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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.
The NAND 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.
There are three symbols for NAND gates: the MIL/ANSI symbol, the IEC symbol and the deprecated DIN symbol sometimes found on old schematics. The ANSI symbol for the NAND gate is a standard AND gate with an inversion bubble connected.
MIL/ANSI Symbol
IEC Symbol
DIN Symbol
Logicedit
The function NAND(a1, a2, ..., an) is logically equivalent to NOT(a1 AND a2 AND ... AND an).
One way of expressing A NAND B is , where the symbol signifies AND and the bar signifies the negation of the expression under it: in essence, simply .
Hardware design and pinoutedit
Diagram of the NAND gates in a CMOS type 4011 integrated circuit
NAND gates are basic logic gates, and as such they are recognised in TTL and CMOSICs.
The standard, 4000 series, CMOSIC is the 4011, which includes four independent, two-input, NAND gates. These devices are available from many semiconductor manufacturers. These are usually available in both through-hole DIL and SOIC formats. Datasheets are readily available in most datasheet databases.
The standard two-, three-, four- and eight-input NAND gates are available:
The NAND gate has the property of functional completeness, which it shares with the NOR gate. That is, any other logic function (AND, OR, etc.) can be implemented using only NAND gates.[1] An entire processor can be created using NAND gates alone. In TTL ICs using multiple-emitter transistors, it also requires fewer transistors than a NOR gate.
As NOR gates are also functionally complete, if no specific NAND gates are available, one can be made from NOR gates using NOR logic.[1]
^ abMano, M. Morris and Charles R. Kime. Logic and Computer Design Fundamentals, Third Edition. Prentice Hall, 2004. p. 73.
External linksedit
Wikimedia Commons has media related to NAND gates.
TTL NAND and AND gates at All About Circuits
January 01, 1970
nand, gate, this, article, relies, largely, entirely, single, source, relevant, discussion, found, talk, page, please, help, improve, this, article, introducing, citations, additional, sources, find, sources, news, newspapers, books, scholar, jstor, july, 2023. This article relies largely or entirely on a single source Relevant discussion may be found on the talk page Please help improve this article by introducing citations to additional sources Find sources NAND gate news newspapers books scholar JSTOR July 2023 NAND gate truth table Input Output A B A NAND B 0 0 1 0 1 1 1 0 1 1 1 0 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 A B A B displaystyle overline A lor overline B overline A cdot B making a NAND gate equivalent to inverters followed by an OR gate The NAND 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 NAND gates with two or more inputs are available as integrated circuits in transistor transistor logic CMOS and other logic families Contents 1 Symbols 2 Logic 3 Hardware design and pinout 4 Functional completeness 5 See also 6 References 7 External linksSymbols editThere are three symbols for NAND gates the MIL ANSI symbol the IEC symbol and the deprecated DIN symbol sometimes found on old schematics The ANSI symbol for the NAND gate is a standard AND gate with an inversion bubble connected nbsp nbsp nbsp MIL ANSI Symbol IEC Symbol DIN SymbolLogic editThe function NAND a1 a2 an is logically equivalent to NOT a1 AND a2 AND AND an One way of expressing A NAND B is A B displaystyle overline A land B nbsp where the symbol displaystyle land nbsp signifies AND and the bar signifies the negation of the expression under it in essence simply A B displaystyle displaystyle lnot A land B nbsp Hardware design and pinout edit nbsp Diagram of the NAND gates in a CMOS type 4011 integrated circuit NAND gates are basic logic gates and as such they are recognised in TTL and CMOS ICs The standard 4000 series CMOS IC is the 4011 which includes four independent two input NAND gates These devices are available from many semiconductor manufacturers These are usually available in both through hole DIL and SOIC formats Datasheets are readily available in most datasheet databases The standard two three four and eight input NAND gates are available CMOS 4011 Quad two input NAND gate 4023 Triple three input NAND gate 4012 Dual four input NAND gate 4068 Mono eight input NAND gate TTL 7400 Quad two input NAND gate 7410 Triple three input NAND gate 7420 Dual four input NAND gate 7430 Mono eight input NAND gateFunctional completeness edit nbsp construction of a NAND gate from NOR gates Main articles NAND logic and NOR logic The NAND gate has the property of functional completeness which it shares with the NOR gate That is any other logic function AND OR etc can be implemented using only NAND gates 1 An entire processor can be created using NAND gates alone In TTL ICs using multiple emitter transistors it also requires fewer transistors than a NOR gate As NOR gates are also functionally complete if no specific NAND gates are available one can be made from NOR gates using NOR logic 1 See also editBoolean algebra Flash memory Logic gate symbols Sheffer strokeReferences edit a b Mano M Morris and Charles R Kime Logic and Computer Design Fundamentals Third Edition Prentice Hall 2004 p 73 External links edit nbsp Wikimedia Commons has media related to NAND gates TTL NAND and AND gates at All About Circuits Retrieved from https en wikipedia org w index php title NAND gate amp oldid 1193055815, wikipedia, wiki, book, books, library,
