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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.
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.
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 ...
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 .
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.
Due to the functional completeness property of the NAND and NOR gates, a full adder can also be implemented using nine NAND gates, [4] or nine NOR gates. Using only two types of gates is convenient if the circuit is being implemented using simple integrated circuit chips which contain only one gate type per chip.
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]
An XNOR gate circuit can be made from four NOR gates. In fact, both NAND and NOR gates are so-called "universal gates" and any logical function can be constructed from either NAND logic or NOR logic alone. If the four NOR gates are replaced by NAND gates, this results in an XOR gate, which can be converted to an XNOR gate by inverting the ...