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Sometimes only the circle portion of the symbol is used, and it is attached to the input or output of another gate; the symbols for NAND and NOR are formed in this way. [3] A bar or overline ( ‾ ) above a variable can denote negation (or inversion or complement) performed by a NOT gate. [4] A slash (/) before the variable is also used. [3]
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.
Within an expression containing two or more of the same associative connectives in a row, the order of the operations does not matter as long as the sequence of the operands is not changed. Commutativity The operands of the connective may be swapped, preserving logical equivalence to the original expression. Distributivity
See also: Diode logic § Active-high OR logic gate. The wired OR connection electrically performs the Boolean logic operation of an OR gate using open emitter or similar inputs (which can be identified by the ⎏ symbol in schematics) connected to a shared output with a pull-down resistor. This gate can also be easily extended with more inputs.
Diagram showing a way of making a logical inverter (NOT gate) from a NAND gate. Date: 22 December 2008: Source: Own work: Author: Inductiveload: Permission (Reusing this file) Own work, all rights released (Public domain)
The model assumes one line or node in the digital circuit is stuck at logic high or logic low. When a line is stuck, it is called a fault. Digital circuits can be divided into: Gate level or combinational circuits which contain no storage (latches and/or flip flops) but only gates like NAND, OR, XOR, etc. Sequential circuits which contain storage.
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 .