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A Boolean function with multiple outputs, : {,} {,} with > is a vectorial or vector-valued Boolean function (an S-box in symmetric cryptography). [ 6 ] There are 2 2 k {\displaystyle 2^{2^{k}}} different Boolean functions with k {\displaystyle k} arguments; equal to the number of different truth tables with 2 k {\displaystyle 2^{k}} entries.
The free distributive lattices of monotonic Boolean functions on up to three variables The Boolean functions are represented by their Hasse diagrams. (Which are dual to Venn diagrams, as can be seen here.) A Boolean function is monotonic, when in it's Hasse Diagram there is no 1 (red vertex) connected to a higher 0 (white vertex). To avoid ...
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 ...
If V is a set of n Boolean variables, an antichain A of subsets of V defines a monotone Boolean function f, where the value of f is true for a given set of inputs if some subset of the true inputs to f belongs to A and false otherwise. Conversely every monotone Boolean function defines in this way an antichain, of the minimal subsets of Boolean ...
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 ≡ ...
A Boolean-valued function (sometimes called a predicate or a proposition) is a function of the type f : X → B, where X is an arbitrary set and where B is a Boolean domain, i.e. a generic two-element set, (for example B = {0, 1}), whose elements are interpreted as logical values, for example, 0 = false and 1 = true, i.e., a single bit of information.
Boolean algebra operations are known as "bitwise operations" in computer science. Boolean functions are also well-studied theoretically and easily implementable, either with computer programs or by so-named logic gates in digital electronics. This contributes to the use of bits to represent different data, even those originally not binary.
In computer science, the Boolean (sometimes shortened to Bool) is a data type that has one of two possible values (usually denoted true and false) which is intended to represent the two truth values of logic and Boolean algebra.