In digital logic, an inverter or NOT gate is a

logic gate A logic gate is an idealized or physical device implementing a Boolean function, a logical operation performed on one or more binary inputs that produces a single binary output. Depending on the context, the term may refer to an ideal logic gate, ...

which implements

logical negation In logic, negation, also called the logical complement, is an operation that takes a proposition P to another proposition "not P", written \neg P, \mathord P or \overline. It is interpreted intuitively as being true when P is false, and false ...

. It outputs a

bit The bit is the most basic unit of information in computing and digital communications. The name is a portmanteau of binary digit. The bit represents a logical state with one of two possible values. These values are most commonly represente ...

opposite of the bit that is put into it. The bits are typically implemented as two differing

voltage Voltage, also known as electric pressure, electric tension, or (electric) potential difference, is the difference in electric potential between two points. In a static electric field, it corresponds to the work needed per unit of charge to m ...

levels.

Description

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. As with all binary logic gates, other pairs of symbols such as true and false, or high and low may be used in lieu of one and zero. It is equivalent to the

operator (¬) in

mathematical logic Mathematical logic is the study of logic, formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory. Research in mathematical logic commonly addresses the mathematical properties of for ...

. Because it has only one input, it is a

unary operation In mathematics, an unary operation is an operation with only one operand, i.e. a single input. This is in contrast to binary operations, which use two operands. An example is any function , where is a set. The function is a unary operation on ...

and has the simplest type of

truth table A truth table is a mathematical table used in logic—specifically in connection with Boolean algebra, boolean functions, and propositional calculus—which sets out the functional values of logical expressions on each of their functional argumen ...

. It is also called the complement gate because it produces the

ones' complement The ones' complement of a binary number is the value obtained by inverting all the bits in the binary representation of the number (swapping 0s and 1s). The name "ones' complement" (''note this is possessive of the plural "ones", not of a sing ...

of a binary number, swapping 0s and 1s. The NOT gate is one of three basic logic gates from which any

Boolean circuit In computational complexity theory and circuit complexity, a Boolean circuit is a mathematical model for combinational digital logic circuits. A formal language can be decided by a family of Boolean circuits, one circuit for each possible input ...

may be built up. Together with the

AND gate The AND gate is a basic digital logic gate that implements logical conjunction (∧) from mathematical logic AND gate behaves according to the truth table. A HIGH output (1) results only if all the inputs to the AND gate are HIGH (1). If not all ...

and the

OR gate The OR gate is a digital logic gate that implements logical disjunction. The OR gate returns true if either or both of its inputs are true; otherwise it returns false. The input and output states are normally represented by different voltage le ...

, any function in binary mathematics may be implemented. All other

logic gates A logic gate is an idealized or physical device implementing a Boolean function, a logical operation performed on one or more binary inputs that produces a single binary output. Depending on the context, the term may refer to an ideal logic gate ...

may be made from these three. The terms "programmable inverter" or "controlled inverter" do not refer to this gate; instead, these terms refer to the

XOR gate XOR gate (sometimes EOR, or EXOR and pronounced as Exclusive OR) is a digital logic gate that gives a true (1 or HIGH) output when the number of true inputs is odd. An XOR gate implements an exclusive or (\nleftrightarrow) from mathematical log ...

because it can conditionally function like a NOT gate.

Symbols

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 active-low input, sometimes the bubble is instead placed on the input line. 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 and NOR are formed in this way. A bar or

overline An overline, overscore, or overbar, is a typographical feature of a horizontal line drawn immediately above the text. In old mathematical notation, an overline was called a '' vinculum'', a notation for grouping symbols which is expressed in m ...

( ‾ ) above a variable can denote negation (or inversion or complement) performed by a NOT gate. A slash (/) before the variable is also used.

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 transistor or a single PMOS transistor coupled with a

resistor A resistor is a passive two-terminal electrical component that implements electrical resistance as a circuit element. In electronic circuits, resistors are used to reduce current flow, adjust signal levels, to divide voltages, bias active el ...

