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In electronics, a **digital-to-analog converter** (**DAC**, **D/A**, **D2A**, or **D-to-A**) is a system that converts a digital signal into an analog signal. An analog-to-digital converter (ADC) performs the reverse function.

**Electronics** comprises the physics, engineering, technology and applications that deal with the emission, flow and control of electrons in vacuum and matter. The identification of the electron in 1897, along with the invention of the vacuum tube, which could amplify and rectify small electrical signals, inaugurated the field of electronics and the electron age.

In the context of digital signal processing (DSP), a **digital signal** is a discrete-time signal for which not only the time but also the amplitude has discrete values; in other words, its samples take on only values from a discrete set. If that discrete set is finite, the discrete values can be represented with digital words of a finite width. Most commonly, these discrete values are represented as fixed-point words or floating-point words.

An **analog signal** is any continuous signal for which the time-varying feature (variable) of the signal is a representation of some other time varying quantity, i.e., *analogous* to another time varying signal. For example, in an analog audio signal, the instantaneous voltage of the signal varies continuously with the pressure of the sound waves. It differs from a digital signal, in which the continuous quantity is a representation of a sequence of discrete values which can only take on one of a finite number of values. The term *analog signal* usually refers to electrical signals; however, mechanical, pneumatic, hydraulic, human speech, and other systems may also convey or be considered analog signals.

- Overview
- Applications
- Audio
- Video
- Mechanical
- Types
- Performance
- Figures of merit
- See also
- References
- Further reading
- External links

There are several DAC architectures; the suitability of a DAC for a particular application is determined by figures of merit including: resolution, maximum sampling frequency and others. Digital-to-analog conversion can degrade a signal, so a DAC should be specified that has insignificant errors in terms of the application.

In engineering, **hardware architecture** refers to the identification of a system's physical components and their interrelationships. This description, often called a **hardware design model**, allows hardware designers to understand how their components fit into a system architecture and provides to software component designers important information needed for software development and integration. Clear definition of a hardware architecture allows the various traditional engineering disciplines to work more effectively together to develop and manufacture new machines, devices and components.

DACs are commonly used in music players to convert digital data streams into analog audio signals. They are also used in televisions and mobile phones to convert digital video data into analog video signals which connect to the screen drivers to display monochrome or color images. These two applications use DACs at opposite ends of the frequency/resolution trade-off. The audio DAC is a low-frequency, high-resolution type while the video DAC is a high-frequency low- to medium-resolution type.

**Television** (**TV**), sometimes shortened to **tele** or **telly**, is a telecommunication medium used for transmitting moving images in monochrome, or in colour, and in two or three dimensions and sound. The term can refer to a television set, a television program, or the medium of television transmission. Television is a mass medium for advertising, entertainment and news.

A **mobile phone**, **cell phone**, **cellphone**, or **hand phone**, sometimes shortened to simply **mobile**, **cell** or just **phone**, is a portable telephone that can make and receive calls over a radio frequency link while the user is moving within a telephone service area. The radio frequency link establishes a connection to the switching systems of a mobile phone operator, which provides access to the public switched telephone network (PSTN). Modern mobile telephone services use a cellular network architecture, and, therefore, mobile telephones are called *cellular telephones* or *cell phones*, in North America. In addition to telephony, 2000s-era mobile phones support a variety of other services, such as text messaging, MMS, email, Internet access, short-range wireless communications, business applications, video games, and digital photography. Mobile phones offering only those capabilities are known as feature phones; mobile phones which offer greatly advanced computing capabilities are referred to as smartphones.

Due to the complexity and the need for precisely matched components, all but the most specialized DACs are implemented as integrated circuits (ICs). Discrete DACs would typically be extremely high speed low resolution power hungry types, as used in military radar systems. Very high speed test equipment, especially sampling oscilloscopes, may also use discrete DACs.

**Radar** is a detection system that uses radio waves to determine the range, angle, or velocity of objects. It can be used to detect aircraft, ships, spacecraft, guided missiles, motor vehicles, weather formations, and terrain. A radar system consists of a transmitter producing electromagnetic waves in the radio or microwaves domain, a transmitting antenna, a receiving antenna and a receiver and processor to determine properties of the object(s). Radio waves from the transmitter reflect off the object and return to the receiver, giving information about the object's location and speed.

