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Négabinary

Tool to convert numbers with negabinary. The Negabinary system allows 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) : Informatics, Arithmetics

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# Négabinary

## Binary to Negabinary Converter

### What is negabinary? (Definition)

Negabinary writing corresponds to a base $-2$ numeral system.

### 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 (ordered from the end to the beginning).

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: 12 (decimal) in negabinary is written 11100 (its successive remainders are 0,0,1,1,1 :

 12 / -2 = -6 remainder 0 -6*-2 = 12 -6 / -2 = 3 remainder 0 3*-2 = -6 3 / -2 = -1 remainder 1 -1*-2 = 2 and 2+1 = 3 -1 / -2 = 1 remainder 1 1*-2=-2 and -2+1 = -1 1 / -2 = 0 remainder 1 0*-2 = 0 and 0+1 = 1

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

To convert a number from base $-2$ to base 10, apply numeric base change algorithms.

Example: 110 (negabinary) is equivalent to 2 (base 10) $1 \times (-2)^2 + 1 \times (-2)^1 + 0 \times (-2)^0 = 2$

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

In nega-binary, negative integers(with a minus sign in base 10) have an even number of bits, while the positive integers(with a plus sign in base 10) have an odd number of bits.

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Négabinary on dCode.fr [online website], retrieved on 2023-02-08, https://www.dcode.fr/negabinary-system

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