# Flip-flop (electronics)

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In electronics, a flip-flop or latch is a circuit that has two stable states and can be used to store state information. A flip-flop is a bistable multivibrator. The circuit can be made to change state by signals applied to one or more control inputs and will have one or two outputs. It is the basic storage element in sequential logic. Flip-flops and latches are fundamental building blocks of digital electronics systems used in computers, communications, and many other types of systems.

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.

An electronic circuit is composed of individual electronic components, such as resistors, transistors, capacitors, inductors and diodes, connected by conductive wires or traces through which electric current can flow. To be referred to as electronic, rather than electrical, generally at least one active component must be present. The combination of components and wires allows various simple and complex operations to be performed: signals can be amplified, computations can be performed, and data can be moved from one place to another.

In communication systems, signal processing, and electrical engineering, a signal is a function that "conveys information about the behavior or attributes of some phenomenon". In its most common usage, in electronics and telecommunication, this is a time varying voltage, current or electromagnetic wave used to carry information. A signal may also be defined as an "observable change in a quantifiable entity". In the physical world, any quantity exhibiting variation in time or variation in space is potentially a signal that might provide information on the status of a physical system, or convey a message between observers, among other possibilities. The IEEE Transactions on Signal Processing states that the term "signal" includes audio, video, speech, image, communication, geophysical, sonar, radar, medical and musical signals. In a later effort of redefining a signal, anything that is only a function of space, such as an image, is excluded from the category of signals. Also, it is stated that a signal may or may not contain any information.

## Contents

Flip-flops and latches are used as data storage elements. A flip-flop is a device which stores a single bit (binary digit) of data; one of its two states represents a "one" and the other represents a "zero". Such data storage can be used for storage of state , and such a circuit is described as sequential logic in electronics. When used in a finite-state machine, the output and next state depend not only on its current input, but also on its current state (and hence, previous inputs). It can also be used for counting of pulses, and for synchronizing variably-timed input signals to some reference timing signal.

The bit is a basic unit of information in information theory, computing, and digital communications. The name is a portmanteau of binary digit.

In information technology and computer science, a program is described as stateful if it is designed to remember preceding events or user interactions; the remembered information is called the state of the system.

In digital circuit theory, sequential logic is a type of logic circuit whose output depends not only on the present value of its input signals but on the sequence of past inputs, the input history as well. This is in contrast to combinational logic, whose output is a function of only the present input. That is, sequential logic has state (memory) while combinational logic does not.

Flip-flops can be either level-triggered (transparent or opaque) or clocked (synchronous or edge-triggered). The term flip-flop has historically referred generically to both level-triggered and edge-triggered circuits that store a single bit of data using gates. Recently, some authors reserve the term flip-flop exclusively for discussing clocked circuits; the simple ones are commonly called latches, [1] [2] . Using this terminology, a level-sensitive flip-flop is called a latch, whereas an edge-triggered flip-flop is simply called a flip-flop. Using either terminology, the term "flip-flop" refers to a device that stores a single bit of data, but the term "latch" may also refer to a device that stores any number of bits of data using a single trigger. The terms "edge-triggered", and "level-triggered" may be used to avoid ambiguity. [3]

In electronics and especially synchronous digital circuits, a clock signal is a particular type of signal that oscillates between a high and a low state and is used like a metronome to coordinate actions of digital circuits.

When a level-triggered latch is enabled it becomes transparent, but an edge-triggered flip-flop's output only changes on a single type (positive going or negative going) of clock edge.

## History

The first electronic flip-flop was invented in 1918 by the British physicists William Eccles and F. W. Jordan. [4] [5] It was initially called the Eccles–Jordan trigger circuit and consisted of two active elements (vacuum tubes). [6] The design was used in the 1943 British Colossus codebreaking computer [7] and such circuits and their transistorized versions were common in computers even after the introduction of integrated circuits, though flip-flops made from logic gates are also common now. [8] [9] Early flip-flops were known variously as trigger circuits or multivibrators.

