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  2. Quine–McCluskey algorithm - Wikipedia

    en.wikipedia.org/wiki/Quine–McCluskey_algorithm

    The Quine–McCluskey algorithm (QMC), also known as the method of prime implicants, is a method used for minimization of Boolean functions that was developed by Willard V. Quine in 1952 [1] [2] and extended by Edward J. McCluskey in 1956. [3]

  3. Binary decision diagram - Wikipedia

    en.wikipedia.org/wiki/Binary_decision_diagram

    To find the value of the Boolean function for a given assignment of (Boolean) values to the variables, we start at the reference edge, which points to the BDD's root, and follow the path that is defined by the given variable values (following a low edge if the variable that labels a node equals FALSE, and following the high edge if the variable ...

  4. Karnaugh map - Wikipedia

    en.wikipedia.org/wiki/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 it in 1953 [ 1 ] [ 2 ] as a refinement of Edward W. Veitch 's 1952 Veitch chart , [ 3 ] [ 4 ] which itself was a rediscovery of Allan Marquand 's 1881 logical diagram [ 5 ] [ 6 ] (aka.

  5. Boolean function - Wikipedia

    en.wikipedia.org/wiki/Boolean_function

    In mathematics, a Boolean function is a function whose arguments and result assume values from a two-element set (usually {true, false}, {0,1} or {-1,1}). [ 1 ] [ 2 ] Alternative names are switching function , used especially in older computer science literature, [ 3 ] [ 4 ] and truth function (or logical function) , used in logic .

  6. Boolean algebra - Wikipedia

    en.wikipedia.org/wiki/Boolean_algebra

    A law of Boolean algebra is an identity such as x ∨ (y ∨ z) = (x ∨ y) ∨ z between two Boolean terms, where a Boolean term is defined as an expression built up from variables and the constants 0 and 1 using the operations ∧, ∨, and ¬. The concept can be extended to terms involving other Boolean operations such as ⊕, →, and ≡ ...

  7. Boolean algebra (structure) - Wikipedia

    en.wikipedia.org/wiki/Boolean_algebra_(structure)

    The term "Boolean algebra" honors George Boole (1815–1864), a self-educated English mathematician. He introduced the algebraic system initially in a small pamphlet, The Mathematical Analysis of Logic, published in 1847 in response to an ongoing public controversy between Augustus De Morgan and William Hamilton, and later as a more substantial book, The Laws of Thought, published in 1854.

  8. Boole's expansion theorem - Wikipedia

    en.wikipedia.org/wiki/Boole's_expansion_theorem

    Boole's expansion theorem, often referred to as the Shannon expansion or decomposition, is the identity: = + ′ ′, where is any Boolean function, is a variable, ′ is the complement of , and and ′ are with the argument set equal to and to respectively.

  9. Boolean circuit - Wikipedia

    en.wikipedia.org/wiki/Boolean_circuit

    [1]: 8 The edges must also have some ordering, to distinguish between different arguments to the same Boolean function. [1]: 9 As a special case, a propositional formula or Boolean expression is a Boolean circuit with a single output node in which every other node has fan-out of 1. Thus, a Boolean circuit can be regarded as a generalization ...

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