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65536
65536 is the natural number following 65535 and preceding 65537. 65536 is a power of two: 2^ (2 to the 16th power). 65536 is the smallest number with ''exactly'' 17 divisors. In mathematics 65536 is 2^, so in tetration notation 65536 is 42. When expressed using Knuth's up-arrow notation, 65536 is 2 \uparrow 16 , which is equal to 2 \uparrow 2 \uparrow 2 \uparrow 2 , which is equivalent to 2 \uparrow\uparrow 4 or 2 \uparrow\uparrow\uparrow 3 . 65536 is a superperfect number – a number such that σ(σ(''n'')) = 2''n''. A 16-bit number can distinguish 65536 different possibilities. For example, unsigned binary notation exhausts all possible 16-bit codes in uniquely identifying the numbers 0 to 65535. In this scheme, 65536 is the least natural number that can ''not'' be represented with 16 bits. Conversely, it is the "first" or smallest positive integer that requires 17 bits. 65536 is the only power of 2 less than 231000 that does not contain the digits ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Knuth's Up-arrow Notation
In mathematics, Knuth's up-arrow notation is a method of notation for very large integers, introduced by Donald Knuth in 1976. In his 1947 paper, R. L. Goodstein introduced the specific sequence of operations that are now called ''hyperoperations''. Goodstein also suggested the Greek names tetration, pentation, etc., for the extended operations beyond exponentiation. The sequence starts with a unary operation (the successor function with ''n'' = 0), and continues with the binary operations of addition (''n'' = 1), multiplication (''n'' = 2), exponentiation (''n'' = 3), tetration (''n'' = 4), pentation (''n'' = 5), etc. Various notations have been used to represent hyperoperations. One such notation is H_n(a,b). Knuth's up-arrow notation \uparrow is an alternative notation. It is obtained by replacing /math> in the square bracket notation by n-2 arrows. For example: * the single arrow \uparrow represents exponentiation (iterated multiplication) 2 \uparrow 4 = H_3(2,4) = 2\times ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
65535 (number)
65535 is the integer after 65534 and before 65536. It is the maximum value of an unsigned 16-bit integer. In mathematics 65535 is the product of the first four Fermat primes: 65535 = (2 + 1)(4 + 1)(16 + 1)(256 + 1). Because of this property, it is possible to construct with compass and straightedge a regular polygon with 65535 sides. See constructible polygon. 65535 is the sum of 20 through 215 (20 + 21 + 22 + ... + 215) and is therefore a repdigit in base 2 (1111111111111111), in base 4 (33333333), and in base 16 (FFFF). 65535 is the 15th 626- gonal number, the 5th 6555-gonal number, and the 3rd 21846-gonal number. In computing *65535 occurs frequently in the field of computing because it is 2^ - 1 (one less than 2 to the 16th power), which is the highest number that can be represented by an unsigned 16-bit binary number. Some computer programming environments may have predefined constant values representing 65535, with names like . *In older computers with processors ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Superperfect Number
In mathematics, a superperfect number is a positive integer ''n'' that satisfies :\sigma^2(n)=\sigma(\sigma(n))=2n\, , where σ is the divisor summatory function. Superperfect numbers are a generalization of perfect numbers. The term was coined by D. Suryanarayana (1969). The first few superperfect numbers are : : 2, 4, 16, 64, 4096, 65536, 262144, 1073741824, ... . To illustrate: it can be seen that 16 is a superperfect number as σ(16) = 1 + 2 + 4 + 8 + 16 = 31, and σ(31) = 1 + 31 = 32, thus σ(σ(16)) = 32 = 2 × 16. If ''n'' is an ''even'' superperfect number, then ''n'' must be a power of 2, 2''k'', such that 2''k''+1 − 1 is a Mersenne prime. It is not known whether there are any odd Odd means unpaired, occasional, strange or unusual, or a person who is viewed as eccentric. Odd may also refer to: Acronym * ODD (Text Encoding Initiative) ("One Document Does it all"), an abstracted literate-programming format for describing X ... superperfect numbers. An odd sup ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1048576 (number)