William Henry Eccles FRS was a British physicist and a pioneer in the development of radio communication.

Frank Wilfred Jordan was a British physicist who together with William Henry Eccles invented the so-called "flip-flop" circuit in 1918. This circuit became the basis of electronic memory in computers.

In electronics, a vacuum tube, an electron tube, or valve or, colloquially, a tube, is a device that controls electric current flow in a high vacuum between electrodes to which an electric potential difference has been applied.

According to P. L. Lindley, an engineer at the US Jet Propulsion Laboratory, the flip-flop types detailed below (SR, D, T, JK) were first discussed in a 1954 UCLA course on computer design by Montgomery Phister, and then appeared in his book Logical Design of Digital Computers. [10] [11] Lindley was at the time working at Hughes Aircraft under Eldred Nelson, who had coined the term JK for a flip-flop which changed states when both inputs were on (a logical "one"). The other names were coined by Phister. They differ slightly from some of the definitions given below. Lindley explains that he heard the story of the JK flip-flop from Eldred Nelson, who is responsible for coining the term while working at Hughes Aircraft. Flip-flops in use at Hughes at the time were all of the type that came to be known as J-K. In designing a logical system, Nelson assigned letters to flip-flop inputs as follows: #1: A & B, #2: C & D, #3: E & F, #4: G & H, #5: J & K. Nelson used the notations "j-input" and "k-input" in a patent application filed in 1953. [12]

The Jet Propulsion Laboratory (JPL) is a federally funded research and development center and NASA field center in La Cañada Flintridge, California, United States, though it is often referred to as residing in Pasadena, California, because it has a Pasadena ZIP Code.

## Implementation

Flip-flops can be either simple (transparent or asynchronous) or clocked (synchronous). In the context of hardware description languages, the simple ones are commonly described as latches, [1] while the clocked ones are described as flip-flops. [2]

Simple flip-flops can be built around a single pair of cross-coupled inverting elements: vacuum tubes, bipolar transistors, field effect transistors, inverters, and inverting logic gates have all been used in practical circuits.

Clocked devices are specially designed for synchronous systems; such devices ignore their inputs except at the transition of a dedicated clock signal (known as clocking, pulsing, or strobing). Clocking causes the flip-flop either to change or to retain its output signal based upon the values of the input signals at the transition. Some flip-flops change output on the rising edge of the clock, others on the falling edge.

Since the elementary amplifying stages are inverting, two stages can be connected in succession (as a cascade) to form the needed non-inverting amplifier. In this configuration, each amplifier may be considered as an active inverting feedback network for the other inverting amplifier. Thus the two stages are connected in a non-inverting loop although the circuit diagram is usually drawn as a symmetric cross-coupled pair (both the drawings are initially introduced in the Eccles–Jordan patent).

## Flip-flop types

Flip-flops can be divided into common types: the SR ("set-reset"), D ("data" or "delay" [13] ), T ("toggle"), and JK. The behavior of a particular type can be described by what is termed the characteristic equation, which derives the "next" (i.e., after the next clock pulse) output, Qnext in terms of the input signal(s) and/or the current output, ${\displaystyle Q}$.

### Simple set-reset latches

#### SR NOR latch

When using static gates as building blocks, the most fundamental latch is the simple SR latch, where S and R stand for set and reset. It can be constructed from a pair of cross-coupled NOR logic gates. The stored bit is present on the output marked Q.

While the R and S inputs are both low, feedback maintains the Q and Q outputs in a constant state, with Q the complement of Q. If S (Set) is pulsed high while R (Reset) is held low, then the Q output is forced high, and stays high when S returns to low; similarly, if R is pulsed high while S is held low, then the Q output is forced low, and stays low when R returns to low.

SR latch operation [14]
Characteristic table Excitation table
SRQnextActionQQnextSR
00Qhold state000X
010reset0110
101set1001
11Xnot allowed11X0

Note: X means don't care, that is, either 0 or 1 is a valid value.

