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Boolean functions play a basic role in questions of complexity theory as well as the design of processors for digital computers, where they are implemented in electronic circuits using logic gates. The properties of Boolean functions are critical in cryptography, particularly in the design of symmetric key algorithms (see substitution box).
Despite the name, digital electronics designs include important analog design considerations. Digital electronic circuits are usually made from large assemblies of logic gates, often packaged in integrated circuits. Complex devices may have simple electronic representations of Boolean logic functions. [1]
A logic gate is a device that performs a Boolean function, a logical operation performed on one or more binary inputs that produces a single binary output. Depending on the context, the term may refer to an ideal logic gate , one that has, for instance, zero rise time and unlimited fan-out , or it may refer to a non-ideal physical device [ 1 ...
Boolean circuits provide a model for many digital components used in computer engineering, including multiplexers, adders, and arithmetic logic units, but they exclude sequential logic. They are an abstraction that omits many aspects relevant to designing real digital logic circuits, such as metastability , fanout , glitches , power consumption ...
Example Boolean circuit. The nodes are AND gates, the nodes are OR gates, and the nodes are NOT gates. In theoretical computer science, circuit complexity is a branch of computational complexity theory in which Boolean functions are classified according to the size or depth of the Boolean circuits that compute them.
5 Notes. 6 References. ... This process is a part of a logic synthesis applied in digital electronics and ... The Boolean function carried out by the circuit is ...
In automata theory, combinational logic (also referred to as time-independent logic [1]) is a type of digital logic that is implemented by Boolean circuits, where the output is a pure function of the present input only.
In Boolean logic, the majority function (also called the median operator) is the Boolean function that evaluates to false when half or more arguments are false and true otherwise, i.e. the value of the function equals the value of the majority of the inputs.