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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.
The NAND gate has the property of functional completeness, which it shares with the NOR gate. That is, any other logic function (AND, OR, etc.) can be implemented using only NAND gates. [2] An entire processor can be created using NAND gates alone. In TTL ICs using multiple-emitter transistors, it also requires fewer transistors than a NOR gate.
Unlike a regular NAND symbol, which suggests AND logic, the De Morgan version, a two negative-input OR gate, correctly shows that OR is of interest. The regular NAND symbol has a bubble at the output and none at the inputs (the opposite of the states that will turn the motor on), but the De Morgan symbol shows both inputs and output in the ...
(the symbol may also indicate the domain and codomain of a function; see table of mathematical symbols). ⊃ {\displaystyle \supset } may mean the same as ⇒ {\displaystyle \Rightarrow } (the symbol may also mean superset ).
Note that an electronic circuit or a software function can be optimized by reuse, to reduce the number of gates. For instance, the "A ∧ B" operation, when expressed by ↑ gates, is implemented with the reuse of "A ↑ B", X ≡ (A ↑ B); A ∧ B ≡ X ↑ X
OR-AND-invert gates or OAI-gates are logic gates comprising OR gates followed by a NAND gate. They can be efficiently implemented in logic families like CMOS and TTL . They are dual to AND-OR-invert gates.
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.
Unfortunately, there are reversible functions that cannot be computed using just those gates. For example, AND cannot be achieved by those gates. In other words, the set consisting of NOT and XOR gates is not universal. To compute an arbitrary function using reversible gates, the Toffoli gate, proposed in 1980 by Toffoli, can indeed achieve the ...