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Negative Bases
A negative base (or negative radix) may be used to construct a non-standard positional numeral system. Like other place-value systems, each position holds multiples of the appropriate power of the system's base; but that base is negative—that is to say, the base is equal to for some natural number (). Negative-base systems can accommodate all the same numbers as standard place-value systems, but both positive and negative numbers are represented without the use of a minus sign (or, in computer representation, a sign bit); this advantage is countered by an increased complexity of arithmetic operations. The need to store the information normally contained by a negative sign often results in a negative-base number being one digit longer than its positive-base equivalent. The common names for negative-base positional numeral systems are formed by prefix (linguistics), prefixing ''nega-'' to the name of the corresponding positive-base system; for example, negadecimal (base −10) ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Radix
In a positional numeral system, the radix or base is the number of unique digits, including the digit zero, used to represent numbers. For example, for the decimal/denary system (the most common system in use today) the radix (base number) is ten, because it uses the ten digits from 0 through 9. In any standard positional numeral system, a number is conventionally written as with ''x'' as the string of digits and ''y'' as its base, although for base ten the subscript is usually assumed (and omitted, together with the pair of parentheses), as it is the most common way to express value. For example, (the decimal system is implied in the latter) and represents the number one hundred, while (100)2 (in the binary system with base 2) represents the number four. Etymology ''Radix'' is a Latin word for "root". ''Root'' can be considered a synonym for ''base,'' in the arithmetical sense. In numeral systems In the system with radix 13, for example, a string of digits such as 398 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Institute Of Mathematics Of The Polish Academy Of Sciences
The Institute of Mathematics of the Polish Academy of Sciences is a research institute of the Polish Academy of Sciences.Instytut Matematyczny official web page Polish Academy of Sciences About the Institute The institute is located at 8 Śniadeckich Street in . It was established on November 20, 1948 as the National Mathematical Institute and in the same year the Mathematical Devices Group (Pol: ''Grupę Aparatów Matematycznych'') was established there, and this can be considered the beginning of computer science in Poland.The educa ...[...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Adder (electronics)
An adder, or summer, is a digital circuit that performs addition of numbers. In many computers and other kinds of microprocessor, processors adders are used in the arithmetic logic units (ALUs). They are also used in other parts of the processor, where they are used to calculate address space, addresses, database index, table indices, increment and decrement operators and similar operations. Although adders can be constructed for many number representations, such as binary-coded decimal or excess-3, the most common adders operate on binary numbers. In cases where two's complement or ones' complement is being used to represent negative numbers, it is trivial to modify an adder into an adder–subtractor. Other signed number representations require more logic around the basic adder. Binary adders Half adder The half adder adds two single binary digits ''A'' and ''B''. It has two outputs, sum (''S'') and carry (''C''). The carry signal represents an Integer overflow, overflow int ... [...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 binary 1s 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'' or ''right-most bit'', due to the convention in positional notation of writing less significant digits further to the right. 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 order. Rather, it is a property of the numeri ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Richard Schroeppel
Richard C. Schroeppel (born 1948) is an American mathematician born in Illinois. His research has included magic squares, elliptic curves, and cryptography. In 1964, Schroeppel won first place in the United States among over 225,000 high school students in the Annual High School Mathematics Examination, a contest sponsored by the Mathematical Association of America and the Society of Actuaries. In both 1966 and 1967, Schroeppel scored among the top 5 in the U.S. in the William Lowell Putnam Mathematical Competition. In 1973 he discovered that there are 275,305,224 normal magic squares of order 5. In 1998–1999 he designed the Hasty Pudding Cipher, which was a candidate for the Advanced Encryption Standard, and he is one of the designers of the SANDstorm hash, a submission to the NIST SHA-3 competition. Among other contributions, Schroeppel was the first to recognize the sub-exponential running time of certain integer factoring algorithms. While not entirely rigorous, his proof ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bitstring
A bit array (also known as bitmask, bit map, bit set, bit string, or bit vector) is an array data structure that compactly stores bits. It can be used to implement a simple set data structure. A bit array is effective at exploiting bit-level parallelism in hardware to perform operations quickly. A typical bit array stores ''kw'' bits, where ''w'' is the number of bits in the unit of storage, such as a byte or word, and ''k'' is some nonnegative integer. If ''w'' does not divide the number of bits to be stored, some space is wasted due to internal fragmentation. Definition A bit array is a mapping from some domain (almost always a range of integers) to values in the set . The values can be interpreted as dark/light, absent/present, locked/unlocked, valid/invalid, et cetera. The point is that there are only two possible values, so they can be stored in one bit. As with other arrays, the access to a single bit can be managed by applying an index to the array. Assuming its size (or ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Python (programming Language)
