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Négabinary

Tool to convert numbers with negabinary. The Negabinary system allow to represent positive and negative numbers without bit sign in a binary format (0 and 1) using the base -2.

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Négabinary -

Tag(s) : Mathematics, Informatics

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# Négabinary

## Binary to Negabinary Converter

Tool to convert numbers with negabinary. The Negabinary system allow to represent positive and negative numbers without bit sign in a binary format (0 and 1) using the base -2.

### How to convert a decimal number into negabinary?

The numbers in the negabinary system are described by the formula:

$$\sum_{i=0}^{n}b_{i}(-2)^{i}$$

With $$b$$ a bit and $$i$$ its rank in the inverted negabinary development.

To convert an integer, it is enough to make a division repeated by $$-2$$ and to concatenate the obtained remainders starting with the end.

Example: If we want to represent 12 in negabinary:
12 / -2 = -6, remainder 0
-6 / -2 = 3, remainder 0
3 / -2 = -1, remainder 1
-1 / -2 = 1, remainder 1
1 / -2 = 0, remainder 1
12 (decimal) in negabinary is written 11100.

### How to convert a Negabinay number to Decimal?

Negabinary writing corresponds to a writing in base -2.

Example: 110 (negabinary) is equivalent to $$1 \times (-2)^2 + 1 \times (-2)^1 + 0 \times (-2)^0 = 2$$

### How to recognize a positive or negative integer in negabinary?

In nega-binary, negative integers have an even number of bits, while the positive integers have an odd number of bits.