Tool for encoding/decoding numbers using NegaFibonacci encoding (binary words never having two consecutive 1 values)
NegaFibonacci Encoding - dCode
Tag(s) : Compression, Mathematics
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!
NegaFibonacci Encoding
Number to NegaFibonacci Coding Encoder
NegaFibonacci Code to Numbers Decoder
Answers to Questions (FAQ)
How to encode using NegaFibonacci encoding?
The NegaFibonacci code uses a variant of Zeckendorf's theorem which states that any integer (relative) can be written as the sum of non-consecutive generalized (positive or negative) Fibonnacci numbers.
$$ n = \sum_{i=1}^{k} \beta_i F_{-i} $$
(note the negative index $ i $) with $ \beta_i $ (equal to 0 or 1)
Example: $ 12 $ is the sum of $ F_{-7} = 13 $ and $ F_{-2} = -1 $ or 1000010 in binary (the two 1 are in position 7 and 2 starting from the right).
This representation similar to Zeckendorf never has 2 consecutive Fibonnacci numbers and therefore the binary value never has 2 consecutive digit 1.
How to decode NegaFibonacci encoding?
Each 1 of the binary word corresponds to a NegaFibonacci number (number of the Fibonacci sequence generalized to negative numbers). So, to calculate the original decimal number, add all the NegaFibonacci numbers corresponding to the 1 of the binary word.
Example: 10100 corresponds to $ 1 \times F_{-5} + 0 \times F_{-4} + 0 \times F_{-3} + 1 \times F_{-2} + 0 \times F_{-1} = F_{-5} + F_{-3} = 5 + 2 = 7 $
What are the variants of the NegaFibonacci encoding?
NegaFibonacci encoding is already a variant of Fibonacci encoding. It has the advantage of being generalizable to relative numbers (positive or negative integers).
Source code
dCode retains ownership of the "NegaFibonacci Encoding" source code. Except explicit open source licence (indicated Creative Commons / free), the "NegaFibonacci Encoding" algorithm, the applet or snippet (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, breaker, translator), or the "NegaFibonacci Encoding" 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 "NegaFibonacci Encoding" 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 "NegaFibonacci Encoding" 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):
NegaFibonacci Encoding on dCode.fr [online website], retrieved on 2024-11-21,
