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Product Term
In Boolean logic, a product term is a conjunction of literals, where each literal is either a variable or its negation. Examples Examples of product terms include: :A \wedge B :A \wedge (\neg B) \wedge (\neg C) :\neg A Origin The terminology comes from the similarity of AND to multiplication as in the ring structure of Boolean rings. Minterms For a 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 ( ... of n variables , a product term in which each of the n variables appears once (in either its complemented or uncomplemented form) is called a ''minterm''. Thus, a ''minterm'' is a logical expression of ''n'' variables that employs only the ''complement'' operator and the ''conjunction'' operator. References *Fredrick J. Hill, and Gerald R. Peterson, 1974, ''Introduction ... [...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 1 and 0, whereas in elementary algebra the values of the variables are numbers. Second, Boolean algebra uses Logical connective, logical operators such as Logical conjunction, conjunction (''and'') denoted as ∧, Logical disjunction, disjunction (''or'') denoted as ∨, and the negation (''not'') denoted as ¬. Elementary algebra, on the other hand, uses arithmetic operators such as addition, multiplication, subtraction and division. So Boolean algebra is 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 ''The Laws of Thought, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Boolean Ring
In mathematics, a Boolean ring ''R'' is a ring for which ''x''2 = ''x'' for all ''x'' in ''R'', that is, a ring that consists only of idempotent elements. An example is the ring of integers modulo 2. Every Boolean ring gives rise to a Boolean algebra, with ring multiplication corresponding to conjunction or meet ∧, and ring addition to exclusive disjunction or symmetric difference (not disjunction ∨, which would constitute a semiring). Conversely, every Boolean algebra gives rise to a Boolean ring. Boolean rings are named after the founder of Boolean algebra, George Boole. Notations There are at least four different and incompatible systems of notation for Boolean rings and algebras: *In commutative algebra the standard notation is to use ''x'' + ''y'' = (''x'' ∧ ¬ ''y'') ∨ (¬ ''x'' ∧ ''y'') for the ring sum of ''x'' and ''y'', and use ''xy'' = ''x'' ∧ ''y'' for their product. *In logic, a common notati ... [...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 are ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
