Editing Inverter (logic gate)

{{short description|Logic gate implementing negation}}
[[File:Not-gate-en.svg|class=skin-invert-image|thumb|128px|right|Traditional NOT gate (inverter) symbol]]

In digital logic, an '''inverter''' or '''NOT gate''' is a [[logic gate]] which implements [[logical negation]]. It outputs a [[bit]] opposite of the bit that is put into it. The bits are typically implemented as two differing [[voltage]] levels.

==Description==
{| class="wikitable floatright" style="text-align:center"
|-
! colspan="2" | Inverter [[truth table]]
|- bgcolor="#ddeeff"
|colspan=1|'''Input''' || '''Output'''
|- bgcolor="#ddeeff"
| A || NOT A
|-
|{{no2|0}} || {{yes2|1}}
|-
|{{yes2|1}} || {{no2|0}}
|}
The NOT gate outputs a zero when given a one, and a one when given a zero. Hence, it inverts its inputs. Colloquially, this inversion of bits is called "flipping" bits.<ref name="VanHoutven2017">{{cite book |url=https://github.com/crypto101/crypto101.github.io/raw/master/Crypto101.pdf |first=Laurens |last=Van Houtven |year=2017 |title=Crypto 101 |page=17 }}</ref> As with all binary logic gates, other pairs of symbols {{mdash}} such as true and false, or high and low {{mdash}} may be used in lieu of one and zero.

It is equivalent to the [[logical negation]] operator (¬) in [[mathematical logic]]. Because it has only one input, it is a [[unary operation]] and has the simplest type of [[truth table]]. It is also called the complement gate<ref>{{ cite web |url=https://www.uobabylon.edu.iq/eprints/publication_4_21167_1447.pdf |title=2.9 Digital Logic Gates |website=University of Babylon }}</ref> because it produces the [[ones' complement]] of a binary number, swapping 0s and 1s. 

The NOT gate is one of three basic logic gates from which any [[Boolean circuit]] may be built up. Together with the [[AND gate]] and the [[OR gate]], any function in binary mathematics may be implemented. All other [[logic gates]] may be made from these three.<ref name="Broesch2012">{{cite book |title=Practical Programmable Circuits: A Guide to PLDs, State Machines, and Microcontrollers |first=James D. |last=Broesch |year=2012 |page=19 |publisher=Elsevier Science |isbn=978-0323139267 |url=https://books.google.com/books?id=I7-v5CBVmfIC&pg=PA20 }}</ref>

The terms "programmable inverter" or "controlled inverter" do not refer to this gate; instead, these terms refer to the [[XOR gate]] because it can conditionally function like a NOT gate.<ref name="VanHoutven2017" /><ref name="Broesch2012" />

==Symbols==
<div class=skin-invert-image>
{{multiple image
 | image1 = Not-gate-en.svg
 | alt1 = Triangular not gate symbol
 | caption1 = Traditional NOT gate symbol; sometimes the triangle is omitted, or the circle may be placed on the input line<ref name="Broesch2012" />
 | image2 = IEC NOT.svg
 | alt2 = Rectangular not gate symbol
 | caption2 = [[List of IEC standards#60617|IEC 60617]] NOT gate symbol
}}
</div>
The traditional symbol for an inverter circuit is a triangle touching a small circle or "bubble". Input and output lines are attached to the symbol; the bubble is typically attached to the output line. To symbolize [[Logic level#2-level logic|active-low input]], sometimes the bubble is instead placed on the input line.<ref name="ElectronicsTutorials">{{cite web |title=Logic NOT Gate Tutorial |website=Electronics Tutorials |date=20 August 2013 |url=https://www.electronics-tutorials.ws/logic/logic_4.html}}</ref> Sometimes only the circle portion of the symbol is used, and it is attached to the input or output of another gate; the symbols for [[NAND gate|NAND]] and [[NOR gate|NOR]] are formed in this way.<ref name="Broesch2012" />

A bar or [[overline]] ( ‾ ) above a variable can denote negation (or inversion or complement) performed by a NOT gate.<ref name="ElectronicsTutorials" /> A slash (/) before the variable is also used.<ref name="Broesch2012" />