The R = S = 1 combination is called a restricted combination or a forbidden state because, as both NOR gates then output zeros, it breaks the logical equation Q = notQ. The combination is also inappropriate in circuits where both inputs may go low simultaneously (i.e. a transition from restricted to keep). The output would lock at either 1 or 0 depending on the propagation time relations between the gates (a race condition).

To overcome the restricted combination, one can add gates to the inputs that would convert (S,R) = (1,1) to one of the non-restricted combinations. That can be:

• Q = 1 (1,0) – referred to as an S (dominated)-latch
• Q = 0 (0,1) – referred to as an R (dominated)-latch

This is done in nearly every programmable logic controller.

• Keep state (0,0) – referred to as an E-latch

Alternatively, the restricted combination can be made to toggle the output. The result is the JK latch.

The characteristic equation for the SR latch is :

${\displaystyle Q_{\text{next}}={\bar {R}}Q+{\bar {R}}S}$ or ${\displaystyle Q_{\text{next}}={\bar {R}}(Q+S).}$ [15]

Another expression is :

${\displaystyle Q_{\text{next}}=S+{\bar {R}}Q}$ with ${\displaystyle SR=0}$. [16]

#### SR NAND latch

This is an alternate model of the simple SR latch which is built with NAND logic gates. Set and reset now become active low signals, denoted S and R respectively. Otherwise, operation is identical to that of the SR latch. Historically, SR-latches have been predominant from the mathematical convenience of active-low inputs.

SR latch operation
SRAction
00Not allowed
01Q = 1
10Q = 0
11No change

#### SR AND-OR latch

From the teaching point of view, SR latches realised as a pair of cross-coupled components (transistors, gates, tubes, etc.) are rather hard to understand for beginners. A didactically easier to understand model uses a single feedback loop instead of the cross-coupling. The following is an SR latch built with an AND gate with one inverted input and an OR gate.

SR AND-OR latch operation
SRAction
00No change
10Q = 1
X1Q = 0

#### JK latch

The JK latch is much less frequently used than the JK flip-flop. The JK latch follows the following state table:

 JK latch truth table J K Qnext Comment 0 0 Q No change 0 1 0 Reset 1 0 1 Set 1 1 Q Toggle

Hence, the JK latch is an SR latch that is made to toggle its output (oscillate between 0 and 1) when passed the input combination of 11. [17] Unlike the JK flip-flop, the 11 input combination for the JK latch is not very useful because there is no clock that directs toggling. [18]

### Gated latches and conditional transparency

Latches are designed to be transparent. That is, input signal changes cause immediate changes in output. Additional logic can be added to a simple transparent latch to make it non-transparent or opaque when another input (an "enable" input) is not asserted. When several transparent latches follow each other, using the same enable signal, signals can propagate through all of them at once. However, by following a transparent-high latch with a transparent-low (or opaque-high) latch, a master–slave flip-flop is implemented.

#### Gated SR latch

A synchronous SR latch (sometimes clocked SR flip-flop) can be made by adding a second level of NAND gates to the inverted SR latch (or a second level of AND gates to the direct SR latch). The extra NAND gates further invert the inputs so the simple SR latch becomes a gated SR latch (and a simple SR latch would transform into a gated SR latch with inverted enable).

With E high (enable true), the signals can pass through the input gates to the encapsulated latch; all signal combinations except for (0,0) = hold then immediately reproduce on the (Q,Q) output, i.e. the latch is transparent.

With E low (enable false) the latch is closed (opaque) and remains in the state it was left the last time E was high.

The enable input is sometimes a clock signal, but more often a read or write strobe. When the enable input is a clock signal, the latch is said to be level-sensitive (to the level of the clock signal), as opposed to edge-sensitive like flip-flops below.

