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Maxterm
In Boolean algebra, any Boolean function can be expressed in the canonical disjunctive normal form ( CDNF), minterm canonical form, or Sum of Products (SoP or SOP) as a disjunction (OR) of minterms. The De Morgan dual is the canonical conjunctive normal form ( CCNF), maxterm canonical form, or Product of Sums (PoS or POS) which is a conjunction (AND) of maxterms. These forms can be useful for the simplification of Boolean functions, which is of great importance in the optimization of Boolean formulas in general and digital circuits in particular. Other canonical forms include the complete sum of prime implicants or Blake canonical form (and its dual), and the algebraic normal form (also called Zhegalkin or Reed–Muller). Minterms For a boolean function of n variables , a minterm is a product term in which each of the n variables appears ''exactly once'' (either in its complemented or uncomplemented form). Thus, a ''minterm'' is a logical expression of ''n'' variables that em ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Karnaugh Map
A Karnaugh map (KM or K-map) is a diagram that can be used to simplify a Boolean algebra expression. Maurice Karnaugh introduced the technique in 1953 as a refinement of Edward W. Veitch's 1952 Veitch chart, which itself was a rediscovery of Allan Marquand's 1881 ''logical diagram'' or Marquand diagram. They are also known as Marquand–Veitch diagrams, Karnaugh–Veitch (KV) maps, and (rarely) Svoboda charts. An early advance in the history of formal logic methodology, Karnaugh maps remain relevant in the digital age, especially in the fields of logical circuit design and digital engineering. Definition A Karnaugh map reduces the need for extensive calculations by taking advantage of humans' pattern-recognition capability. It also permits the rapid identification and elimination of potential race conditions. The required Boolean results are transferred from a truth table onto a two-dimensional grid where, in Karnaugh maps, the cells are ordered in Gray code, and each cell ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Boolean Function
In mathematics, a Boolean function is a function whose arguments and result assume values from a two-element set (usually , or ). Alternative names are switching function, used especially in older computer science literature, and truth function (or logical function), used in logic. Boolean functions are the subject of Boolean algebra and switching theory. A Boolean function takes the form f:\^k \to \, where \ is known as the Boolean domain and k is a non-negative integer called the arity of the function. In the case where k=0, the function is a constant element of \. A Boolean function with multiple outputs, f:\^k \to \^m with m>1 is a vectorial or ''vector-valued'' Boolean function (an S-box in symmetric cryptography). There are 2^ different Boolean functions with k arguments; equal to the number of different truth tables with 2^k entries. Every k-ary Boolean function can be expressed as a propositional formula in k variables x_1,...,x_k, and two propositional formulas a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Boolean Algebra (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] |
De Morgan's Law
In propositional logic and Boolean algebra, De Morgan's laws, also known as De Morgan's theorem, are a pair of transformation rules that are both valid rules of inference. They are named after Augustus De Morgan, a 19th-century British mathematician. The rules allow the expression of conjunctions and disjunctions purely in terms of each other via negation. The rules can be expressed in English as: * The negation of "A and B" is the same as "not A or not B". * The negation of "A or B" is the same as "not A and not B". or * The complement of the union of two sets is the same as the intersection of their complements * The complement of the intersection of two sets is the same as the union of their complements or * not (A or B) = (not A) and (not B) * not (A and B) = (not A) or (not B) where "A or B" is an " inclusive or" meaning ''at least'' one of A or B rather than an "exclusive or" that means ''exactly'' one of A or B. Another form of De Morgan's law is the following as see ... [...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] |
Boolean Algebra
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] |
List Of Boolean Algebra Topics
This is a list of topics around Boolean algebra and propositional logic. Articles with a wide scope and introductions * Algebra of sets * Boolean algebra (structure) * Boolean algebra * Field of sets * Logical connective * Propositional calculus Boolean functions and connectives * Ampheck * Analysis of Boolean functions * Balanced Boolean function * Bent function * Boolean algebras canonically defined * Boolean function * Boolean matrix * Boolean-valued function * Conditioned disjunction * Evasive Boolean function * Exclusive or * Functional completeness * Logical biconditional * Logical conjunction * Logical disjunction * Logical equality * Logical implication * Logical negation * Logical NOR * Lupanov representation * Majority function * Material conditional * Minimal axioms for Boolean algebra * Peirce arrow * Read-once function * Sheffer stroke * Sole sufficient operator ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Apollo Guidance Computer
The Apollo Guidance Computer (AGC) was a digital computer produced for the Apollo program that was installed on board each Apollo command module (CM) and Apollo Lunar Module (LM). The AGC provided computation and electronic interfaces for guidance, navigation, and control of the spacecraft. The AGC was among the first computers based on silicon integrated circuits (ICs). The computer's performance was comparable to the first generation of home computers from the late 1970s, such as the Apple II, TRS-80, and Commodore PET. At around 2 cubic feet in size, AGC held 4,100 IC packages. The AGC has a 16-bit Word (computer architecture), word length, with 15 data bits and one [ arity bit. Most of the software on the AGC is stored in a special read-only memory known as core rope memory, fashioned by weaving wires through and around magnetic cores, though a small amount of read/write core memory is available. Astronauts communicated with the AGC using a numeric display and keyboard call ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
