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NOR Gate
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 be seen as an AND gate
AND gate
with all the inputs inverted. 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
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. The original Apollo Guidance Computer
Apollo Guidance Computer
used 4,100 ICs, each one containing only a single 3-input NOR gate. CONTENTS * 1 Symbols * 2 Hardware description and pinout * 2.1 Availability * 3 Implementations * 3.1 Alternatives * 4 See also * 5 References * 6 External links SYMBOLSThere 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
DIN
symbol
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Logical NOR
In boolean logic , LOGICAL NOR or JOINT DENIAL is a truth-functional operator which produces a result that is the negation of logical or . That is, a sentence of the form (p NOR q) is true precisely when neither p nor q is true—i.e. when both of p and q are false. In grammar , NOR is a coordinating conjunction . The NOR operator is also known as PEIRCE\'S ARROW—Charles Sanders Peirce introduced the symbol ↓ for it, and demonstrated that the logical NOR is completely expressible: by combining uses of the logical NOR it is possible to express any logical operation on two variables. Thus, as with its dual , the NAND operator (a.k.a. the Sheffer stroke
Sheffer stroke
—symbolized as either or /), NOR can be used by itself, without any other logical operator, to constitute a logical formal system (making NOR functionally complete ). It is also known as QUINE \'S DAGGER (his symbol was †), the AMPHECK (from Greek αμφηκης, "cutting both ways") by Peirce, or NEITHER-NOR. One way of expressing p NOR q is p q {displaystyle {overline {plor q}}} , where the symbol {displaystyle lor } signifies OR and the bar signifies the negation of the expression under it: in essence, simply ( p q ) {displaystyle neg (plor q)} . Other ways of expressing p NOR q are Xpq, and p + q {displaystyle {overline {p+q}}}
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Nor (other)
NOR may refer to: * Nor, a grammatical conjunction * Nór , the eponymous founder-king of Norway
Norway
in Norse mythology * Nor (Wicked) , a character in the novel Wicked * nor- , a chemical prefix for "stripped-down" molecules lacking groups (such as methyl-groups); for example, noradrenaline * Norma (constellation)
Norma (constellation)
, standard astronomical abbreviationNøR may refer to: *
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5th Millennium
"4400" redirects here. For the science fiction TV series, see The 4400 . The FIFTH MILLENNIUM of the Gregorian calendar
Gregorian calendar
will begin on January 1, 4001, and end on December 31, 5000. It will be the fifth millennium in the Anno Domini
Anno Domini
or Common Era
Common Era
. CONTENTS * 1 Astronomical events * 2 Fictional events * 2.1 Music * 3 References ASTRONOMICAL EVENTS This section NEEDS ADDITIONAL CITATIONS FOR VERIFICATION . Please help improve this article by adding citations to reliable sources . Unsourced material may be challenged and removed. (October 2008) (Learn how and when to remove this template message ) * 4285 (August 6): Venus
Venus
occults Regulus
Regulus
. * 4296 (November 22): Venus
Venus
occults Antares . * 4385: Comet Hale–Bopp
Comet Hale–Bopp
is expected to return to the inner Solar System
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Logic Gate
In electronics , a LOGIC GATE is an idealized or physical device implementing a Boolean function ; that is, it performs a logical operation on one or more binary inputs and produces a single binary output. Depending on the context, the term may refer to an IDEAL LOGIC GATE, one that has for instance zero rise time and unlimited fan-out , or it may refer to a non-ideal physical device (see Ideal and real op-amps for comparison). Logic gates are primarily implemented using diodes or transistors acting as electronic switches , but can also be constructed using vacuum tubes , electromagnetic relays (relay logic ), fluidic logic , pneumatic logic , optics , molecules , or even mechanical elements. With amplification, logic gates can be cascaded in the same way that Boolean functions can be composed, allowing the construction of a physical model of all of Boolean logic , and therefore, all of the algorithms and mathematics that can be described with Boolean logic. Logic circuits include such devices as multiplexers , registers , arithmetic logic units (ALUs), and computer memory , all the way up through complete microprocessors , which may contain more than 100 million gates. In modern practice, most gates are made from field-effect transistors (FETs), particularly metal–oxide–semiconductor field-effect transistors (MOSFETs)
