NOR gate The NOR (NOT OR) gate is a digital logic gate that implements logical NOR - it behaves according to the truth table to the right. A HIGH output (1) results if both the inputs to the gate are LOW (0); if one or both input is HIGH (1), a LOW o ...

or a NOT OR gate is a logic gate which gives a positive output only when both inputs are negative. Like NAND gates, NOR gates are so-called " universal gates" that can be combined to form any other kind of

logic gate A logic gate is a device that performs a Boolean function, a logical operation performed on one or more binary inputs that produces a single binary output. Depending on the context, the term may refer to an ideal logic gate, one that has, for ...

. For example, the first

embedded system An embedded system is a specialized computer system—a combination of a computer processor, computer memory, and input/output peripheral devices—that has a dedicated function within a larger mechanical or electronic system. It is e ...

, the

Apollo Guidance Computer The Apollo Guidance Computer (AGC) was a digital computer produced for the Apollo program that was installed on board each Apollo command module (CM) and Apollo Lunar Module (LM). The AGC provided computation and electronic interfaces for guidanc ...

, was built exclusively from NOR gates, about 5,600 in total for the later versions. Today,

integrated circuit An integrated circuit (IC), also known as a microchip or simply chip, is a set of electronic circuits, consisting of various electronic components (such as transistors, resistors, and capacitors) and their interconnections. These components a ...

s are not constructed exclusively from a single type of gate. Instead, EDA tools are used to convert the description of a logical circuit to a

netlist In electronic design, a netlist is a description of the connectivity of an electronic circuit. In its simplest form, a netlist consists of a list of the electronic components in a circuit and a list of the nodes they are connected to. A netwo ...

of complex gates ( standard cells) or transistors ( full custom approach).

NOR

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

Making other gates by using NOR gates

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

NOT

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.

OR

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.

AND

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.

NAND

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.

XNOR

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. Alternatively, an XNOR gate is made by considering the

conjunctive normal form In Boolean algebra, a formula is in conjunctive normal form (CNF) or clausal normal form if it is a conjunction of one or more clauses, where a clause is a disjunction of literals; otherwise put, it is a product of sums or an AND of ORs. In au ...

(A + \overline) \cdot (\overline + B)

, noting from

de Morgan's Law In propositional logic and Boolean algebra, De Morgan's laws, also known as De Morgan's theorem, are a pair of transformation rules that are both valid rules of inference. They are named after Augustus De Morgan, a 19th-century British mathemat ...

that a NOR gate is an inverted-input AND gate. This construction uses five gates instead of four.

XOR

An XOR gate is made by considering the

(A + B) \cdot ( \overline A + \overline B )

, noting from

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. 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.

References

{{DEFAULTSORT:Nor Logic Logic gates

NOR

Making other gates by using NOR gates

NOT

OR

AND

NAND

XNOR

XOR

See also

References