. 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 Complementary metal–oxide–semiconductor (CMOS, pronounced "sea-moss", ) is a type of metal–oxide–semiconductor field-effect transistor (MOSFET) fabrication process that uses complementary and symmetrical pairs of p-type and n-type MOSFE ...

configuration. This configuration greatly reduces power consumption since one of the transistors is always off in both logic states. 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 A bipolar junction transistor (BJT) is a type of transistor that uses both electrons and electron holes as charge carriers. In contrast, a unipolar transistor, such as a field-effect transistor, uses only one kind of charge carrier. A bipolar ...

s (BJT) in either a

resistor–transistor logic Resistor–transistor logic (RTL) (sometimes also transistor–resistor logic (TRL)) is a class of digital circuits built using resistors as the input network and bipolar junction transistors (BJTs) as switching devices. RTL is the earliest class o ...

(RTL) or a

transistor–transistor logic Transistor–transistor logic (TTL) is a logic family built from bipolar junction transistors. Its name signifies that transistors perform both the logic function (the first "transistor") and the amplifying function (the second "transistor"), as opp ...

(TTL) configuration.

Digital Digital usually refers to something using discrete digits, often binary digits. Technology and computing Hardware *Digital electronics, electronic circuits which operate using digital signals **Digital camera, which captures and stores digital i ...

electronics circuits operate at fixed voltage levels corresponding to a logical 0 or 1 (see

binary Binary may refer to: Science and technology Mathematics * Binary number, a representation of numbers using only two digits (0 and 1) * Binary function, a function that takes two arguments * Binary operation, a mathematical operation that t ...

). 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. Image:NMOS NOT.svg,

NMOS logic N-type metal-oxide-semiconductor logic uses n-type (-) MOSFETs (metal-oxide-semiconductor field-effect transistors) to implement logic gates and other digital circuits. These nMOS transistors operate by creating an inversion layer in a p-type ...

inverter Image:PMOS NOT.svg,

PMOS logic PMOS or pMOS logic (from p-channel metal–oxide–semiconductor) is a family of digital circuits based on p-channel, enhancement mode metal–oxide–semiconductor field-effect transistors (MOSFETs). In the late 1960s and early 1970s, PMOS log ...

inverter Image:CMOS Inverter.svg, Static

CMOS logic Complementary metal–oxide–semiconductor (CMOS, pronounced "sea-moss", ) is a type of metal–oxide–semiconductor field-effect transistor (MOSFET) fabrication process that uses complementary and symmetrical pairs of p-type and n-type MOSFE ...

inverter Image:RTL NOT Gate.svg, NPN

inverter Image:Puertas NOT con transistores.jpg, NPN

inverter

Digital building block

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 An integrated circuit or monolithic integrated circuit (also referred to as an IC, a chip, or a microchip) is a set of electronic circuits on one small flat piece (or "chip") of semiconductor material, usually silicon. Large numbers of tiny ...

that contains six (''

hexa- Numeral or number prefixes are prefixes derived from numerals or occasionally other numbers. In English and many other languages, they are used to coin numerous series of words. For example: * unicycle, bicycle, tricycle (1-cycle, 2-cycle, 3-cyc ...

'') inverters. For example, the 7404

TTL TTL may refer to: Photography * Through-the-lens metering, a camera feature * Zenit TTL, an SLR film camera named for its TTL metering capability Technology * Time to live, a computer data lifespan-limiting mechanism * Transistor–transistor lo ...

chip which has 14 pins and the 4049

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

f(a)=1-a

is the analytical representation of NOT gate: *

f(0)=1-0=1

f(1)=1-1=0

Alternatives

If no specific NOT gates are available, one can be made from the universal NAND or NOR gates, or an

by setting one input to high.

Performance measurement

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 infinity) 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).

References

External links

The NOT gate
on "All About Circuits"
The NOT gate
in 1971 "Designing With TTL Integrated Circuits" book {{Logical connectives Logic gates Integrated circuits