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Like NAND gates, NOR gates are so-called "universal gates" that can be combined to form any other kind of logic gate. For example, the first embedded system, Apollo Guidance Computer, was built exclusively from NOR gates, about 5,600 in total for the later versions. Today, contrary to popular belief, integrated circuits 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 of complex gates (standard cells) or transistors (full custom approach).
NAND gates are one of the two basic logic gates (along with NOR gates) from which any other logic gates can be built. Due to this property, NAND and NOR gates are sometimes called "universal gates". However, contrary to popular belief, modern integrated circuits 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 of complex gates (standard cells) or transistors (full custom approach).
The NAND gate is a digital logic gate that behaves in a manner that corresponds to the truth table to the left. A LOW output results only if both the inputs to the gate are HIGH. If one or both inputs are LOW, a HIGH output results.The nand gate is a universal gate in the sense that any boolean function can be implemented by nand gates.
Digital systems employing certain logic circuits take advantage of NAND's functional completeness. In complicated logical expressions, normally written in terms of other logic functions such as AND, OR, and NOT, writing these in terms of NAND saves on cost, because implementing such circuits using NAND gate yields a more compact result than the alternatives.
NAND gates can also be made with more than two inputs, yielding an output of LOW if all of the inputs are HIGH, and an output of HIGH if any of the inputs is LOW. These kinds of gates therefore operate as n-ary operators instead of a simple binary operator. Algebraically, these can be expressed as the function NAND(a, b, ..., n), which is logically equivalent to NOT(a AND b AND ... AND n).
The NOR 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 output (0) results. NOR is the result of the negation of the OR operator. NOR is a functionally complete operation -- combinations of NOR gates can be combined to generate any other logical function. By contrast, the OR operator is monotonic as it can only change LOW to HIGH but not vice versa.
In most, but not all, circuit implementations, the negation comes for free -- including CMOS and TTL. In such logic families, the only way to implement OR is with 2 or more gates, such as a NOR followed by an inverter. A significant exception is some forms of the domino logic family.
The XOR gate (sometimes EOR gate) is a digital logic gate that implements exclusive disjunction - it behaves according to the truth table above. A HIGH output (1) results if one, and only one, of the inputs to the gate is HIGH (1). If both inputs are LOW (0) or both are HIGH (1), a LOW output (0) results.
XOR gate is short for exclusive OR. This means that precisely one input must be 1 (true) for the output to be 1 (true). A way to remember XOR is "one or the other but not both."
This function is addition modulo 2. As a result, XOR gates are used to implement binary addition in computers. A half adder consists of an XOR gate and an AND gate. <br clear="all">
The AND gate is a digital logic gate that implements logical conjunction - it behaves according to the truth table to the right. A HIGH output (1) results only if both the inputs to the AND gate are HIGH (1). If neither or only one input to the AND gate is HIGH, a LOW output results.
The XNOR gate (sometimes spelled 'exnor') is a digital logic gate whose function is the inverse of the exclusive OR (XOR) gate. The two-input version implements logical equality, behaving according to the truth table to the right. A HIGH output (1) results if both of the inputs to the gate are the same. If one but not both inputs are HIGH (1), a LOW output (0) results.
The OR gate is a digital logic gate that implements logical disjunction - it behaves according to the truth table to the right. A HIGH output (1) results if one or both the inputs to the gate are HIGH (1). If neither input is HIGH, a LOW output (0) results.
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