An **oscilloscope**, previously called an **oscillograph**, and informally known as a **scope** or **o-scope**, **CRO**, or **DSO**, is a type of electronic test instrument that graphically displays varying signal voltages, usually as a two-dimensional plot of one or more signals as a function of time. Other signals can be converted to voltages and displayed.

A DAC converts an abstract finite-precision number (usually a fixed-point binary number) into a physical quantity (e.g., a voltage or a pressure). In particular, DACs are often used to convert finite-precision time series data to a continually varying physical signal.

In computing, a **fixed-point number** representation is a real data type for a number that has a fixed number of digits after the radix point. Fixed-point number representation can be compared to the more complicated floating-point number representation.

In mathematics and digital electronics, a **binary number** is a number expressed in the **base-2 numeral system** or **binary numeral system**, which uses only two symbols: typically "0" (zero) and "1" (one).

**Voltage**, **electric potential difference**, **electric pressure **or **electric tension** is the difference in electric potential between two points. The difference in electric potential between two points in a static electric field is defined as the work needed per unit of charge to move a test charge between the two points. In the International System of Units, the derived unit for voltage is named *volt*. In SI units, work per unit charge is expressed as joules per coulomb, where 1 volt = 1 joule per 1 coulomb. The official SI definition for *volt* uses power and current, where 1 volt = 1 watt per 1 ampere. This definition is equivalent to the more commonly used 'joules per coulomb'. Voltage or electric potential difference is denoted symbolically by ∆*V*, but more often simply as *V*, for instance in the context of Ohm's or Kirchhoff's circuit laws.

An *ideal* DAC converts the abstract numbers into a conceptual sequence of impulses that are then processed by a reconstruction filter using some form of interpolation to fill in data between the impulses. A conventional *practical* DAC converts the numbers into a piecewise constant function made up of a sequence of rectangular functions that is modeled with the zero-order hold. Other DAC methods (such as those based on delta-sigma modulation) produce a pulse-density modulated output that can be similarly filtered to produce a smoothly varying signal.

In mathematics, the **Dirac delta function** is a generalized function or distribution introduced by the physicist Paul Dirac. It is used to model the density of an idealized point mass or point charge as a function equal to zero everywhere except for zero and whose integral over the entire real line is equal to one. As there is no function that has these properties, the computations made by the theoretical physicists appeared to mathematicians as nonsense until the introduction of distributions by Laurent Schwartz to formalize and validate the computations. As a distribution, the Dirac delta function is a linear functional that maps every function to its value at zero. The Kronecker delta function, which is usually defined on a discrete domain and takes values 0 and 1, is a discrete analog of the Dirac delta function.

In a mixed-signal system, a **reconstruction filter** is used to construct a smooth analog signal from a digital input, as in the case of a digital to analog converter (DAC) or other sampled data output device.

In the mathematical field of numerical analysis, **interpolation** is a method of constructing new data points within the range of a discrete set of known data points.

As per the Nyquist–Shannon sampling theorem, a DAC can reconstruct the original signal from the sampled data provided that its bandwidth meets certain requirements (e.g., a baseband signal with bandwidth less than the Nyquist frequency). Digital sampling introduces quantization error that manifests as low-level noise in the reconstructed signal.

DACs and ADCs are part of an enabling technology that has contributed greatly to the digital revolution. To illustrate, consider a typical long-distance telephone call. The caller's voice is converted into an analog electrical signal by a microphone, then the analog signal is converted to a digital stream by an ADC. The digital stream is then divided into network packets where it may be sent along with other digital data, not necessarily audio. The packets are then received at the destination, but each packet may take a completely different route and may not even arrive at the destination in the correct time order. The digital voice data is then extracted from the packets and assembled into a digital data stream. A DAC converts this back into an analog electrical signal, which drives an audio amplifier, which in turn drives a loudspeaker, which finally produces sound.

Most modern audio signals are stored in digital form (for example MP3s and CDs) and, in order to be heard through speakers, they must be converted into an analog signal. DACs are therefore found in CD players, digital music players, and PC sound cards.

Specialist standalone DACs can also be found in high-end hi-fi systems. These normally take the digital output of a compatible CD player or dedicated transport (which is basically a CD player with no internal DAC) and convert the signal into an analog line-level output that can then be fed into an amplifier to drive speakers.

