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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.
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.
definition: is defined as metalanguage:= means "from now on, is defined to be another name for ." This is a statement in the metalanguage, not the object language. The notation may occasionally be seen in physics, meaning the same as :=.
A truth-functional approach to logical operators is implemented as logic gates in digital circuits. Practically all digital circuits (the major exception is DRAM) are built up from NAND, NOR, NOT, and transmission gates; see more details in Truth function in computer science.
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.
The logical NAND is an operation on two logical values, typically the values of two propositions, that produces a value of false if both of its operands are true. In other words, it produces a value of true if at least one of its operands is false. The truth table for p NAND q (also written as p ↑ q, Dpq, or p | q) is as follows:
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.
Wherever logic is applied, especially in mathematical discussions, it has the same meaning as above: it is an abbreviation for if and only if, indicating that one statement is both necessary and sufficient for the other. This is an example of mathematical jargon (although, as noted above, if is more often used than iff in statements of definition).