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Negation
In logic , NEGATION, also called LOGICAL COMPLEMENT, is an operation that takes a proposition p to another proposition "not p", written ¬p, which is interpreted intuitively as being true when p is false, and false when p is true. Negation is thus a unary (single-argument) logical connective . It may be applied as an operation on propositions , truth values , or semantic values more generally. In classical logic , negation is normally identified with the truth function that takes truth to falsity and vice versa. In intuitionistic logic , according to the Brouwer–Heyting–Kolmogorov interpretation , the negation of a proposition p is the proposition whose proofs are the refutations of p. CONTENTS * 1 Definition * 2 Notation * 3 Properties * 3.1 Double negation * 3.2 Distributivity * 3.3 Linearity * 3.4 Self dual * 4 Rules of inference * 5 Programming * 6 Kripke semantics * 7 See also * 8 References * 9 Further reading * 10 External links DEFINITIONNo agreement exists as to the possibility of defining negation, as to its logical status, function, and meaning, as to its field of applicability..., and as to the interpretation of the negative judgment, (F.H. Heinemann 1944). Classical negation is an operation on one logical value , typically the value of a proposition , that produces a value of true when its operand is false and a value of false when its operand is true
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OR Gate
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. In another sense, the function of OR effectively finds the maximum between two binary digits, just as the complementary AND function finds the minimum. CONTENTS * 1 Symbols * 2 Hardware description and pinout * 3 Implementations * 3.1 Alternatives * 4 Wired-OR * 5 See also * 6 References SYMBOLSThere are two symbols of OR gates: the American (ANSI or 'military') symbol and the IEC ('European' or 'rectangular') symbol, as well as the deprecated DIN
DIN
symbol. For more information see Logic Gate Symbols . MIL/ANSI Symbol IEC Symbol DIN
DIN
Symbol This schematic diagram shows the arrangement of four OR gates within a standard 4071 CMOS
CMOS
integrated circuit. HARDWARE DESCRIPTION AND PINOUTOR Gates are basic logic gates, and as such they are available in TTL and CMOS
CMOS
ICs logic families . The standard 4000 series CMOS
CMOS
IC is the 4071, which includes four independent two-input OR gates. The ancestral TTL device is the 7432
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Functionally Complete
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 }, consisting of binary conjunction and negation . Each of the singleton sets { NAND } and { NOR } is functionally complete. In a context of propositional logic , functionally complete sets of connectives are also called (EXPRESSIVELY) ADEQUATE. From the point of view of digital electronics , functional completeness means that every possible logic gate can be realized as a network of gates of the types prescribed by the set. In particular, all logic gates can be assembled from either only binary NAND gates , or only binary NOR gates . CONTENTS * 1 Introduction * 2 Formal definition * 3 Characterization of functional completeness * 4 Minimal functionally complete operator sets * 5 Examples * 6 In other domains * 7 Set theory * 8 See also * 9 References INTRODUCTIONModern texts on logic typically take as primitive some subset of the connectives: conjunction ( {displaystyle land } ); disjunction ( {displaystyle lor } ); negation ( {displaystyle neg } ); material conditional ( {displaystyle to } ); and possibly the biconditional ( {displaystyle leftrightarrow } )
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NAND Gate
In digital electronics , a NAND GATE (NEGATIVE-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 the AND gate
AND gate
. A LOW (0) output results only if both the inputs to the gate are HIGH (1); if one or both inputs are LOW (0), a HIGH (1) output results. It is made using transistors and junction diodes. By De Morgan\'s theorem , AB=A+B, and thus a N AND gate
AND gate
is equivalent to inverters followed by an OR gate
OR gate
. The N AND gate
AND gate
is significant because any boolean function can be implemented by using a combination of NAND gates. This property is called functional completeness . It shares this property with the NOR gate . Digital systems employing certain logic circuits take advantage of NAND's functional completeness. The function NAND(a1, a2, ..., an) is logically equivalent to NOT(a1 AND a2 AND ... AND an). CONTENTS * 1 Symbols * 2 Hardware description and pinout * 3 Implementations * 4 See also * 5 References * 6 External links SYMBOLSThere are three symbols for NAND gates: the MIL/ ANSI
ANSI
symbol, the IEC symbol and the deprecated DIN
