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. It can also in some senses be seen as the inverse of an AND gate. NOR is a functionally complete operation—NOR gates can be combined to generate any other logical function. It shares this property with the NAND gate. 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, OR is the more complicated operation; it may use a NOR followed by a NOT. A significant exception is some forms of the domino logic family.
There are three symbols for NOR gates: the American (ANSI or 'military') symbol and the IEC ('European' or 'rectangular') symbol, as well as the deprecated DIN symbol. For more information see Logic Gate Symbols. The ANSI symbol for the NOR gate is a standard OR gate with an inversion bubble connected.
The bubble indicates that the function of the or gate has been inverted.
NOR Gates are basic logic gates, and as such they are recognised in TTL and CMOS ICs. The standard, 4000 series, CMOS IC is the 4001, which includes four independent, two-input, NOR gates. The pinout diagram is as follows:
These devices are available from most semiconductor manufacturers such as Fairchild Semiconductor, Philips or Texas Instruments. These are usually available in both through-hole DIP and SOIC format. Datasheets are readily available in most datasheet databases.
In the popular CMOS and TTL logic families, NOR gates with up to 8 inputs are available:
CMOS
4001: Quad 2-input NOR gate
4025: Triple 3-input NOR gate
4002: Dual 4-input NOR gate
4078: Single 8-input NOR gate
TTL
7402: Quad 2-input NOR gate
7427: Triple 3-input NOR gate
7425: Dual 4-input NOR gate (with strobe, obsolete)
74260: Dual 5-Input NOR Gate
744078: Single 8-input NOR Gate
In the older RTL and ECL families, NOR gates were efficient and most commonly used.
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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. A NAND gate is made using transistors and junction diodes. By De Morgan's laws, a two-input NAND gate's logic may be expressed as =+, making a NAND gate equivalent to inverters followed by an OR gate.
In logic, a functionally complete set of logical connectives or Boolean operators is one which can be used to express all possible truth tables by combining members of the set into a Boolean expression. A well-known complete set of connectives is { AND, NOT }. Each of the singleton sets { NAND } and { NOR } is functionally complete. However, the set { AND, OR } is incomplete, due to its inability to express NOT. A gate or set of gates which is functionally complete can also be called a universal gate / gates.
In mathematics and mathematical logic, Boolean algebra is a branch of algebra. It differs from elementary algebra in two ways. First, the values of the variables are the truth values true and false, usually denoted 1 and 0, whereas in elementary algebra the values of the variables are numbers. Second, Boolean algebra uses logical operators such as conjunction (and) denoted as ∧, disjunction (or) denoted as ∨, and the negation (not) denoted as ¬.
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