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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.
Together with the AND gate and the OR gate, any function in binary mathematics may be implemented. All other logic gates may be made from these three. [3] The terms "programmable inverter" or "controlled inverter" do not refer to this gate; instead, these terms refer to the XOR gate because it can conditionally function like a NOT gate. [1] [3]
A NOT gate, for example, can be constructed from a Toffoli gate by setting the three input bits to {a, 1, 1}, making the third output bit (1 XOR (a AND 1)) = NOT a; (a AND b) is the third output bit from {a, b, 0}. Essentially, this means that one can use Toffoli gates to build systems that will perform any desired Boolean function computation ...
While the Implication gate isn't functionally complete by itself, it is in conjunction with the constant 0 source. This can be shown via the following: := = =. Thus as the implication gate with the addition of the constant 0 source can create both the NOT gate and the OR gate, it can create the NOR gate, which is a universal gate.
A NAND gate is equivalent to an OR gate with negated inputs, and a NOR gate is equivalent to an AND gate with negated inputs. This leads to an alternative set of symbols for basic gates that use the opposite core symbol (AND or OR) but with the inputs and outputs negated. Use of these alternative symbols can make logic circuit diagrams much ...
Huntington borrowed the symbol from Gottfried Wilhelm Leibniz in 1890 (the original date is not definitely known, but almost certainly it is written after 1685; and 1890 is the publishing time). [15] While both Huntington in 1904 and Leibniz in 1890 used the symbol as an algebraic operation.
A single NOR gate. A NOR gate or a NOT OR gate is a logic gate which gives a positive output only when both inputs are negative.. Like NAND gates, NOR gates are so-called "universal gates" that can be combined to form any other kind of logic gate.
Because the logical or means a disjunction formula is true when either one or both of its parts are true, it is referred to as an inclusive disjunction. This is in contrast with an exclusive disjunction, which is true when one or the other of the arguments are true, but not both (referred to as exclusive or, or XOR).