Similar digital-to-analog converters can be found in digital speakers such as USB speakers, and in sound cards.

In voice over IP applications, the source must first be digitized for transmission, so it undergoes conversion via an ADC, and is then reconstructed into analog using a DAC on the receiving party's end.

Video sampling tends to work on a completely different scale altogether thanks to the highly nonlinear response both of cathode ray tubes (for which the vast majority of digital video foundation work was targeted) and the human eye, using a "gamma curve" to provide an appearance of evenly distributed brightness steps across the display's full dynamic range - hence the need to use RAMDACs in computer video applications with deep enough colour resolution to make engineering a hardcoded value into the DAC for each output level of each channel impractical (e.g. an Atari ST or Sega Genesis would require 24 such values; a 24-bit video card would need 768...). Given this inherent distortion, it is not unusual for a television or video projector to truthfully claim a linear contrast ratio (difference between darkest and brightest output levels) of 1000:1 or greater, equivalent to 10 bits of audio precision even though it may only accept signals with 8-bit precision and use an LCD panel that only represents 6 or 7 bits per channel.

Video signals from a digital source, such as a computer, must be converted to analog form if they are to be displayed on an analog monitor. As of 2007, analog inputs were more commonly used than digital, but this changed as flat panel displays with DVI and/or HDMI connections became more widespread.^{[ citation needed ]} A video DAC is, however, incorporated in any digital video player with analog outputs. The DAC is usually integrated with some memory (RAM), which contains conversion tables for gamma correction, contrast and brightness, to make a device called a RAMDAC.

A device that is distantly related to the DAC is the digitally controlled potentiometer, used to control an analog signal digitally.

A one-bit mechanical actuator assumes two positions: one when on, another when off. The motion of several one-bit actuators can be combined and weighted with a whiffletree mechanism to produce finer steps. The IBM Selectric typewriter uses such a system.^{ [1] }

The most common types of electronic DACs are:^{ [2] }

- The pulse-width modulator where a stable current or voltage is switched into a low-pass analog filter with a duration determined by the digital input code. This technique is often used for electric motor speed control and dimming LED lamps.
- Oversampling DACs or interpolating DACs such as those employing delta-sigma modulation, use a pulse density conversion technique with oversampling. Speeds of greater than 100 thousand samples per second (for example, 192 kHz) and resolutions of 24 bits are attainable with delta-sigma DACs.
- The binary-weighted DAC, which contains individual electrical components for each bit of the DAC connected to a summing point, typically an operational amplifier. Each input in the summing has powers-of-two values with most current or voltage at the most-significant bit. These precise voltages or currents sum to the correct output value. This is one of the fastest conversion methods but suffers from poor accuracy because of the high precision required for each individual voltage or current.
^{ [3] }This type of converter is usually limited to 8-bit resolution or less.^{[ citation needed ]}- Switched resistor DAC contains a parallel resistor network. Individual resistors are enabled or bypassed in the network based on the digital input.
- Switched current source DAC, from which different current sources are selected based on the digital input.
- Switched capacitor DAC contains a parallel capacitor network. Individual capacitors are connected or disconnected with switches based on the input.
- The R-2R ladder DAC which is a binary-weighted DAC that uses a repeating cascaded structure of resistor values R and 2R. This improves the precision due to the relative ease of producing equal valued-matched resistors (or current sources).

- The successive approximation or cyclic DAC,
^{ [4] }which successively constructs the output during each cycle. Individual bits of the digital input are processed each cycle until the entire input is accounted for. - The thermometer-coded DAC, which contains an equal resistor or current-source segment for each possible value of DAC output. An 8-bit thermometer DAC would have 255 segments, and a 16-bit thermometer DAC would have 65,535 segments. This is perhaps the fastest and highest precision DAC architecture but at the expense of high cost. Conversion speeds of >1 billion samples per second have been reached with this type of DAC.
^{[ citation needed ]} - Hybrid DACs, which use a combination of the above techniques in a single converter. Most DAC integrated circuits are of this type due to the difficulty of getting low cost, high speed and high precision in one device.
- The segmented DAC, which combines the thermometer-coded principle for the most significant bits and the binary-weighted principle for the least significant bits. In this way, a compromise is obtained between precision (by the use of the thermometer-coded principle) and number of resistors or current sources (by the use of the binary-weighted principle). The full binary-weighted design means 0% segmentation, the full thermometer-coded design means 100% segmentation.

