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Skew Binary Number System
The skew binary number system is a non-standard positional numeral system in which the ''n''th digit contributes a value of 2^ - 1 times the digit (digits are indexed from 0) instead of 2^ times as they do in binary. Each digit has a value of 0, 1, or 2. A number can have many skew binary representations. For example, a decimal number 15 can be written as 1000, 201 and 122. Each number can be written uniquely in skew binary canonical form where there is only at most one instance of the digit 2, which must be the least significant nonzero digit. In this case 15 is written canonically as 1000. Examples Canonical skew binary representations of the numbers from 0 to 15 are shown in following table: Arithmetical operations The advantage of skew binary is that each increment operation can be done with at most one carry operation. This exploits the fact that 2 (2^ - 1) + 1 = 2^ - 1 . Incrementing a skew binary number is done by setting the only two to a zero and incrementing the ne ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Non-standard Positional Numeral Systems
Non-standard positional numeral systems here designates numeral systems that may loosely be described as positional systems, but that do not entirely comply with the following description of standard positional systems: :In a standard positional numeral system, the base ''b'' is a positive integer, and ''b'' different numerals are used to represent all non-negative integers. The standard set of numerals contains the ''b'' values 0, 1, 2, etc., up to ''b'' − 1, but the value is weighted according to the position of the digit in a number. The value of a digit string like ''pqrs'' in base ''b'' is given by the polynomial form ::p\times b^3+q\times b^2+r\times b+s. :The numbers written in superscript represent the powers of the base used. :For instance, in hexadecimal (''b'' = 16), using the numerals A for 10, B for 11 etc., the digit string 7A3F means ::7\times16^3+10\times16^2+3\times16+15, :which written in our normal decimal notation is 31295. :Upon in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Binary Number
A binary number is a number expressed in the Radix, base-2 numeral system or binary numeral system, a method for representing numbers that uses only two symbols for the natural numbers: typically "0" (zero) and "1" (one). A ''binary number'' may also refer to a rational number that has a finite representation in the binary numeral system, that is, the quotient of an integer by a power of two. The base-2 numeral system is a positional notation with a radix of 2. Each digit is referred to as a bit, or binary digit. Because of its straightforward implementation in digital electronic circuitry using logic gates, the binary system is used by almost all modern computer, computers and computer-based devices, as a preferred system of use, over various other human techniques of communication, because of the simplicity of the language and the noise immunity in physical implementation. History The modern binary number system was studied in Europe in the 16th and 17th centuries by Thoma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Least Significant Bit
In computing, bit numbering is the convention used to identify the bit positions in a binary number. Bit significance and indexing In computing, the least significant bit (LSb) is the bit position in a binary integer representing the lowest-order place of the integer. Similarly, the most significant bit (MSb) represents the highest-order place of the binary integer. The LSb is sometimes referred to as the ''low-order bit''. Due to the convention in positional notation of writing less significant digits further to the right, the LSb also might be referred to as the ''right-most bit''. The MSb is similarly referred to as the ''high-order bit'' or ''left-most bit''. In both cases, the LSb and MSb correlate directly to the least significant digit and most significant digit of a decimal integer. Bit indexing correlates to the positional notation of the value in base 2. For this reason, bit index is not affected by how the value is stored on the device, such as the value's byte ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Carry (arithmetic)
In elementary arithmetic, a carry is a Numerical digit, digit that is transferred from one column of digits to another column of more significant digits. It is part of the standard algorithm to addition, add numbers together by starting with the rightmost digits and working to the left. For example, when 6 and 7 are added to make 13, the "3" is written to the same column and the "1" is carried to the left. When used in subtraction the operation is called a borrow. Carrying is emphasized in traditional mathematics, while curricula based on reform mathematics do not emphasize any specific method to find a correct answer. Carrying makes a few appearances in higher mathematics as well. In computing, carrying is an important function of adder (electronics), adder circuits. Manual arithmetic A typical example of carry is in the following pencil-and-paper addition: 1 27 + 59 ---- 86 7 + 9 = 16, and the digit 1 (number), 1 is the carry. The opposite is a borrow, as in − ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Run-length Encoding
Run-length encoding (RLE) is a form of lossless data compression in which ''runs'' of data (consecutive occurrences of the same data value) are stored as a single occurrence of that data value and a count of its consecutive occurrences, rather than as the original run. As an imaginary example of the concept, when encoding an image built up from colored dots, the sequence "green green green green green green green green green" is shortened to "green x 9". This is most efficient on data that contains many such runs, for example, simple graphic images such as icons, line drawings, games, and animations. For files that do not have many runs, encoding them with RLE could increase the file size. RLE may also refer in particular to an early graphics file format supported by CompuServe for compressing black and white images, that was widely supplanted by their later Graphics Interchange Format (GIF). RLE also refers to a little-used image format in Windows 3.x that is saved with the fil ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Eugene Myers