DIN
symbol sometimes found on old schematics. For more information see logic gate symbols
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Logical Disjunction
In logic and mathematics , OR is the truth-functional operator of (INCLUSIVE) DISJUNCTION, also known as ALTERNATION; the _or_ of a set of operands is true if and only if _one or more_ of its operands is true. The logical connective that represents this operator is typically written as ∨ or +. "_A_ or _B_" is true if _A_ is true, or if _B_ is true, or if both _A_ and _B_ are true. In logic, _or_ by itself means the _inclusive_ _or_, distinguished from an exclusive or , which is false when both of its arguments are true, while an "or" is true in that case. An operand of a disjunction is called a DISJUNCT. Related concepts in other fields are: * In natural language , the coordinating conjunction "or". * In programming languages, the short-circuit or control structure . * In set theory , union . * In predicate logic , existential quantification .CONTENTS * 1 Notation * 2 Definition * 2.1 Truth table * 3 Properties * 4 Symbol * 5 Applications in computer science * 5.1 Bitwise operation * 5.2 Logical operation * 5.3 Constructive disjunction * 6 Union * 7 Natural language * 8 See also * 9 Notes * 10 References * 11 External links NOTATIONOR is usually expressed with an infix operator: in mathematics and logic, ∨; in electronics, +; and in most programming languages, , , or OR
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CMOS
COMPLEMENTARY METAL–OXIDE–SEMICONDUCTOR, abbreviated as CMOS /ˈsiːmɒs/ , is a technology for constructing integrated circuits . CMOS
CMOS
technology is used in microprocessors , microcontrollers , static RAM , and other digital logic circuits. CMOS
CMOS
technology is also used for several analog circuits such as image sensors ( CMOS sensor
CMOS sensor
), data converters , and highly integrated transceivers for many types of communication. In 1963, while working for Fairchild Semiconductor
Fairchild Semiconductor
, Frank Wanlass patented CMOS
CMOS
(US patent 3,356,858). CMOS
CMOS
is also sometimes referred to as COMPLEMENTARY-SYMMETRY METAL–OXIDE–SEMICONDUCTOR (or COS-MOS). The words "complementary-symmetry" refer to the fact that the typical design style with CMOS
CMOS
uses complementary and symmetrical pairs of p-type and n-type metal oxide semiconductor field effect transistors (MOSFETs) for logic functions. Two important characteristics of CMOS
CMOS
devices are high noise immunity and low static power consumption . Since one transistor of the pair is always off, the series combination draws significant power only momentarily during switching between on and off states
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Transistor–transistor Logic
TRANSISTOR–TRANSISTOR LOGIC (TTL) is a class of digital circuits built from bipolar junction transistors (BJTs) and resistors . It is called transistor–transistor logic because transistors perform both the logic function (e.g., AND ) and the amplifying function (compare with resistor–transistor logic (RTL) and diode–transistor logic (DTL)). TTL integrated circuits (ICs) were widely used in applications such as computers , industrial controls, test equipment and instrumentation, consumer electronics, and synthesizers . The designation TTL is sometimes used to mean TTL-compatible logic levels , even when not associated directly with TTL integrated circuits, for example as a label on the inputs and outputs of electronic instruments. After their introduction in integrated circuit form in 1963 by Sylvania , TTL integrated circuits were manufactured by several semiconductor companies. The 7400 series (also called 74xx) by Texas Instruments became particularly popular. TTL manufacturers offered a wide range of logic gate, flip-flops, counters, and other circuits. Several variations of the original TTL circuit design were developed. The variations offered interchangeable functions that had higher speed or lower power dissipation to allow design optimization. TTL devices were originally made in ceramic and plastic dual-in-line (DIP) packages, and flat-pack form. TTL chips are now also made in surface-mount packages
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Domino Logic
DOMINO LOGIC is a CMOS
CMOS
