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De Morgan's laws represented with Venn diagrams.In each case, the resultant set is the set of all points in any shade of blue. In propositional logic and Boolean algebra, De Morgan's laws, [1] [2] [3] also known as De Morgan's theorem, [4] are a pair of transformation rules that are both valid rules of inference.
An XNOR gate is made by considering the disjunctive normal form + ¯ ¯, noting from de Morgan's law that a NAND gate is an inverted-input OR gate. This construction entails a propagation delay three times that of a single NAND gate and uses five gates.
By use of De Morgan's laws, an AND function is identical to an OR function with negated inputs and outputs. Likewise, an OR function is identical to an AND function with negated inputs and outputs. 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.
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.
Integrated injection logic (IIL, I 2 L, or I2L) is a class of digital circuits built with multiple collector bipolar junction transistors (BJT). [1] When introduced it had speed comparable to TTL yet was almost as low power as CMOS, making it ideal for use in VLSI (and larger) integrated circuits. The gates can be made smaller with this logic ...
See also: Diode logic § Active-high AND logic gate Open-collector buffers connected as wired AND.. The wired AND connection is a form of AND gate.When using open collector or similar outputs (which can be identified by the ⎐ symbol in schematics), wired AND only requires a pull up resistor on the shared output wire.
An XOR gate is made by considering the conjunctive normal form (+) (¯ + ¯), noting from de Morgan's Law that a NOR gate is an inverted-input OR gate. This construction entails a propagation delay three times that of a single NOR gate and uses five gates.
The principle of inclusion–exclusion, combined with De Morgan's law, can be used to count the cardinality of the intersection of sets as well. Let A k ¯ {\displaystyle {\overline {A_{k}}}} represent the complement of A k with respect to some universal set A such that A k ⊆ A {\displaystyle A_{k}\subseteq A} for each k .