==Electronic implementation==
An inverter circuit outputs a voltage representing the opposite logic-level to its input. Its main function is to invert the input signal applied. If the applied input is low then the output becomes high and vice versa. Inverters can be constructed using a single [[NMOS logic|NMOS]] transistor or a single [[PMOS logic|PMOS]] transistor coupled with a [[resistor]].  Since this "resistive-drain" approach uses only a single type of transistor, it can be fabricated at a low cost.  However, because current flows through the resistor in one of the two states, the resistive-drain configuration is disadvantaged for power consumption and processing speed.  Alternatively, inverters can be constructed using two complementary transistors in a [[CMOS]] configuration.  This configuration greatly reduces power consumption since one of the transistors is always off in both logic states.<ref>{{cite book |last1=Nair |first1=B. Somanathan |title=Digital electronics and logic design |date=2002 |publisher=PHI Learning Pvt. Ltd. |isbn=9788120319561 |page=240 |url=https://books.google.com/books?id=WK45wLHL-ycC&pg=PA240 |language=en}}</ref>  Processing speed can also be improved due to the relatively low resistance compared to the NMOS-only or PMOS-only type devices.  Inverters can also be constructed with [[bipolar junction transistor]]s (BJT) in either a  [[resistor–transistor logic]] (RTL) or a [[transistor–transistor logic]] (TTL) configuration.

[[Digital data|Digital]] electronics circuits operate at fixed voltage levels corresponding to a logical 0 or 1 (see [[Binary numeral system|binary]]).  An inverter circuit serves as the basic logic gate to swap between those two voltage levels.  Implementation determines the actual voltage, but common levels include (0, +5V) for TTL circuits.

<gallery heights="170px" widths="180px" class="skin-invert-image">
Image:NMOS NOT.svg|[[NMOS logic]] inverter
Image:PMOS NOT.svg|[[PMOS logic]] inverter
Image:CMOS Inverter.svg|Static [[CMOS logic]] inverter
Image:RTL NOT Gate.svg|NPN [[resistor–transistor logic]] inverter
Image:Puertas NOT con transistores.jpg|NPN [[transistor–transistor logic]] inverter
</gallery>

===Digital building block===
[[File:CMOS 4049 diagram.svg|class=skin-invert-image|thumb|right|150px|This schematic diagram shows the arrangement of NOT gates within a standard 4049 CMOS hex inverting buffer.]]

The inverter is a basic building block in digital electronics. Multiplexers, decoders, state machines, and other sophisticated digital devices may use inverters.

The ''hex inverter'' is an [[integrated circuit]] that contains six (''[[wikt:hexa-|hexa-]]'') inverters. For example, the [[7400 series|7404]] [[Transistor–transistor logic|TTL]] chip which has 14 pins and the 4049 [[CMOS]] chip which has 16 pins, 2 of which are used for power/referencing, and 12 of which are used by the inputs and outputs of the six inverters (the 4049 has 2 pins with no connection).

==== Analytical representation ====
<math>f(a)=1-a</math> is the analytical representation of NOT gate:
* <math>f(0)=1-0=1</math>
* <math>f(1)=1-1=0</math>

=== Alternatives ===
{{further|NAND logic|NOR logic}}
If no specific NOT gates are available, one can be made from the universal [[NAND gate|NAND]] or [[NOR gate|NOR]] gates,<ref>{{cite book |last1=M. Morris |first1=Mano |last2=R. Kime |first2=Charles |title=Logic and computer design fundamentals |date=2004 |publisher=Prentice Hall |isbn=0133760634 |page=73 |edition=3 |url=https://books.google.com/books?id=jPEWogEACAAJ&q=Logic+and+Computer+Design+Fundamentals}}</ref> or an [[XOR gate]] by setting one input to high.

{| align=center style="text-align:center" class=skin-invert-image
! width="250" |Desired gate!! width="150" |NAND construction!! width="150" |NOR construction
|-
| [[File:NOT ANSI Labelled.svg]] || [[Image:NOT from NAND.svg]] || [[File:NOT from NOR.svg]]
|}

===Performance measurement===
[[File:Inverter voltage transfer curve.png|thumb|300px|Voltage transfer curve for a 20 μm inverter fabricated at [[North Carolina State University]]]]

Digital inverter quality is often measured using the voltage transfer curve (VTC), which is a plot of output vs. input voltage. From such a graph, device parameters including noise tolerance, gain, and operating logic levels can be obtained.