A power of two is a number of the form where is an integer, that is, the result of exponentiation with number two as the base and integer as the exponent. In a context where only integers are considered, is restricted to non-negative values, so there are 1, 2, and 2 multiplied by itself a certain number of times. The first ten powers of 2 for non-negative values of are: : 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, ... Because two is the base of the binary numeral system, powers of two are common in computer science. Written in binary, a power of two always has the form 100...000 or 0.00...001, just like a power of 10 in the decimal system. Computer science Two to the exponent of , written as , is the number of ways the bits in a binary word of length can be arranged. A word, interpreted as an unsigned integer, can represent values from 0 () to () inclusively. Corresponding signed integer values can be positive, negative and zero; see signed nu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
65537 (number)
65537 is the integer after 65536 and before 65538. In mathematics 65537 is the largest known prime number of the form 2^ +1 (n = 4). Therefore, a regular polygon with 65537 sides is constructible with compass and unmarked straightedge. Johann Gustav Hermes gave the first explicit construction of this polygon. In number theory, primes of this form are known as Fermat primes, named after the mathematician Pierre de Fermat. The only known prime Fermat numbers are 2^ + 1 = 2^ + 1 = 3, 2^ + 1= 2^ +1 = 5, 2^ + 1 = 2^ +1 = 17, 2^ + 1= 2^ + 1= 257, 2^ + 1 = 2^ + 1 = 65537. In 1732, Leonhard Euler found that the next Fermat number is composite: 2^ + 1 = 2^ + 1 = 4294967297 = 641 \times 6700417 In 1880, showed that 2^ + 1 = 2^ + 1 = 274177 \times 67280421310721 65537 is also the 17th Jacobsthal–Lucas number, and currently the largest known integer ''n'' for which the number 10^ + 27 is a probable prime. Applications 65537 is commonly used as a public exponent in the RSA cr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Power Of Two
A power of two is a number of the form where is an integer, that is, the result of exponentiation with number two as the base and integer as the exponent. In a context where only integers are considered, is restricted to non-negative values, so there are 1, 2, and 2 multiplied by itself a certain number of times. The first ten powers of 2 for non-negative values of are: : 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, ... Because two is the base of the binary numeral system, powers of two are common in computer science. Written in binary, a power of two always has the form 100...000 or 0.00...001, just like a power of 10 in the decimal system. Computer science Two to the exponent of , written as , is the number of ways the bits in a binary word of length can be arranged. A word, interpreted as an unsigned integer, can represent values from 0 () to () inclusively. Corresponding signed integer values can be positive, negative and zero; see signed n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
65537
65537 is the integer after 65536 and before 65538. In mathematics 65537 is the largest known prime number of the form 2^ +1 (n = 4). Therefore, a regular polygon with 65537 sides is constructible with compass and unmarked straightedge. Johann Gustav Hermes gave the first explicit construction of this polygon. In number theory, primes of this form are known as Fermat primes, named after the mathematician Pierre de Fermat. The only known prime Fermat numbers are 2^ + 1 = 2^ + 1 = 3, 2^ + 1= 2^ +1 = 5, 2^ + 1 = 2^ +1 = 17, 2^ + 1= 2^ + 1= 257, 2^ + 1 = 2^ + 1 = 65537. In 1732, Leonhard Euler found that the next Fermat number is composite: 2^ + 1 = 2^ + 1 = 4294967297 = 641 \times 6700417 In 1880, showed that 2^ + 1 = 2^ + 1 = 274177 \times 67280421310721 65537 is also the 17th Jacobsthal–Lucas number, and currently the largest known integer ''n'' for which the number 10^ + 27 is a probable prime. Applications 65537 is commonly used as a public exponent in the RSA cr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Word (data Type)
In computing, a word is the natural unit of data used by a particular processor design. A word is a fixed-sized datum handled as a unit by the instruction set or the hardware of the processor. The number of bits or digits in a word (the ''word size'', ''word width'', or ''word length'') is an important characteristic of any specific processor design or computer architecture. The size of a word is reflected in many aspects of a computer's structure and operation; the majority of the registers in a processor are usually word-sized and the largest datum that can be transferred to and from the working memory in a single operation is a word in many (not all) architectures. The largest possible address size, used to designate a location in memory, is typically a hardware word (here, "hardware word" means the full-sized natural word of the processor, as opposed to any other definition used). Documentation for older computers with fixed word size commonly states memory sizes in words ra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Microsoft Excel
