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- Q16254296 subject Q5463728.
- Q16254296 subject Q7145923.
- Q16254296 subject Q7216422.
- Q16254296 abstract "In mathematics, negaFibonacci coding is a universal code which encodes nonzero integers into binary code words. It is similar to Fibonacci coding, except that it allows both positive and negative integers to be represented. All codes end with "11" and have no "11" before the end. The code for the integers from -11 to 11 is given below.xx negaFibonacci representation negaFibonacci code-11 101000 0001011-10 101001 1001011-9 100010 0100011-8 100000 0000011-7 100001 1000011-6 100100 0010011-5 100101 1010011-4 1010 01011-3 1000 00011-2 1001 10011-1 10 0110 0 (cannot be encoded)1 1 112 100 00113 101 10114 10010 0100115 10000 0000116 10001 1000117 10100 0010118 10101 1010119 1001010 0101001110 1001000 0001001111 1001001 10010011The Fibonacci code is closely related to negaFibonacci representation, a positional numeral system sometimes used by mathematicians. The negaFibonacci code for a particular nonzero integer is exactly that of the integer's negaFibonacci representation, except with the order of its digits reversed and an additional "1" appended to the end. The negaFibonacci code for all negative numbers has an oddnumber of digits, while those of all positive numbers have an even number of digits.To encode a nonzero integer X: Calculate the largest (or smallest) encodeable number with N bits by summing the odd (or even) negafibonacci numbers from 1 to N. When it is determined that N bits is just enough to contain X, subtract the Nth negaFibonacci number from X, keeping track of the remainder, and put a one in the Nth bit of the output. Working downward from the Nth bit to the first one, compare each of the corresponding negaFibonacci numbers to the remainder. Subtract it from the remainder if the absolute value of the difference is less, AND if the next higher bit does not already have a one in it. A one is placed in the appropriate bit if the subtraction is made, or a zero if not. Put a one in the N+1th bit to finish.To decode a token in the code, remove the last "1", assign the remaining bits the values 1,-1,2,-3,5,-8,13... (the negafibonacci numbers), and add the "1" bits.".
- Q16254296 wikiPageExternalLink books?id=eEgvfic3A4kC&pg=PA79.
- Q16254296 wikiPageExternalLink fasc1a.ps.gz.
- Q16254296 wikiPageWikiLink Q1188392.
- Q16254296 wikiPageWikiLink Q122653.
- Q16254296 wikiPageWikiLink Q2633.
- Q16254296 wikiPageWikiLink Q2886580.
- Q16254296 wikiPageWikiLink Q395.
- Q16254296 wikiPageWikiLink Q4176366.
- Q16254296 wikiPageWikiLink Q47577.
- Q16254296 wikiPageWikiLink Q5463728.
- Q16254296 wikiPageWikiLink Q7145923.
- Q16254296 wikiPageWikiLink Q7216422.
- Q16254296 wikiPageWikiLink Q82438.
- Q16254296 wikiPageWikiLink Q863873.
- Q16254296 comment "In mathematics, negaFibonacci coding is a universal code which encodes nonzero integers into binary code words. It is similar to Fibonacci coding, except that it allows both positive and negative integers to be represented. All codes end with "11" and have no "11" before the end.".
- Q16254296 label "NegaFibonacci coding".