- Most DACs, shown in this list, rely on a constant reference voltage to create their output value. Alternatively, a
*multiplying DAC*^{ [5] }takes a variable input voltage for their conversion. This puts additional design constraints on the bandwidth of the conversion circuit.

DACs are very important to system performance. The most important characteristics of these devices are:^{[ citation needed ]}

- Resolution
- The number of possible output levels the DAC is designed to reproduce. This is usually stated as the number of bits it uses, which is the base two logarithm of the number of levels. For instance a 1 bit DAC is designed to reproduce 2 (2
^{1}) levels while an 8 bit DAC is designed for 256 (2^{8}) levels. Resolution is related to the effective number of bits which is a measurement of the actual resolution attained by the DAC. Resolution determines color depth in video applications and audio bit depth in audio applications. - Maximum sampling rate
- A measurement of the maximum speed at which the DACs circuitry can operate and still produce the correct output. As stated above, the Nyquist–Shannon sampling theorem defines a relationship between this and the bandwidth of the sampled signal.
- Monotonicity
- The ability of a DAC's analog output to move only in the direction that the digital input moves (i.e., if the input increases, the output doesn't dip before asserting the correct output.) This characteristic is very important for DACs used as a low frequency signal source or as a digitally programmable trim element.
- Total harmonic distortion and noise (THD+N)
- A measurement of the distortion and noise introduced to the signal by the DAC. It is expressed as a percentage of the total power of unwanted harmonic distortion and noise that accompany the desired signal. This is a very important DAC characteristic for dynamic and small signal DAC applications.
- Dynamic range
- A measurement of the difference between the largest and smallest signals the DAC can reproduce expressed in decibels. This is usually related to resolution and noise floor.

Other measurements, such as phase distortion and jitter, can also be very important for some applications, some of which (e.g. wireless data transmission, composite video) may even *rely* on accurate production of phase-adjusted signals.

Linear PCM audio sampling usually works on the basis of each bit of resolution being equivalent to 6 decibels of amplitude (a 2x increase in volume or precision).

Non-linear PCM encodings (A-law / μ-law, ADPCM, NICAM) attempt to improve their effective dynamic ranges by a variety of methods - logarithmic step sizes between the output signal strengths represented by each data bit (trading greater quantisation distortion of loud signals for better performance of quiet signals)

- Static performance:
- Differential nonlinearity (DNL) shows how much two adjacent code analog values deviate from the ideal 1 LSB step.
^{ [6] } - Integral nonlinearity (INL) shows how much the DAC transfer characteristic deviates from an ideal one. That is, the ideal characteristic is usually a straight line; INL shows how much the actual voltage at a given code value differs from that line, in LSBs (1 LSB steps).
- Gain
- Offset
- Noise is ultimately limited by the thermal noise generated by passive components such as resistors. For audio applications and in room temperatures, such noise is usually a little less than 1 μV (microvolt) of white noise. This limits performance to less than 20~21 bits even in 24-bit DACs.

- Differential nonlinearity (DNL) shows how much two adjacent code analog values deviate from the ideal 1 LSB step.
- Frequency domain performance
- Spurious-free dynamic range (SFDR) indicates in dB the ratio between the powers of the converted main signal and the greatest undesired spur.
- Signal-to-noise and distortion ratio (SNDR) indicates in dB the ratio between the powers of the converted main signal and the sum of the noise and the generated harmonic spurs
- i-th harmonic distortion (HDi) indicates the power of the i-th harmonic of the converted main signal
- Total harmonic distortion (THD) is the sum of the powers of all HDi
- If the maximum DNL error is less than 1 LSB, then the D/A converter is guaranteed to be monotonic. However, many monotonic converters may have a maximum DNL greater than 1 LSB.

- Time domain performance:
- Glitch impulse area (glitch energy)
- Response uncertainty
- Time nonlinearity (TNL)

In electronics, an **analog-to-digital converter** is a system that converts an analog signal, such as a sound picked up by a microphone or light entering a digital camera, into a digital signal. An ADC may also provide an isolated measurement such as an electronic device that converts an input analog voltage or current to a digital number representing the magnitude of the voltage or current. Typically the digital output is a two's complement binary number that is proportional to the input, but there are other possibilities.