Gated SR latch operation
E/CAction
0No action (keep state)
1The same as non-clocked SR latch

#### Gated D latch

This latch exploits the fact that, in the two active input combinations (01 and 10) of a gated SR latch, R is the complement of S. The input NAND stage converts the two D input states (0 and 1) to these two input combinations for the next SR latch by inverting the data input signal. The low state of the enable signal produces the inactive "11" combination. Thus a gated D-latch may be considered as a one-input synchronous SR latch. This configuration prevents application of the restricted input combination. It is also known as transparent latch, data latch, or simply gated latch. It has a data input and an enable signal (sometimes named clock, or control). The word transparent comes from the fact that, when the enable input is on, the signal propagates directly through the circuit, from the input D to the output Q. Gated D-latches are also level-sensitive with respect to the level of the clock or enable signal.

Transparent latches are typically used as I/O ports or in asynchronous systems, or in synchronous two-phase systems (synchronous systems that use a two-phase clock), where two latches operating on different clock phases prevent data transparency as in a master–slave flip-flop.

Latches are available as integrated circuits, usually with multiple latches per chip. For example, 74HC75 is a quadruple transparent latch in the 7400 series.

Gated D latch truth table
E/CDQQComment
0XQprevQprevNo change
1001Reset
1110Set

The truth table shows that when the enable/clock input is 0, the D input has no effect on the output. When E/C is high, the output equals D.

#### Earle latch

The classic gated latch designs have some undesirable characteristics. [19] They require double-rail logic or an inverter. The input-to-output propagation may take up to three gate delays. The input-to-output propagation is not constant – some outputs take two gate delays while others take three.

Designers looked for alternatives. [20] A successful alternative is the Earle latch. It requires only a single data input, and its output takes a constant two gate delays. In addition, the two gate levels of the Earle latch can, in some cases, be merged with the last two gate levels of the circuits driving the latch because many common computational circuits have an OR layer followed by an AND layer as their last two levels. Merging the latch function can implement the latch with no additional gate delays. [19] The merge is commonly exploited in the design of pipelined computers, and, in fact, was originally developed by John G. Earle to be used in the IBM System/360 Model 91 for that purpose. [21]

The Earle latch is hazard free. [22] If the middle NAND gate is omitted, then one gets the polarity hold latch, which is commonly used because it demands less logic. [22] [23] However, it is susceptible to logic hazard. Intentionally skewing the clock signal can avoid the hazard. [23]

### D flip-flop

The D flip-flop is widely used. It is also known as a "data" or "delay" flip-flop.

The D flip-flop captures the value of the D-input at a definite portion of the clock cycle (such as the rising edge of the clock). That captured value becomes the Q output. At other times, the output Q does not change. [24] [25] The D flip-flop can be viewed as a memory cell, a zero-order hold, or a delay line. [26]

Truth table:

 Clock D Qnext Rising edge 0 0 Rising edge 1 1 Non-Rising X Q

('X' denotes a Don't care condition, meaning the signal is irrelevant)

Most D-type flip-flops in ICs have the capability to be forced to the set or reset state (which ignores the D and clock inputs), much like an SR flip-flop. Usually, the illegal S = R = 1 condition is resolved in D-type flip-flops. By setting S = R = 0, the flip-flop can be used as described above. Here is the truth table for the others S and R possible configurations:

InputsOutputs
SRD>QQ'
01XX01
10XX10
11XX11

These flip-flops are very useful, as they form the basis for shift registers, which are an essential part of many electronic devices. The advantage of the D flip-flop over the D-type "transparent latch" is that the signal on the D input pin is captured the moment the flip-flop is clocked, and subsequent changes on the D input will be ignored until the next clock event. An exception is that some flip-flops have a "reset" signal input, which will reset Q (to zero), and may be either asynchronous or synchronous with the clock.

The above circuit shifts the contents of the register to the right, one bit position on each active transition of the clock. The input X is shifted into the leftmost bit position.

