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A CMOS transistor NAND element. V dd denotes positive voltage.. In CMOS logic, if both of the A and B inputs are high, then both the NMOS transistors (bottom half of the diagram) will conduct, neither of the PMOS transistors (top half) will conduct, and a conductive path will be established between the output and Vss (ground), bringing the output low.
In digital electronics, a NAND gate (NOT-AND) is a logic gate which produces an output which is false only if all its inputs are true; thus its output is complement to that of an AND gate. A LOW (0) output results only if all the inputs to the gate are HIGH (1); if any input is LOW (0), a HIGH (1) output results.
Logic gates can be made from quantum mechanical effects, see quantum logic gate. Photonic logic gates use nonlinear optical effects. In principle any method that leads to a gate that is functionally complete (for example, either a NOR or a NAND gate) can be used to make any kind of digital logic circuit. Note that the use of 3-state logic for ...
For example, the size complexity of a Boolean circuit is the number of gates in the circuit. There is a natural connection between circuit size complexity and time complexity . [ 2 ] : 355 Intuitively, a language with small time complexity (that is, requires relatively few sequential operations on a Turing machine ), also has a small circuit ...
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).
[1] [2] A well-known complete set of connectives is { AND, NOT}. Each of the singleton sets { NAND} and { NOR} is functionally complete. However, the set { AND, OR} is incomplete, due to its inability to express NOT. A gate (or set of gates) that is functionally complete can also be called a universal gate (or a universal set of gates).
The logical effort of a two-input NAND gate is calculated to be g = 4/3 because a NAND gate with input capacitance 4 can drive the same current as the inverter can, with input capacitance 3. Similarly, the logical effort of a two-input NOR gate can be found to be g = 5/3. Due to the lower logical effort, NAND gates are typically preferred to ...
The few systems that calculate the majority function on an even number of inputs are often biased towards "0" – they produce "0" when exactly half the inputs are 0 – for example, a 4-input majority gate has a 0 output only when two or more 0's appear at its inputs. [1] In a few systems, the tie can be broken randomly. [2]
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