even positions are positive, odd positions are negative.
Read a negabinary number
Add the place values wherever there is a 1, exactly as in binary, but respect the signs. Negabinary 110 has 1s in the 4 and -2 positions, so it is 4 plus -2, which is 2. Negabinary 111 is 4 plus -2 plus 1, which is 3. Negabinary 11 is -2 plus 1, which is -1. Converting longer values by hand is error prone, so the binary to negabinary converter handles both directions, and you can sanity check a result with the binary to decimal converter for the positive parts.
Why it has no sign bit
Ordinary signed binary needs a convention such as two’s complement to mark negatives, which ties the meaning of a bit string to a fixed width. Negabinary encodes the sign directly in the place values, so a number is negative or positive purely from its digits, with no extra bit and no width assumption. That elegance is the reason it keeps reappearing in computer science, even though it is rarely used in practice.
Where it is used
Negabinary is mostly a teaching and theory tool. It appears in courses on number representation to show that the choice of base is flexible, and it turns up in a few specialized algorithms and historical computer designs. You are unlikely to meet it in everyday code, but understanding it deepens how you think about positional systems and signed numbers in general.
Free converters used in this guide
Frequently asked questions
What is negabinary?
Negabinary is base -2, a positional system using only 0 and 1 but with place values that are powers of negative two, so it can store negative numbers without a sign bit.
What is negabinary 110 in decimal?
Negabinary 110 has 1s in the 4 and -2 places, so it is 4 plus -2, which is 2.
How does negabinary show negative numbers?
The odd positions carry negative place values, so a number becomes negative when those positions outweigh the positive ones, with no separate sign bit needed.
Is negabinary used in real systems?
Rarely. It is mainly a teaching example and appears in a few specialized algorithms, not in everyday programming.
How do I convert binary to negabinary?
The digit patterns differ, so it is not a direct swap. A binary to negabinary converter computes the base -2 representation for you.