#### Classical positive-edge-triggered D flip-flop

This circuit [27] consists of two stages implemented by SR NAND latches. The input stage (the two latches on the left) processes the clock and data signals to ensure correct input signals for the output stage (the single latch on the right). If the clock is low, both the output signals of the input stage are high regardless of the data input; the output latch is unaffected and it stores the previous state. When the clock signal changes from low to high, only one of the output voltages (depending on the data signal) goes low and sets/resets the output latch: if D = 0, the lower output becomes low; if D = 1, the upper output becomes low. If the clock signal continues staying high, the outputs keep their states regardless of the data input and force the output latch to stay in the corresponding state as the input logical zero (of the output stage) remains active while the clock is high. Hence the role of the output latch is to store the data only while the clock is low.

The circuit is closely related to the gated D latch as both the circuits convert the two D input states (0 and 1) to two input combinations (01 and 10) for the output SR latch by inverting the data input signal (both the circuits split the single D signal in two complementary S and R signals). The difference is that in the gated D latch simple NAND logical gates are used while in the positive-edge-triggered D flip-flop SR NAND latches are used for this purpose. The role of these latches is to "lock" the active output producing low voltage (a logical zero); thus the positive-edge-triggered D flip-flop can also be thought of as a gated D latch with latched input gates.

#### Master–slave edge-triggered D flip-flop

A master–slave D flip-flop is created by connecting two gated D latches in series, and inverting the enable input to one of them. It is called master–slave because the second latch in the series only changes in response to a change in the first (master) latch.

For a positive-edge triggered master–slave D flip-flop, when the clock signal is low (logical 0) the "enable" seen by the first or "master" D latch (the inverted clock signal) is high (logical 1). This allows the "master" latch to store the input value when the clock signal transitions from low to high. As the clock signal goes high (0 to 1) the inverted "enable" of the first latch goes low (1 to 0) and the value seen at the input to the master latch is "locked". Nearly simultaneously, the twice inverted "enable" of the second or "slave" D latch transitions from low to high (0 to 1) with the clock signal. This allows the signal captured at the rising edge of the clock by the now "locked" master latch to pass through the "slave" latch. When the clock signal returns to low (1 to 0), the output of the "slave" latch is "locked", and the value seen at the last rising edge of the clock is held while the "master" latch begins to accept new values in preparation for the next rising clock edge.

By removing the leftmost inverter in the circuit at side, a D-type flip-flop that strobes on the falling edge of a clock signal can be obtained. This has a truth table like this:

 D Q > Qnext 0 X Falling 0 1 X Falling 1

#### Dual-edge-triggered D flip-flop

Flip-Flops that read in a new value on the rising and the falling edge of the clock are called dual-edge-triggered flip-flops. Such a flip-flop may be built using two single-edge -triggered D-type flip-flops and a multiplexer as shown in the image.

#### Edge-triggered dynamic D storage element

An efficient functional alternative to a D flip-flop can be made with dynamic circuits (where information is stored in a capacitance) as long as it is clocked often enough; while not a true flip-flop, it is still called a flip-flop for its functional role. While the master–slave D element is triggered on the edge of a clock, its components are each triggered by clock levels. The "edge-triggered D flip-flop", as it is called even though it is not a true flip-flop, does not have the master–slave properties.

Edge-triggered D flip-flops are often implemented in integrated high-speed operations using dynamic logic. This means that the digital output is stored on parasitic device capacitance while the device is not transitioning. This design of dynamic flip flops also enables simple resetting since the reset operation can be performed by simply discharging one or more internal nodes. A common dynamic flip-flop variety is the true single-phase clock (TSPC) type which performs the flip-flop operation with little power and at high speeds. However, dynamic flip-flops will typically not work at static or low clock speeds: given enough time, leakage paths may discharge the parasitic capacitance enough to cause the flip-flop to enter invalid states.