Ideally, the VTC appears as an inverted step function – this would indicate precise switching between ''on'' and ''off'' – but in real devices, a gradual transition region exists. The VTC indicates that for low input voltage, the circuit outputs high voltage; for high input, the output tapers off towards the low level. The slope of this transition region is a measure of quality – steep (close to vertical) slopes yield precise switching.

The tolerance to noise can be measured by comparing the minimum input to the maximum output for each region of operation (on / off).

==== Linear region as analog amplifier ====
Since the transition region is steep and approximately linear, a properly-biased CMOS inverter digital logic gate may be used as a high-gain analog [[linear amplifier]]<ref>{{Cite web |orig-date=July 1973 |date=April 2003 |title=Application Note 88: CMOS Linear Applications |url=https://www.elektronik-kompendium.de/public/schaerer/FILES/an-88.pdf |website=[[National Semiconductor]]}}</ref><ref>{{Cite web |last=Stonier-Gibson |first=David |title=CMOS gate as linear amplifier |url=http://melbmcu.weebly.com/cmos-gate-as-analogue-amplifier.html |url-status=live |archive-url=https://web.archive.org/web/20220331092505/http://melbmcu.weebly.com/cmos-gate-as-analogue-amplifier.html |archive-date=2022-03-31 |access-date=2023-05-18 |website=Microcontroller Group, Moorabbin, Melbourne |language=en}}</ref><ref>{{Citation |title=CMOS Inverters as Analog Amplifiers (Adventures in Field Programmable Analog Arrays) | date=14 December 2021 |url=https://www.youtube.com/watch?v=DnO5sMU5DqU |access-date=2023-05-18 |language=en}}, Aaron Lanterman, Georgia Tech</ref><ref>{{Cite web |title=CMOS-Inverter-as-an-Amplifier {{!}} Analog-CMOS-Design {{!}}{{!}} Electronics Tutorial |url=https://www.electronics-tutorial.net/Analog-CMOS-Design/MOSFET-Amplifiers/CMOS-Inverter-as-an-Amplifier/ |access-date=2023-05-18 |website=www.electronics-tutorial.net}}</ref><ref>{{Cite web |title=Activity: CMOS Amplifier stages - ADALM2000 [Analog Devices Wiki] |url=https://wiki.analog.com/university/courses/electronics/electronics-lab-20 |url-status=live |archive-url=https://web.archive.org/web/20220808072638/https://wiki.analog.com/university/courses/electronics/electronics-lab-20 |archive-date=2022-08-08 |access-date=2023-05-18 |website=wiki.analog.com}}</ref> or even combined to form an [[opamp]].<ref>{{Cite web |last=Weltin-Wu |first=Colin |date=2013-11-18 |title=A true op-amp made from inverters |url=https://www.edn.com/a-true-op-amp-made-from-inverters/ |access-date=2023-05-18 |website=EDN |language=en-US}}</ref> Maximum gain is achieved when the input and output operating points are the same voltage, which can be biased by connecting a resistor between the output and input.<ref>{{Cite journal |last=Bae |first=Woorham |date=2019-09-20 |title=CMOS Inverter as Analog Circuit: An Overview |journal=Journal of Low Power Electronics and Applications |language=en |volume=9 |issue=3 |pages=26 |doi=10.3390/jlpea9030026 |doi-access=free |issn=2079-9268}}</ref>

==See also==
* [[Controlled NOT gate]]
* [[AND gate]]
* [[OR gate]]
* [[NAND gate]]
* [[NOR gate]]
* [[XOR gate]]
* [[XNOR gate]]
* [[IMPLY gate]]
* [[Boolean algebra]]
* [[Logic gate]]

==References==
{{Reflist}}

==External links==
* [http://www.allaboutcircuits.com/vol_4/chpt_3/2.html The NOT gate] on "All About Circuits"
* [https://archive.org/details/bitsavers_tiTexasInsSeriesMorrisDesigningWithTTLIntegratedCi_11927910/page/n13/mode/2up The NOT gate] in 1971 "Designing With TTL Integrated Circuits" book

{{Logical connectives}}

[[Category:Logic gates]]
[[Category:Integrated circuits]]