Microsoft Excel is a spreadsheet developed by Microsoft for Microsoft Windows, Windows, macOS, Android (operating system), Android and iOS. It features calculation or computation capabilities, graphing tools, pivot tables, and a macro (computer science), macro programming language called Visual Basic for Applications (VBA). Excel forms part of the Microsoft Office suite of software. Features Basic operation Microsoft Excel has the basic features of all spreadsheets, using a grid of ''cells'' arranged in numbered ''rows'' and letter-named ''columns'' to organize data manipulations like arithmetic operations. It has a battery of supplied functions to answer statistical, engineering, and financial needs. In addition, it can display data as line graphs, histograms and charts, and with a very limited three-dimensional graphical display. It allows sectioning of data to view its dependencies on various factors for different perspectives (using ''pivot tables'' and the ''sce ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
X86 Architecture
x86 (also known as 80x86 or the 8086 family) is a family of complex instruction set computer (CISC) instruction set architectures initially developed by Intel based on the Intel 8086 microprocessor and its 8088 variant. The 8086 was introduced in 1978 as a fully 16-bit extension of Intel's 8-bit 8080 microprocessor, with memory segmentation as a solution for addressing more memory than can be covered by a plain 16-bit address. The term "x86" came into being because the names of several successors to Intel's 8086 processor end in "86", including the 80186, 80286, 80386 and 80486 processors. The term is not synonymous with IBM PC compatibility, as this implies a multitude of other computer hardware. Embedded systems and general-purpose computers used x86 chips before the PC-compatible market started, some of them before the IBM PC (1981) debut. , most desktop and laptop computers sold are based on the x86 architecture family, while mobile categories such as smartphones o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computing Platform
A computing platform or digital platform is an environment in which a piece of software is executed. It may be the hardware or the operating system (OS), even a web browser and associated application programming interfaces, or other underlying software, as long as the program code is executed with it. Computing platforms have different abstraction levels, including a computer architecture, an OS, or runtime libraries. A computing platform is the stage on which computer programs can run. A platform can be seen both as a constraint on the software development process, in that different platforms provide different functionality and restrictions; and as an assistant to the development process, in that they provide low-level functionality ready-made. For example, an OS may be a platform that abstracts the underlying differences in hardware and provides a generic command for saving files or accessing the network. Components Platforms may also include: * Hardware alone, in the cas ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kibibyte
The byte is a unit of digital information that most commonly consists of eight bits. Historically, the byte was the number of bits used to encode a single character of text in a computer and for this reason it is the smallest addressable unit of memory in many computer architectures. To disambiguate arbitrarily sized bytes from the common 8-bit definition, network protocol documents such as The Internet Protocol () refer to an 8-bit byte as an octet. Those bits in an octet are usually counted with numbering from 0 to 7 or 7 to 0 depending on the bit endianness. The first bit is number 0, making the eighth bit number 7. The size of the byte has historically been hardware-dependent and no definitive standards existed that mandated the size. Sizes from 1 to 48 bits have been used. The six-bit character code was an often-used implementation in early encoding systems, and computers using six-bit and nine-bit bytes were common in the 1960s. These systems often had memory words ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