In telecommunication and signal processing **companding** is a method of mitigating the detrimental effects of a channel with limited dynamic range. The name is a portmanteau of the words **com**pressing and ex**panding**. The use of companding allows signals with a large dynamic range to be transmitted over facilities that have a smaller dynamic range capability. Companding is employed in telephony and other audio applications such as professional wireless microphones and analog recording.

**Digital audio** is sound that has been recorded in, or converted into, digital form. In digital audio, the sound wave of the audio signal is encoded as numerical samples in continuous sequence. For example, in CD audio, samples are taken 44100 times per second each with 16 bit sample depth. Digital audio is also the name for the entire technology of sound recording and reproduction using audio signals that have been encoded in digital form. Following significant advances in digital audio technology during the 1970s, it gradually replaced analog audio technology in many areas of audio engineering and telecommunications in the 1990s and 2000s.

In signal processing, **sampling** is the reduction of a continuous-time signal to a discrete-time signal. A common example is the conversion of a sound wave to a sequence of samples.

**Quantization**, in mathematics and digital signal processing, is the process of mapping input values from a large set to output values in a (countable) smaller set, often with a finite number of elements. Rounding and truncation are typical examples of quantization processes. Quantization is involved to some degree in nearly all digital signal processing, as the process of representing a signal in digital form ordinarily involves rounding. Quantization also forms the core of essentially all lossy compression algorithms.

**Noise shaping** is a technique typically used in digital audio, image, and video processing, usually in combination with dithering, as part of the process of quantization or bit-depth reduction of a digital signal. Its purpose is to increase the apparent signal-to-noise ratio of the resultant signal. It does this by altering the spectral shape of the error that is introduced by dithering and quantization; such that the noise power is at a lower level in frequency bands at which noise is considered to be less desirable and at a correspondingly higher level in bands where it is considered to be more desirable. A popular noise shaping algorithm used in image processing is known as ‘Floyd Steinberg dithering’; and many noise shaping algorithms used in audio processing are based on an ‘Absolute threshold of hearing’ model.

In signal processing, **oversampling** is the process of sampling a signal at a sampling frequency significantly higher than the Nyquist rate. Theoretically, a bandwidth-limited signal can be perfectly reconstructed if sampled at the Nyquist rate or above it. The Nyquist rate is defined as twice the highest frequency component in the signal. Oversampling is capable of improving resolution, reducing noise and can be helpful in avoiding aliasing and phase distortion by relaxing anti-aliasing filter performance requirements.

**Analogue electronics** are electronic systems with a continuously variable signal, in contrast to digital electronics where signals usually take only two levels. The term "analogue" describes the proportional relationship between a signal and a voltage or current that represents the signal. The word analogue is derived from the Greek word ανάλογος (analogos) meaning "proportional".

**Delta-sigma** modulation is a method for encoding analog signals into digital signals as found in an analog-to-digital converter (ADC). It is also used to convert high bit-count, low-frequency digital signals into lower bit-count, higher-frequency digital signals as part of the process to convert digital signals into analog as part of a digital-to-analog converter (DAC).

A **resistor ladder** is an electrical circuit made from repeating units of resistors. Two configurations are discussed below, a string resistor ladder and an R–2R ladder.

A **flash ADC** is a type of analog-to-digital converter that uses a linear voltage ladder with a comparator at each "rung" of the ladder to compare the input voltage to successive reference voltages. Often these reference ladders are constructed of many resistors; however, modern implementations show that capacitive voltage division is also possible. The output of these comparators is generally fed into a digital encoder, which converts the inputs into a binary value.

In electronics, **signal conditioning** means manipulating an analog signal in such a way that it meets the requirements of the next stage for further processing. Most common use is in analog-to-digital converters.

A **successive approximation ADC** is a type of analog-to-digital converter that converts a continuous analog waveform into a discrete digital representation via a binary search through all possible quantization levels before finally converging upon a digital output for each conversion.

In digital audio using pulse-code modulation (PCM), **bit depth** is the number of bits of information in each sample, and it directly corresponds to the **resolution** of each sample. Examples of bit depth include Compact Disc Digital Audio, which uses 16 bits per sample, and DVD-Audio and Blu-ray Disc which can support up to 24 bits per sample.

