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Bitwise
In computer programming, a bitwise operation operates on a bit string, a bit array or a binary numeral (considered as a bit string) at the level of its individual bits. It is a fast and simple action, basic to the higher-level arithmetic operations and directly supported by the processor. Most bitwise operations are presented as two-operand instructions where the result replaces one of the input operands. On simple low-cost processors, typically, bitwise operations are substantially faster than division, several times faster than multiplication, and sometimes significantly faster than addition. While modern processors usually perform addition and multiplication just as fast as bitwise operations due to their longer instruction pipelines and other architectural design choices, bitwise operations do commonly use less power because of the reduced use of resources. Bitwise operators In the explanations below, any indication of a bit's position is counted from the right (least sig ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bit Complement
In computer programming, a bitwise operation operates on a bit string, a bit array or a binary numeral (considered as a bit string) at the level of its individual bits. It is a fast and simple action, basic to the higher-level arithmetic operations and directly supported by the processor. Most bitwise operations are presented as two-operand instructions where the result replaces one of the input operands. On simple low-cost processors, typically, bitwise operations are substantially faster than division, several times faster than multiplication, and sometimes significantly faster than addition. While modern processors usually perform addition and multiplication just as fast as bitwise operations due to their longer instruction pipelines and other architectural design choices, bitwise operations do commonly use less power because of the reduced use of resources. Bitwise operators In the explanations below, any indication of a bit's position is counted from the right (least signif ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bit Array
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 (computer architecture), 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 Fragmentation (computing), 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bit String
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 ( ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Two's Complement
Two's complement is the most common method of representing signed (positive, negative, and zero) integers on computers, and more generally, fixed point binary values. Two's complement uses the binary digit with the ''greatest'' value as the ''sign'' to indicate whether the binary number is positive or negative; when the most significant bit is ''1'' the number is signed as negative and when the most significant bit is ''0'' the number is signed as positive. As a result, non-negative numbers are represented as themselves: 6 is 0110, zero is 0000, and −6 is 1010 (the result of applying the bitwise NOT operator to 6 and adding 1). However, while the number of binary bits is fixed throughout a computation it is otherwise arbitrary. Unlike the ones' complement scheme, the two's complement scheme has only one representation for zero. Furthermore, arithmetic implementations can be used on signed as well as unsigned integers and differ only in the integer overflow situations. Proce ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Exclusive Disjunction
Exclusive or, exclusive disjunction, exclusive alternation, logical non-equivalence, or Logical_equality#Inequality, logical inequality is a Logical connective, logical operator whose negation is the logical biconditional. With two inputs, XOR is true if and only if the inputs differ (one is true, one is false). With multiple inputs, XOR is true if and only if the number of true inputs is Parity (mathematics), odd. It gains the name "exclusive or" because the meaning of "or" is ambiguous when both operands are true. XOR ''excludes'' that case. Some informal ways of describing XOR are "one or the other but not both", "either one or the other", and "A or B, but not A and B". It is Table of logic symbols, symbolized by the prefix operator J Translated as and by the infix operators XOR (, , or ), EOR, EXOR, \dot, \overline, \underline, ⩛, \oplus, \nleftrightarrow, and \not\equiv. Definition The truth table of A\nleftrightarrow B shows that it outputs true whenever the inpu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
GF(2)
(also denoted \mathbb F_2, or \mathbb Z/2\mathbb Z) is the finite field with two elements. is the Field (mathematics), field with the smallest possible number of elements, and is unique if the additive identity and the multiplicative identity are denoted respectively and , as usual. The elements of may be identified with the two possible values of a bit and to the Boolean domain, Boolean values ''true'' and ''false''. It follows that is fundamental and ubiquitous in computer science and its mathematical logic, logical foundations. Definition GF(2) is the unique field with two elements with its additive identity, additive and multiplicative identity, multiplicative identities respectively denoted and . Its addition is defined as the usual addition of integers but modulo 2 and corresponds to the table below: If the elements of GF(2) are seen as Boolean values, then the addition is the same as that of the logical XOR operation. Since each element equals its opposite (m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Logical Disjunction
In logic, disjunction (also known as logical disjunction, logical or, logical addition, or inclusive disjunction) is a logical connective typically notated as \lor and read aloud as "or". For instance, the English language sentence "it is sunny or it is warm" can be represented in logic using the disjunctive formula S \lor W , assuming that S abbreviates "it is sunny" and W abbreviates "it is warm". In classical logic, disjunction is given a truth functional semantics according to which a formula \phi \lor \psi is true unless both \phi and \psi are false. Because this semantics allows a disjunctive formula to be true when both of its disjuncts are true, it is an ''inclusive'' interpretation of disjunction, in contrast with exclusive disjunction. Classical proof theoretical treatments are often given in terms of rules such as disjunction introduction and disjunction elimination. Disjunction has also been given numerous non-classical treatments, motivated by problems ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Logical AND
In logic, mathematics and linguistics, ''and'' (\wedge) is the truth-functional operator of conjunction or logical conjunction. The logical connective of this operator is typically represented as \wedge or \& or K (prefix) or \times or \cdot in which \wedge is the most modern and widely used. The ''and'' of a set of operands is true if and only if ''all'' of its operands are true, i.e., A \land B is true if and only if A is true and B is true. An operand of a conjunction is a conjunct. Beyond logic, the term "conjunction" also refers to similar concepts in other fields: * In natural language, the denotation of expressions such as English " and"; * In programming languages, the short-circuit and control structure; * In set theory, intersection. * In lattice theory, logical conjunction ( greatest lower bound). Notation And is usually denoted by an infix operator: in mathematics and logic, it is denoted by a "wedge" \wedge (Unicode ), \& or \times; in electronics, \cdot ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Flag Word
A bit field is a data structure that maps to one or more adjacent bits which have been allocated for specific purposes, so that any single bit or group of bits within the structure can be set or inspected. A bit field is most commonly used to represent Primitive data type, integral types of known, fixed bit-width, such as single-bit Boolean data type, Booleans. The meaning of the individual bits within the field is determined by the programmer; for example, the first bit in a bit field (located at the field's base address) is sometimes used to determine the state of a particular attribute associated with the bit field. Within CPUs and other logic devices, collections of bit fields called flags are commonly used to control or to indicate the outcome of particular operations. Processors have a status register that is composed of flags. For example, if the result of an addition cannot be represented in the destination an arithmetic overflow is set. The flags can be used to decide subs ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Assembly Language
In computing, assembly language (alternatively assembler language or symbolic machine code), often referred to simply as assembly and commonly abbreviated as ASM or asm, is any low-level programming language with a very strong correspondence between the instructions in the language and the architecture's machine code instructions. Assembly language usually has one statement per machine instruction (1:1), but constants, comments, assembler directives, symbolic labels of, e.g., memory locations, registers, and macros are generally also supported. The first assembly code in which a language is used to represent machine code instructions is found in Kathleen and Andrew Donald Booth's 1947 work, ''Coding for A.R.C.''. Assembly code is converted into executable machine code by a utility program referred to as an '' assembler''. The term "assembler" is generally attributed to Wilkes, Wheeler and Gill in their 1951 book '' The Preparation of Programs for an Electronic Dig ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