Eugene Wimberly "Gene" Myers Jr. (born December 31, 1953) is an American computer scientist and bioinformatician, who is best known for contributing to the early development of the NCBI's BLAST tool for sequence analysis. Education Myers received his Bachelor of Science in mathematics from the California Institute of Technology and a Doctor of Philosophy in computer science from the University of Colorado. Research Myers' 1990 paper (with Stephen Altschul and others) describing BLAST has received over 62,000+ citations making it amongst the most highly cited papers ever. Along with Udi Manber, Myers invented the suffix array data structure. Myers was a member of the faculty of the University of Arizona, the Vice President of Informatics Research at Celera Genomics, and a member of the faculty at UC Berkeley. At Celera Genomics, Myers was involved in the sequencing of the human genome, as well as the genomes of ''Drosophila'' and mouse. In particular, Myers advocated the use o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Purely Functional Data Structure
In computer science, a purely functional data structure is a data structure that can be directly implemented in a purely functional language. The main difference between an arbitrary data structure and a purely functional one is that the latter is (strongly) immutable. This restriction ensures the data structure possesses the advantages of immutable objects: (full) persistency, quick copy of objects, and thread safety. Efficient purely functional data structures may require the use of lazy evaluation and memoization. Definition Persistent data structures have the property of keeping previous versions of themselves unmodified. On the other hand, non-persistent structures such as arrays admit a destructive update, [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stack (abstract Data Type)
In computer science, a stack is an abstract data type that serves as a collection (abstract data type), collection of elements with two main operations: * Push, which adds an element to the collection, and * Pop, which removes the most recently added element. Additionally, a peek (data type operation), peek operation can, without modifying the stack, return the value of the last element added. The name ''stack'' is an analogy to a set of physical items stacked one atop another, such as a stack of plates. The order in which an element added to or removed from a stack is described as last in, first out, referred to by the acronym LIFO. As with a stack of physical objects, this structure makes it easy to take an item off the top of the stack, but accessing a Data, datum deeper in the stack may require removing multiple other items first. Considered a sequential collection, a stack has one end which is the only position at which the push and pop operations may occur, the ''top'' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Skew Binomial Heap
In computer science, a skew binomial heap (or skew binomial queue) is a data structure for priority queue operations. It is a variant of the binomial heap that supports constant-time insertion operations in the worst case, rather than amortized time. Motivation Just as binomial heaps are based on the binary number system, skew binary heaps are based on the skew binary number system. Ordinary binomial heaps suffer from worst case logarithmic complexity for insertion, because a carry operation may cascade, analogous to binary addition. Skew binomial heaps are based on the skew binary number system, where the kth digit (zero-indexed) represents 2^-1, instead of 2^k. Digits are either 0 or 1, except the lowest non-zero digit, which may be 2. An advantage of this system is that at most one carry operation is needed. For example, 60 is represented as 11200 in skew binary (31 + 15 + 7 + 7), and adding 1 produces 12000 (31 + 15 + 15). Since the next higher digit is guaranteed not to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Binomial Heap
In computer science, a binomial heap is a data structure that acts as a priority queue. It is an example of a mergeable heap (also called meldable heap), as it supports merging two heaps in logarithmic time. It is implemented as a Heap (data structure), heap similar to a binary heap but using a special tree structure that is different from the complete binary trees used by binary heaps. Binomial heaps were invented in 1978 by Jean Vuillemin. Binomial heap A binomial heap is implemented as a set of binomial tree data structure, trees (compare with a binary heap, which has a shape of a single binary tree), which are defined recursively as follows: * A binomial tree of order 0 is a single node * A binomial tree of order k has a root node whose children are roots of binomial trees of orders k-1, k-2, ..., 2, 1, 0 (in this order). A binomial tree of order k has 2^k nodes, and height k. The name comes from the shape: a binomial tree of order k has \tbinom k d nodes at depth d, a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Three-valued Logic
In logic, a three-valued logic (also trinary logic, trivalent, ternary, or trilean, sometimes abbreviated 3VL) is any of several many-valued logic systems in which there are three truth values indicating ''true'', ''false'', and some third value. This is contrasted with the more commonly known bivalent logics (such as classical sentential or Boolean logic) which provide only for ''true'' and ''false''. Emil Leon Post is credited with first introducing additional logical truth degrees in his 1921 theory of elementary propositions. The conceptual form and basic ideas of three-valued logic were initially published by Jan Łukasiewicz and Clarence Irving Lewis. These were then re-formulated by Grigore Constantin Moisil in an axiomatic algebraic form, and also extended to ''n''-valued logics in 1945. Pre-discovery Around 1910, Charles Sanders Peirce defined a many-valued logic system. He never published it. In fact, he did not even number the three pages of notes where he defined ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Redundant Binary Representation
A redundant binary representation (RBR) is a numeral system that uses more bits than needed to represent a single binary digit so that most numbers have several representations. An RBR is unlike usual binary numeral systems, including two's complement, which use a single bit for each digit. Many of an RBR's properties differ from those of regular binary representation systems. Most importantly, an RBR allows addition without using a typical carry. When compared to non-redundant representation, an RBR makes bitwise logical operation slower, but arithmetic operations are faster when a greater bit width is used. Usually, each digit has its own sign that is not necessarily the same as the sign of the number represented. When digits have signs, that RBR is also a signed-digit representation. Conversion from RBR An RBR is a place-value notation system. In an RBR, digits are ''pairs'' of bits, that is, for every place, an RBR uses a pair of bits. The value represented by a redundant dig ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
