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In logic, a set of symbols is commonly used to express logical representation. The following table lists many common symbols, together with their name, how they should be read out loud, and the related field of mathematics.
It is also called the complement gate [2] because it produces the ones' complement of a binary number, swapping 0s and 1s. The NOT gate is one of three basic logic gates from which any Boolean circuit may be built up. Together with the AND gate and the OR gate, any function in binary mathematics may be implemented.
An input-consuming logic gate L is reversible if it meets the following conditions: (1) L(x) = y is a gate where for any output y, there is a unique input x; (2) The gate L is reversible if there is a gate L´(y) = x which maps y to x, for all y. An example of a reversible logic gate is a NOT, which can be described from its truth table below:
A logic circuit diagram for a 4-bit carry lookahead binary adder design using only the AND, OR, and XOR logic gates. 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.
The classical analog of the CNOT gate is a reversible XOR gate. How the CNOT gate can be used (with Hadamard gates) in a computation.. In computer science, the controlled NOT gate (also C-NOT or CNOT), controlled-X gate, controlled-bit-flip gate, Feynman gate or controlled Pauli-X is a quantum logic gate that is an essential component in the construction of a gate-based quantum computer.
The Cirac–Zoller controlled-NOT gate is an implementation of the controlled-NOT (CNOT) quantum logic gate using cold trapped ions that was proposed by Ignacio Cirac and Peter Zoller in 1995 and represents the central ingredient of the Cirac–Zoller proposal for a trapped-ion quantum computer. [1]
In logic, negation, also called the logical not or logical complement, is an operation that takes a proposition to another proposition "not ", written , , ′ [1] or ¯. [ citation needed ] It is interpreted intuitively as being true when P {\displaystyle P} is false, and false when P {\displaystyle P} is true.
The stroke is named after Henry Maurice Sheffer, who in 1913 published a paper in the Transactions of the American Mathematical Society [10] providing an axiomatization of Boolean algebras using the stroke, and proved its equivalence to a standard formulation thereof by Huntington employing the familiar operators of propositional logic (AND, OR, NOT).