### T flip-flop

If the T input is high, the T flip-flop changes state ("toggles") whenever the clock input is strobed. If the T input is low, the flip-flop holds the previous value. This behavior is described by the characteristic equation:

${\displaystyle Q_{\text{next}}=T\oplus Q=T{\overline {Q}}+{\overline {T}}Q}$ (expanding the XOR operator)

and can be described in a truth table:

T flip-flop operation [28]
Characteristic table Excitation table
${\displaystyle T}$${\displaystyle Q}$${\displaystyle Q_{\text{next}}}$Comment${\displaystyle Q}$${\displaystyle Q_{\text{next}}}$${\displaystyle T}$Comment
000hold state (no clk)000No change
011hold state (no clk)110No change
101toggle011Complement
110toggle101Complement

When T is held high, the toggle flip-flop divides the clock frequency by two; that is, if clock frequency is 4 MHz, the output frequency obtained from the flip-flop will be 2 MHz. This "divide by" feature has application in various types of digital counters. A T flip-flop can also be built using a JK flip-flop (J & K pins are connected together and act as T) or a D flip-flop (T input XOR Qprevious drives the D input).

### JK flip-flop

The JK flip-flop augments the behavior of the SR flip-flop (J=Set, K=Reset) by interpreting the J = K = 1 condition as a "flip" or toggle command. Specifically, the combination J = 1, K = 0 is a command to set the flip-flop; the combination J = 0, K = 1 is a command to reset the flip-flop; and the combination J = K = 1 is a command to toggle the flip-flop, i.e., change its output to the logical complement of its current value. Setting J = K = 0 maintains the current state. To synthesize a D flip-flop, simply set K equal to the complement of J. Similarly, to synthesize a T flip-flop, set K equal to J. The JK flip-flop is therefore a universal flip-flop, because it can be configured to work as an SR flip-flop, a D flip-flop, or a T flip-flop.

The characteristic equation of the JK flip-flop is:

${\displaystyle Q_{\text{next}}=J{\overline {Q}}+{\overline {K}}Q}$

and the corresponding truth table is:

JK flip-flop operation [28]
Characteristic table Excitation table
JKCommentQnextQQnextCommentJK
00hold stateQ00No Change0X
01reset001Set1X
10set110ResetX1
11toggleQ11No ChangeX0

## Timing considerations

### Timing parameters

The input must be held steady in a period around the rising edge of the clock known as the aperture. Imagine taking a picture of a frog on a lily-pad. [29] Suppose the frog then jumps into the water. If you take a picture of the frog as it jumps into the water, you will get a blurry picture of the frog jumping into the water—it's not clear which state the frog was in. But if you take a picture while the frog sits steadily on the pad (or is steadily in the water), you will get a clear picture. In the same way, the input to a flip-flop must be held steady during the aperture of the flip-flop.

Setup time is the minimum amount of time the data input should be held steady before the clock event, so that the data is reliably sampled by the clock.

Hold time is the minimum amount of time the data input should be held steady after the clock event, so that the data is reliably sampled by the clock.

Aperture is the sum of setup and hold time. The data input should be held steady throughout this time period. [29]

Recovery time is the minimum amount of time the asynchronous set or reset input should be inactive before the clock event, so that the data is reliably sampled by the clock. The recovery time for the asynchronous set or reset input is thereby similar to the setup time for the data input.

Removal time is the minimum amount of time the asynchronous set or reset input should be inactive after the clock event, so that the data is reliably sampled by the clock. The removal time for the asynchronous set or reset input is thereby similar to the hold time for the data input.

Short impulses applied to asynchronous inputs (set, reset) should not be applied completely within the recovery-removal period, or else it becomes entirely indeterminable whether the flip-flop will transition to the appropriate state. In another case, where an asynchronous signal simply makes one transition that happens to fall between the recovery/removal time, eventually the flip-flop will transition to the appropriate state, but a very short glitch may or may not appear on the output, dependent on the synchronous input signal. This second situation may or may not have significance to a circuit design.

Set and Reset (and other) signals may be either synchronous or asynchronous and therefore may be characterized with either Setup/Hold or Recovery/Removal times, and synchronicity is very dependent on the design of the flip-flop.

