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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.
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).
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.
Corner quotes, also called “Quine quotes”; for quasi-quotation, i.e. quoting specific context of unspecified (“variable”) expressions; [3] also used for denoting Gödel number; [4] for example “⌜G⌝” denotes the Gödel number of G. (Typographical note: although the quotes appears as a “pair” in unicode (231C and 231D), they ...
In Boolean logic, logical NOR, [1] non-disjunction, or joint denial [1] is a truth-functional operator which produces a result that is the negation of logical or.That is, a sentence of the form (p NOR q) is true precisely when neither p nor q is true—i.e. when both p and q are false.
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 ...
As an example, consider the static logic implementation of a CMOS NAND gate: This circuit implements the logic function = ¯ If A and B are both high, the output will be pulled low. If either A or B are low, the output will be pulled high. At all times, the output is pulled either low or high.
Schematic of basic two-input DTL NAND gate. R3, R4 and V− shift the positive output voltage of the input DL stage below the ground (to cut off the transistor at low input voltage). Diode–transistor logic ( DTL ) is a class of digital circuits that is the direct ancestor of transistor–transistor logic .
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