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Four-valued Logic
In logic, a four-valued logic is any logic with four truth values. Several types of four-valued logic have been advanced. Belnap Nuel Belnap considered the challenge of question answering by computer in 1975. Noting human fallibility, he was concerned with the case where two contradictory facts were loaded into memory, and then a query was made. "We all know about the fecundity of contradictions in two-valued logic: contradictions are never isolated, infecting as they do the whole system." Belnap proposed a four-valued logic as a means of containing contradiction. He called the table of values A4: Its possible values are ''true'', ''false'', ''both'' (true and false), and ''neither'' (true nor false). Belnap's logic is designed to cope with multiple information sources such that if only true is found then ''true'' is assigned, if only false is found then ''false'' is assigned, if some sources say true and others say false then ''both'' is assigned, and if no information is given ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Logic
Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the study of deductively valid inferences or logical truths. It examines how conclusions follow from premises based on the structure of arguments alone, independent of their topic and content. Informal logic is associated with informal fallacies, critical thinking, and argumentation theory. Informal logic examines arguments expressed in natural language whereas formal logic uses formal language. When used as a countable noun, the term "a logic" refers to a specific logical formal system that articulates a proof system. Logic plays a central role in many fields, such as philosophy, mathematics, computer science, and linguistics. Logic studies arguments, which consist of a set of premises that leads to a conclusion. An example is the argument from the premises "it's Sunday" and "if it's Sunday then I don't have to work" leading to the conclusion "I don't have to wor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bit (computing)
The bit is the most basic unit of information in computing and digital communication. The name is a portmanteau of binary digit. The bit represents a logical state with one of two possible values. These values are most commonly represented as either , but other representations such as ''true''/''false'', ''yes''/''no'', ''on''/''off'', or ''+''/''−'' are also widely used. The relation between these values and the physical states of the underlying storage or device is a matter of convention, and different assignments may be used even within the same device or program. It may be physically implemented with a two-state device. A contiguous group of binary digits is commonly called a '' bit string'', a bit vector, or a single-dimensional (or multi-dimensional) ''bit array''. A group of eight bits is called one ''byte'', but historically the size of the byte is not strictly defined. Frequently, half, full, double and quadruple words consist of a number of bytes which is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
IEEE 1164
The IEEE 1164 standard (''Multivalue Logic System for VHDL Model Interoperability'') is a technical standard published by the IEEE in 1993. It describes the definitions of logic values to be used in electronic design automation, for the VHDL hardware description language. It was sponsored by the Design Automation Standards Committee of the Institute of Electrical and Electronics Engineers (IEEE). The standardization effort was based on the donation of the Synopsys MVL-9 type declaration. The primary data type (standard unresolved logic) consists of nine character literals (see table on the right). This system promoted a useful set of logic values that typical CMOS logic designs could implement in the vast majority of modeling situations, including: * 'Z' literal to make tri-state buffer logic easy * 'H' and 'L' weak drives to permit wired-AND and wired-OR logic. * 'U' for default value for all object declarations so that during simulations uninitialized values are easily d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Don't-care Term
In digital logic, a don't-care term (abbreviated DC, historically also known as ''redundancies'', ''irrelevancies'', ''optional entries'', ''invalid combinations'', ''vacuous combinations'', ''forbidden combinations'', ''unused states'' or ''logical remainders'') for a function is an input-sequence (a series of bits) for which the function output does not matter. An input that is known never to occur is a can't-happen term. Both these types of conditions are treated the same way in logic design and may be referred to collectively as ''don't-care conditions'' for brevity. The designer of a logic circuit to implement the function need not care about such inputs, but can choose the circuit's output arbitrarily, usually such that the simplest, smallest, fastest or cheapest circuit results ( minimization) or the power-consumption is minimized. Don't-care terms are important to consider in minimizing logic circuit design, including graphical methods like Karnaugh–Veitch maps and a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
High Impedance
In electronics, high impedance means that a point in a circuit (a node) allows a relatively small amount of current through, per unit of applied voltage at that point. High impedance circuits are low current and potentially high voltage, whereas low impedance circuits are the opposite (low voltage and potentially high current). Numerical definitions of "high impedance" vary by application. High impedance inputs are preferred on measuring instruments such as voltmeters or oscilloscopes. In audio systems, a high-impedance input may be required for use with devices such as crystal microphones or other devices with high internal impedance. Analog electronics In analog circuits a high impedance node is one that does not have any low impedance paths to any other nodes ''in the frequency range being considered''. Since the terms low and high depend on context to some extent, it is possible in principle for some high impedance nodes to be described as low impedance in one context, and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Boolean Logic
In mathematics and mathematical logic, Boolean algebra is a branch of algebra. It differs from elementary algebra in two ways. First, the values of the variable (mathematics), variables are the truth values ''true'' and ''false'', usually denoted by 1 and 0, whereas in elementary algebra the values of the variables are numbers. Second, Boolean algebra uses logical operators such as Logical conjunction, conjunction (''and'') denoted as , disjunction (''or'') denoted as , and negation (''not'') denoted as . Elementary algebra, on the other hand, uses arithmetic operators such as addition, multiplication, subtraction, and division. Boolean algebra is therefore a formal way of describing logical operations in the same way that elementary algebra describes numerical operations. Boolean algebra was introduced by George Boole in his first book ''The Mathematical Analysis of Logic'' (1847), and set forth more fully in his ''An Investigation of the Laws of Thought'' (1854). According to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
