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.
Négabinary - dCode
Tag(s) : Informatics, Arithmetics
dCode is free and its tools are a valuable help in games, maths, geocaching, puzzles and problems to solve every day!
A suggestion ? a feedback ? a bug ? an idea ? Write to dCode!
Négabinary
Negabinary to Decimal Converter
Decimal to Negabinary Converter
Binary to Negabinary Converter
Answers to Questions (FAQ)
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.
Source code
dCode retains ownership of the "Négabinary" source code. Except explicit open source licence (indicated Creative Commons / free), the "Négabinary" algorithm, the applet or snippet (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, breaker, translator), or the "Négabinary" functions (calculate, convert, solve, decrypt / encrypt, decipher / cipher, decode / encode, translate) written in any informatic language (Python, Java, PHP, C#, Javascript, Matlab, etc.) and all data download, script, or API access for "Négabinary" are not public, same for offline use on PC, mobile, tablet, iPhone or Android app!
Reminder : dCode is free to use.
Cite dCode
The copy-paste of the page "Négabinary" or any of its results, is allowed (even for commercial purposes) as long as you credit dCode!
Exporting results as a .csv or .txt file is free by clicking on the export icon
Cite as source (bibliography):
Négabinary on dCode.fr [online website], retrieved on 2024-12-21,