Differentiation between Setup/Hold and Recovery/Removal times is often necessary when verifying the timing of larger circuits because asynchronous signals may be found to be less critical than synchronous signals. The differentiation offers circuit designers the ability to define the verification conditions for these types of signals independently.

### Metastability

Flip-flops are subject to a problem called metastability, which can happen when two inputs, such as data and clock or clock and reset, are changing at about the same time. When the order is not clear, within appropriate timing constraints, the result is that the output may behave unpredictably, taking many times longer than normal to settle to one state or the other, or even oscillating several times before settling. Theoretically, the time to settle down is not bounded. In a computer system, this metastability can cause corruption of data or a program crash if the state is not stable before another circuit uses its value; in particular, if two different logical paths use the output of a flip-flop, one path can interpret it as a 0 and the other as a 1 when it has not resolved to stable state, putting the machine into an inconsistent state. [30]

The metastability in flip-flops can be avoided by ensuring that the data and control inputs are held valid and constant for specified periods before and after the clock pulse, called the setup time (tsu) and the hold time (th) respectively. These times are specified in the data sheet for the device, and are typically between a few nanoseconds and a few hundred picoseconds for modern devices. Depending upon the flip-flop's internal organization, it is possible to build a device with a zero (or even negative) setup or hold time requirement but not both simultaneously.

Unfortunately, it is not always possible to meet the setup and hold criteria, because the flip-flop may be connected to a real-time signal that could change at any time, outside the control of the designer. In this case, the best the designer can do is to reduce the probability of error to a certain level, depending on the required reliability of the circuit. One technique for suppressing metastability is to connect two or more flip-flops in a chain, so that the output of each one feeds the data input of the next, and all devices share a common clock. With this method, the probability of a metastable event can be reduced to a negligible value, but never to zero. The probability of metastability gets closer and closer to zero as the number of flip-flops connected in series is increased. The number of flip-flops being cascaded is referred to as the "ranking"; "dual-ranked" flip flops (two flip-flops in series) is a common situation.

So-called metastable-hardened flip-flops are available, which work by reducing the setup and hold times as much as possible, but even these cannot eliminate the problem entirely. This is because metastability is more than simply a matter of circuit design. When the transitions in the clock and the data are close together in time, the flip-flop is forced to decide which event happened first. However fast the device is made, there is always the possibility that the input events will be so close together that it cannot detect which one happened first. It is therefore logically impossible to build a perfectly metastable-proof flip-flop. Flip-flops are sometimes characterized for a maximum settling time (the maximum time they will remain metastable under specified conditions). In this case, dual-ranked flip-flops that are clocked slower than the maximum allowed metastability time will provide proper conditioning for asynchronous (e.g., external) signals.

### Propagation delay

Another important timing value for a flip-flop is the clock-to-output delay (common symbol in data sheets: tCO) or propagation delay (tP), which is the time a flip-flop takes to change its output after the clock edge. The time for a high-to-low transition (tPHL) is sometimes different from the time for a low-to-high transition (tPLH).

When cascading flip-flops which share the same clock (as in a shift register), it is important to ensure that the tCO of a preceding flip-flop is longer than the hold time (th) of the following flip-flop, so data present at the input of the succeeding flip-flop is properly "shifted in" following the active edge of the clock. This relationship between tCO and th is normally guaranteed if the flip-flops are physically identical. Furthermore, for correct operation, it is easy to verify that the clock period has to be greater than the sum tsu + th.