Python is a high-level, general-purpose programming language. Its design philosophy emphasizes code readability with the use of significant indentation. Python is dynamically-typed and garbage-collected. It supports multiple programming paradigms, including structured (particularly procedural), object-oriented and functional programming. It is often described as a "batteries included" language due to its comprehensive standard library. Guido van Rossum began working on Python in the late 1980s as a successor to the ABC programming language and first released it in 1991 as Python 0.9.0. Python 2.0 was released in 2000 and introduced new features such as list comprehensions, cycle-detecting garbage collection, reference counting, and Unicode support. Python 3.0, released in 2008, was a major revision that is not completely backward-compatible with earlier versions. Python 2 was discontinued with version 2.7.18 in 2020. Python consistently ranks as ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Visual Basic , an Active Scripting language
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Visual Basic is a name for a family of programming languages from Microsoft. It may refer to: * Visual Basic .NET (now simply referred to as "Visual Basic"), the current version of Visual Basic launched in 2002 which runs on .NET * Visual Basic (classic), the original Visual Basic supported from 1991–2008 * Embedded Visual Basic, the classic version geared toward embedded applications * Visual Basic for Applications, an implementation of Visual Basic 6 built into programs such as Microsoft Office and used for writing macros * VBScript VBScript (''"Microsoft Visual Basic Scripting Edition"'') is an Active Scripting language developed by Microsoft that is modeled on Visual Basic. It allows Microsoft Windows system administrators to generate powerful tools for managing computers ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Programming Languages
A programming language is a system of notation for writing computer programs. Most programming languages are text-based formal languages, but they may also be graphical. They are a kind of computer language. The description of a programming language is usually split into the two components of syntax (form) and semantics (meaning), which are usually defined by a formal language. Some languages are defined by a specification document (for example, the C programming language is specified by an ISO Standard) while other languages (such as Perl) have a dominant implementation that is treated as a reference. Some languages have both, with the basic language defined by a standard and extensions taken from the dominant implementation being common. Programming language theory is the subfield of computer science that studies the design, implementation, analysis, characterization, and classification of programming languages. Definitions There are many considerations when defining w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Odd Number
In mathematics, parity is the property of an integer of whether it is even or odd. An integer is even if it is a multiple of two, and odd if it is not.. For example, −4, 0, 82 are even because \begin -2 \cdot 2 &= -4 \\ 0 \cdot 2 &= 0 \\ 41 \cdot 2 &= 82 \end By contrast, −3, 5, 7, 21 are odd numbers. The above definition of parity applies only to integer numbers, hence it cannot be applied to numbers like 1/2 or 4.201. See the section "Higher mathematics" below for some extensions of the notion of parity to a larger class of "numbers" or in other more general settings. Even and odd numbers have opposite parities, e.g., 22 (even number) and 13 (odd number) have opposite parities. In particular, the parity of zero is even. Any two consecutive integers have opposite parity. A number (i.e., integer) expressed in the decimal numeral system is even or odd according to whether its last digit is even or odd. That is, if the last digit is 1, 3, 5, 7, or 9, then it is odd; otherwis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Even Number
In mathematics, parity is the property of an integer of whether it is even or odd. An integer is even if it is a multiple of two, and odd if it is not.. For example, −4, 0, 82 are even because \begin -2 \cdot 2 &= -4 \\ 0 \cdot 2 &= 0 \\ 41 \cdot 2 &= 82 \end By contrast, −3, 5, 7, 21 are odd numbers. The above definition of parity applies only to integer numbers, hence it cannot be applied to numbers like 1/2 or 4.201. See the section "Higher mathematics" below for some extensions of the notion of parity to a larger class of "numbers" or in other more general settings. Even and odd numbers have opposite parities, e.g., 22 (even number) and 13 (odd number) have opposite parities. In particular, the parity of zero is even. Any two consecutive integers have opposite parity. A number (i.e., integer) expressed in the decimal numeral system is even or odd according to whether its last digit is even or odd. That is, if the last digit is 1, 3, 5, 7, or 9, then it is odd; otherw ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Balanced Ternary
Balanced ternary is a ternary numeral system (i.e. base 3 with three digits) that uses a balanced signed-digit representation of the integers in which the digits have the values −1, 0, and 1. This stands in contrast to the standard (unbalanced) ternary system, in which digits have values 0, 1 and 2. The balanced ternary system can represent all integers without using a separate minus sign; the value of the leading non-zero digit of a number has the sign of the number itself. The balanced ternary system is an example of a non-standard positional numeral system. It was used in some early computers and also in some solutions of balance puzzles. Different sources use different glyphs used to represent the three digits in balanced ternary. In this article, T (which resembles a ligature of the minus sign and 1) represents −1, while 0 and 1 represent themselves. Other conventions include using '−' and '+' to represent −1 and 1 respectively, or using Greek letter theta (Θ), ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
