NOR logic

{{main|NOR gate}}

A NOR gate is logically an inverted OR gate. It has the following truth table:

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A NOR gate is a universal gate, meaning that any other gate can be represented as a combination of NOR gates.

{{see also|NOT gate}}

This is made by joining the inputs of a NOR gate. As a NOR gate is equivalent to an OR gate leading to NOT gate, joining the inputs makes the output of the "OR" part of the NOR gate the same as the input, eliminating it from consideration and leaving only the NOT part.

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{{see also|OR gate}}

An OR gate is made by inverting the output of a NOR gate. Note that we already know that a NOT gate is equivalent to a NOR gate with its inputs joined.

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{{see also|AND gate}}

An AND gate gives a 1 output when both inputs are 1. Therefore, an AND gate is made by inverting the inputs of a NOR gate. Again, note that a NOR gate is equivalent to a NOT with its inputs joined.

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{{see also|NAND gate}}

A NAND gate is made by inverting the output of an AND gate. The word NAND means that it is not AND. As the name suggests, it will give 0 when both the inputs are 1.

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{{see also|XNOR gate}}

An XNOR gate is made by connecting four NOR gates as shown below. This construction entails a propagation delay three times that of a single NOR gate.

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Alternatively, an XNOR gate is made by considering the conjunctive normal form $(A\; +\; \backslash overline\{B\})\; \backslash cdot\; (\backslash overline\{A\}\; +\; B)$, noting from de Morgan's Law that a NOR gate is an inverted-input AND gate. This construction uses five gates instead of four.

{{see also|XOR gate}}

An XOR gate is made by considering the conjunctive normal form $(A\; +\; B)\; \backslash cdot\; (\; \backslash overline\; A\; +\; \backslash overline\; B\; )$, 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.

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Alternatively, the 4-gate version of the XNOR gate can be used with an inverter. This construction has a propagation delay four times (instead of three times) that of a single NOR gate.

• NAND logic — Like NOR gates, NAND gates are also universal gates.
• Functional completeness

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Category:Logic gates