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Negafibonacci
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. Encoding method The following steps describe how to encode a nonzero integer x . Note that f denotes the Negafibonacci sequence. # If x is positive, compute the greatest odd negative integer n such that the sum of the odd negative terms of the Negafibonacci sequence from -1 to n with a step of -2, is greater than or equal to x : n \in \ , \quad \sum_^ f(i) x \geq \sum_^ f(i) # Add a 1 at the , n, ^ bit of the binary word. Subtract f(n) from x . # Repeat the process from step 1 with the new value of ''x'', until it reaches 0. # Add a 1 on the left of the resulting binary word to finish the encoding. To decode an encoded binary word, remove the leftmost 1 from the binary word, since i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many areas of mathematics, which include number theory (the study of numbers), algebra (the study of formulas and related structures), geometry (the study of shapes and spaces that contain them), Mathematical analysis, analysis (the study of continuous changes), and set theory (presently used as a foundation for all mathematics). Mathematics involves the description and manipulation of mathematical object, abstract objects that consist of either abstraction (mathematics), abstractions from nature orin modern mathematicspurely abstract entities that are stipulated to have certain properties, called axioms. Mathematics uses pure reason to proof (mathematics), prove properties of objects, a ''proof'' consisting of a succession of applications of in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Universal Code (data Compression)
In data compression, a universal code for integers is a prefix code that maps the positive integers onto binary codewords, with the additional property that whatever the true probability distribution on integers, as long as the distribution is monotonic (i.e., ''p''(''i'') ≥ ''p''(''i'' + 1) for all positive ''i''), the expected lengths of the codewords are within a constant factor of the expected lengths that the optimal code for that probability distribution would have assigned. A universal code is ''asymptotically optimal'' if the ratio between actual and optimal expected lengths is bounded by a function of the information entropy of the code that, in addition to being bounded, approaches 1 as entropy approaches infinity. In general, most prefix codes for integers assign longer codewords to larger integers. Such a code can be used to efficiently communicate a message drawn from a set of possible messages, by simply ordering the set of messages ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Code Word (communication)
In communication, a code word is an element of a standardized code or protocol. Each code word is assembled in accordance with the specific rules of the code and assigned a unique meaning. Code words are typically used for reasons of reliability, clarity, brevity, or secrecy. See also * Code word (figure of speech) * Coded set * Commercial code (communications) * Compartmentalization (information security) * Duress code * Error correction and detection * Marine VHF radio * Password * Safeword * Spelling alphabet A spelling alphabet (#Terminology, also called by various other names) is a set of words used to represent the Letter (alphabet), letters of an alphabet in Speech, oral communication, especially over a two-way radio or telephone. The words chosen t ... References * * *UNHCR Procedure for Radio Communication External links UNHCR Procedure for Radio Communication Data transmission Cryptography {{crypto-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fibonacci Coding
In mathematics and computing, Fibonacci coding is a universal code which encodes positive integers into binary code words. It is one example of representations of integers based on Fibonacci numbers. Each code word ends with "11" and contains no other instances of "11" before the end. The Fibonacci code is closely related to the Zeckendorf representation, a positional numeral system that uses Zeckendorf's theorem and has the property that no number has a representation with consecutive 1s. The Fibonacci code word for a particular integer is exactly the integer's Zeckendorf representation with the order of its digits reversed and an additional "1" appended to the end. Definition For a number N\!, if d(0),d(1),\ldots,d(k-1),d(k)\! represent the digits of the code word representing N\! then we have: : N = \sum_^ d(i) F(i+2),\textd(k-1)=d(k)=1.\! where is the th Fibonacci number, and so is the th distinct Fibonacci number starting with 1,2,3,5,8,13,\ldots. The last bit d(k) i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