**Effective number of bits** (**ENOB**) is a measure of the dynamic range of an analog-to-digital converter (ADC) and its associated circuitry. The resolution of an ADC is specified by the number of bits used to represent the analog value, in principle giving 2^{N} signal levels for an *N*-bit signal. However, all real ADC circuits introduce noise and distortion. ENOB specifies the resolution of an ideal ADC circuit that would have the same resolution as the circuit under consideration.

A **Bitcrusher** is a lo-fi digital audio effect, which produces a distortion by the reduction of the resolution or bandwidth of digital audio data. The resulting quantization noise may produce a “warmer” sound impression, or a harsh one, depending on the amount of reduction.

**Differential nonlinearity** is a term describing the deviation between two analog values corresponding to adjacent input digital values. It is an important specification for measuring error in a digital-to-analog converter (DAC); the accuracy of a DAC is mainly determined by this specification. Ideally, any two adjacent digital codes correspond to output analog voltages that are exactly one Least Significant Bit (LSB) apart. Differential non-linearity is a measure of the worst case deviation from the ideal 1 LSB step. For example, a DAC with a 1.5 LSB output change for a 1 LSB digital code change exhibits 1⁄2 LSB differential non-linearity. Differential non-linearity may be expressed in fractional bits or as a percentage of full scale. A differential non-linearity greater than 1 LSB may lead to a non-monotonic transfer function in a DAC. It is also known as a *missing code*.

**Spurious-free dynamic range** (**SFDR**) is the strength ratio of the fundamental signal to the strongest spurious signal in the output. It is also defined as a measure used to specify analog-to-digital and digital-to-analog converters and radio receivers.

An **integrating ADC** is a type of analog-to-digital converter that converts an unknown input voltage into a digital representation through the use of an integrator. In its basic implementation, the dual-slope converter, the unknown input voltage is applied to the input of the integrator and allowed to ramp for a fixed time period. Then a known reference voltage of opposite polarity is applied to the integrator and is allowed to ramp until the integrator output returns to zero. The input voltage is computed as a function of the reference voltage, the constant run-up time period, and the measured run-down time period. The run-down time measurement is usually made in units of the converter's clock, so longer integration times allow for higher resolutions. Likewise, the speed of the converter can be improved by sacrificing resolution.

The following outline is provided as an overview of and topical guide to electronics:

- ↑ Brian Brumfield (2014-09-02). "Selectric Repair 10-3A Input: Keyboard" – via YouTube.
- ↑ "Data Converter Architectures" (PDF).
*Analog-Digital Conversion*. Analog Devices. Archived (PDF) from the original on 2017-08-30. Retrieved 2017-08-30. - ↑ "Binary Weighted Resistor DAC".
*Electronics Tutorial*. Retrieved 2018-09-25. - ↑ "Data Converter Architectures", p. 3.29.
- ↑ "Multiplying DACs: Flexible Building Blocks" (PDF). Analog Devices. 2010. Retrieved 2012-03-29.
- ↑ "ADC and DAC Glossary". Maxim. Archived from the original on 2007-03-08.

- Kester, Walt,
*The Data Conversion Handbook*, ISBN 0-7506-7841-0 - S. Norsworthy, Richard Schreier, Gabor C. Temes,
*Delta-Sigma Data Converters*. ISBN 0-7803-1045-4. - Mingliang Liu,
*Demystifying Switched-Capacitor Circuits*. ISBN 0-7506-7907-7. - Behzad Razavi,
*Principles of Data Conversion System Design*. ISBN 0-7803-1093-4. - Phillip E. Allen, Douglas R. Holberg,
*CMOS Analog Circuit Design*. ISBN 0-19-511644-5. - Robert F. Coughlin, Frederick F. Driscoll,
*Operational Amplifiers and Linear Integrated Circuits*. ISBN 0-13-014991-8. - A Anand Kumar,
*Fundamentals of Digital Circuits*. ISBN 81-203-1745-9, ISBN 978-81-203-1745-1. - Ndjountche Tertulien, "CMOS Analog Integrated Circuits: High-Speed and Power-Efficient Design". ISBN 978-1-4398-5491-4.

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