IEEE 1364
Verilog, standardized as IEEE 1364, is a hardware description language (HDL) used to model electronic systems. It is most commonly used in the design and verification of digital circuits, with the highest level of abstraction being at the register-transfer level. It is also used in the verification of analog circuits and mixed-signal circuits, as well as in the design of genetic circuits. In 2009, the Verilog standard (IEEE 1364-2005) was merged into the SystemVerilog standard, creating IEEE Standard 1800-2009. Since then, Verilog has been officially part of the SystemVerilog language. The current version is IEEE standard 1800-2023. Overview Hardware description languages such as Verilog are similar to software programming languages because they include ways of describing the propagation time and signal strengths (sensitivity). There are two types of assignment operators; a blocking assignment (=), and a non-blocking (>>. A generate–endgenerate construct (similar to VHDL' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Identity Matrix
In linear algebra, the identity matrix of size n is the n\times n square matrix with ones on the main diagonal and zeros elsewhere. It has unique properties, for example when the identity matrix represents a geometric transformation, the object remains unchanged by the transformation. In other contexts, it is analogous to multiplying by the number 1. Terminology and notation The identity matrix is often denoted by I_n, or simply by I if the size is immaterial or can be trivially determined by the context. I_1 = \begin 1 \end ,\ I_2 = \begin 1 & 0 \\ 0 & 1 \end ,\ I_3 = \begin 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end ,\ \dots ,\ I_n = \begin 1 & 0 & 0 & \cdots & 0 \\ 0 & 1 & 0 & \cdots & 0 \\ 0 & 0 & 1 & \cdots & 0 \\ \vdots & \vdots & \vdots & \ddots & \vdots \\ 0 & 0 & 0 & \cdots & 1 \end. The term unit matrix has also been widely used, but the term ''identity matrix'' is now standard. The term ''unit matrix'' is ambiguous, because it is also used for a matrix of on ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Matrix Multiplication
In mathematics, specifically in linear algebra, matrix multiplication is a binary operation that produces a matrix (mathematics), matrix from two matrices. For matrix multiplication, the number of columns in the first matrix must be equal to the number of rows in the second matrix. The resulting matrix, known as the matrix product, has the number of rows of the first and the number of columns of the second matrix. The product of matrices and is denoted as . Matrix multiplication was first described by the French mathematician Jacques Philippe Marie Binet in 1812, to represent the composition of functions, composition of linear maps that are represented by matrices. Matrix multiplication is thus a basic tool of linear algebra, and as such has numerous applications in many areas of mathematics, as well as in applied mathematics, statistics, physics, economics, and engineering. Computing matrix products is a central operation in all computational applications of linear algebra. Not ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Transition System
In theoretical computer science, a transition system is a concept used in the study of computation. It is used to describe the potential behavior of discrete systems. It consists of states and transitions between states, which may be labeled with labels chosen from a set; the same label may appear on more than one transition. If the label set is a singleton, the system is essentially unlabeled, and a simpler definition that omits the labels is possible. Transition systems coincide mathematically with abstract rewriting systems (as explained further in this article) and directed graphs. They differ from finite-state automata in several ways: * The set of states is not necessarily finite, or even countable. * The set of transitions is not necessarily finite, or even countable. * No "start" state or "final" states are given. Transition systems can be represented as directed graphs. Formal definition Formally, a transition system is a pair (S, T) where S is a set of states ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Logical Matrices
A logical matrix, binary matrix, relation matrix, Boolean matrix, or (0, 1)-matrix is a matrix with entries from the Boolean domain Such a matrix can be used to represent a binary relation between a pair of finite sets. It is an important tool in combinatorial mathematics and theoretical computer science. Matrix representation of a relation If ''R'' is a binary relation between the finite indexed sets ''X'' and ''Y'' (so ), then ''R'' can be represented by the logical matrix ''M'' whose row and column indices index the elements of ''X'' and ''Y'', respectively, such that the entries of ''M'' are defined by :m_ = \begin 1 & (x_i, y_j) \in R, \\ 0 & (x_i, y_j) \not\in R. \end In order to designate the row and column numbers of the matrix, the sets ''X'' and ''Y'' are indexed with positive integers: ''i'' ranges from 1 to the cardinality (size) of ''X'', and ''j'' ranges from 1 to the cardinality of ''Y''. See the article on indexed sets for more detail. The transpose R ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
State (computer Science)
In information technology and computer science, a system is described as stateful if it is designed to remember preceding events or user interactions; the remembered information is called the state of the system. The set of states a system can occupy is known as its state space. In a discrete system, the state space is countable and often finite. The system's internal behaviour or interaction with its environment consists of separately occurring individual actions or events, such as accepting input or producing output, that may or may not cause the system to change its state. Examples of such systems are digital logic circuits and components, automata and formal language, computer programs, and computers. The output of a digital circuit or deterministic computer program at any time is completely determined by its current inputs and its state. Digital logic circuit state Digital logic circuits can be divided into two types: combinational logic, whose output signals a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