-based evolution of the dynamic logic techniques based on either PMOS or NMOS transistors . It allows a rail-to-rail logic swing. It was developed to speed up circuits. CONTENTS * 1 Terminology * 2 Dynamic logic drawbacks * 3 Logic features * 4 See also * 5 References * 6 External links TERMINOLOGYThe term derives from the fact that in domino logic (cascade structure consisting of several stages), each stage ripples the next stage for evaluation, similar to a Domino falling one after the other. DYNAMIC LOGIC DRAWBACKSIn dynamic logic , a problem arises when cascading one gate to the next. The precharge "1" state of the first gate may cause the second gate to discharge prematurely, before the first gate has reached its correct state. This uses up the "precharge" of the second gate, which cannot be restored until the next clock cycle, so there is no recovery from this error. In order to cascade dynamic logic gates, one solution is Domino Logic, which inserts an ordinary static inverter between stages. While this might seem to defeat the point of dynamic logic, since the inverter has a p FET
FET
(one of the main goals of Dynamic Logic is to avoid pFETs where possible, due to speed), there are two reasons it works well
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Apollo Guidance Computer
The APOLLO GUIDANCE COMPUTER (AGC) was a digital computer produced for the Apollo program
Apollo program
that was installed on board each Apollo Command Module (CM) and Lunar Module (LM). The AGC provided computation and electronic interfaces for guidance, navigation, and control of the spacecraft. The AGC had a 16-bit word length, with 15 data bits and one parity bit . Most of the software on the AGC was stored in a special read only memory known as core rope memory , fashioned by weaving wires through magnetic cores , though a small amount of read-write core memory was provided. Astronauts communicated with the AGC using a numeric display and keyboard called the DSKY (DiSplay"> The display and keyboard (DSKY) interface of the Apollo Guidance Computer
Apollo Guidance Computer
mounted on the control panel of the Command Module, with the Flight Director Attitude Indicator (FDAI) above. Partial list of numeric codes for verbs and nouns in the Apollo Guidance Computer. For a quick reference, they were printed on a side panel
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DIN
DEUTSCHES INSTITUT FüR NORMUNG E.V. (DIN; in English , the GERMAN INSTITUTE FOR STANDARDIZATION) is the German national organization for standardization and is the German ISO member body. DIN is a German Registered Association (e.V. ) headquartered in Berlin
Berlin
. There are currently around thirty thousand DIN Standards , covering nearly every field of technology. CONTENTS * 1 History * 2 DIN standard designation * 3 Examples of DIN standards * 4 See also * 5 External links HISTORYFounded in 1917 as the Normenausschuß der deutschen Industrie (NADI, "Standardisation Committee of German Industry"), the NADI was renamed Deutscher Normenausschuß (DNA, "German Standardisation Committee") in 1926 to reflect that the organization now dealt with standardization issues in many fields; viz., not just for industrial products. In 1975 it was renamed again to Deutsches Institut für Normung, or 'DIN' and is recognized by the German government as the official national-standards body, representing German interests at the international and European levels. The acronym , 'DIN' is often incorrectly expanded as Deutsche Industrienorm ("German Industry Standard"). This is largely due to the historic origin of the DIN as "NADI". The NADI indeed published their standards as DI-Norm (Deutsche Industrienorm). For example, the first published standard was 'DI-Norm 1' (about tapered pins ) in 1918
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Full Adder
An ADDER is a digital circuit that performs addition of numbers. In many computers and other kinds of processors adders are used in the arithmetic logic units or ALU. They are also utilized in other parts of the processor, where they are used to calculate addresses , table indices, increment and decrement operators , and similar operations. Although adders can be constructed for many number representations , such as binary-coded decimal or excess-3 , the most common adders operate on binary numbers . In cases where two\'s complement or ones\' complement is being used to represent negative numbers , it is trivial to modify an adder into an adder–subtractor . Other signed number representations require more logic around the basic adder. CONTENTS* 1 Binary adders * 1.1 Half adder * 1.2 Full adder * 1.3 Adders supporting multiple bits * 1.3.1 Ripple-carry adder * 1.3.2 Carry-lookahead adder * 1.3.3 Carry-save adders * 1.4 3:2 compressors * 2 References * 3 See also * 4 External links BINARY ADDERSHALF ADDER Half adder logic diagram Half adder in action The HALF ADDER adds two single binary digits A and B. It has two outputs, sum (S) and carry (C). The carry signal represents an overflow into the next digit of a multi-digit addition. The value of the sum in decimal system is 2C + S. The simplest half-adder design, pictured on the right, incorporates an XOR gate for S and an AND gate for C
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