## Generalizations

Flip-flops can be generalized in at least two ways: by making them 1-of-N instead of 1-of-2, and by adapting them to logic with more than two states. In the special cases of 1-of-3 encoding, or multi-valued ternary logic, these elements may be referred to as flip-flap-flops. [31]

In a conventional flip-flop, exactly one of the two complementary outputs is high. This can be generalized to a memory element with N outputs, exactly one of which is high (alternatively, where exactly one of N is low). The output is therefore always a one-hot (respectively one-cold) representation. The construction is similar to a conventional cross-coupled flip-flop; each output, when high, inhibits all the other outputs. [32] Alternatively, more or less conventional flip-flops can be used, one per output, with additional circuitry to make sure only one at a time can be true. [33]

Another generalization of the conventional flip-flop is a memory element for multi-valued logic. In this case the memory element retains exactly one of the logic states until the control inputs induce a change. [34] In addition, a multiple-valued clock can also be used, leading to new possible clock transitions. [35]

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In digital logic and computing, a counter is a device which stores the number of times a particular event or process has occurred, often in relationship to a clock signal. The most common type is a sequential digital logic circuit with an input line called the clock and multiple output lines. The values on the output lines represent a number in the binary or BCD number system. Each pulse applied to the clock input increments or decrements the number in the counter.

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.

Digital electronics or digital (electronic) circuits are electronics that operate on digital signals. In contrast, analog circuits manipulate analog signals whose performance is more subject to manufacturing tolerance, signal attenuation and noise. Digital techniques are helpful because it is a lot easier to get an electronic device to switch into one of a number of known states than to accurately reproduce a continuous range of values.

In digital circuits, a shift register is a cascade of flip flops, sharing the same clock, in which the output of each flip-flop is connected to the "data" input of the next flip-flop in the chain, resulting in a circuit that shifts by one position the "bit array" stored in it, "shifting in" the data present at its input and 'shifting out' the last bit in the array, at each transition of the clock input.

Verilog, standardized as IEEE 1364, is a hardware description language (HDL) used to model electronic systems. It is most commonly used in the design and verification of digital circuits at the register-transfer level of abstraction. It is also used in the verification of analog circuits and mixed-signal circuits, as well as in the design of genetic circuits. In 2009, the Verilog standard was merged into the SystemVerilog standard, creating IEEE Standard 1800-2009. Since then, Verilog is officially part of the SystemVerilog language. The current version is IEEE standard 1800-2017.

Static random-access memory is a type of semiconductor memory that uses bistable latching circuitry (flip-flop) to store each bit. SRAM exhibits data remanence, but it is still volatile in the conventional sense that data is eventually lost when the memory is not powered.

The 4000 series is a family of integrated circuits (ICs) first introduced in 1968. Almost all IC manufacturers active during this initial era fabricated models for this series. It is still in use today.

In electronics, a Schmitt trigger is a comparator circuit with hysteresis implemented by applying positive feedback to the noninverting input of a comparator or differential amplifier. It is an active circuit which converts an analog input signal to a digital output signal. The circuit is named a "trigger" because the output retains its value until the input changes sufficiently to trigger a change. In the non-inverting configuration, when the input is higher than a chosen threshold, the output is high. When the input is below a different (lower) chosen threshold the output is low, and when the input is between the two levels the output retains its value. This dual threshold action is called hysteresis and implies that the Schmitt trigger possesses memory and can act as a bistable multivibrator. There is a close relation between the two kinds of circuits: a Schmitt trigger can be converted into a latch and a latch can be converted into a Schmitt trigger.

The Intel 8253 and 8254 are Programmable Interval Timers (PITs), which perform timing and counting functions using three 16-bit music counters.

A synchronous circuit is a digital circuit in which the changes in the state of memory elements are synchronized by a clock signal. In a sequential digital logic circuit, data is stored in memory devices called flip-flops or latches. The output of a flip-flop is constant until a pulse is applied to its "clock" input, upon which the input of the flip-flop is latched into its output. In a synchronous logic circuit, an electronic oscillator called the clock generates a string of pulses, the "clock signal". This clock signal is applied to every storage element, so in an ideal synchronous circuit, every change in the logical levels of its storage components is simultaneous. Ideally, the input to each storage element has reached its final value before the next clock occurs, so the behaviour of the whole circuit can be predicted exactly. Practically, some delay is required for each logical operation, resulting in a maximum speed at which each synchronous system can run.

An asynchronous circuit, or self-timed circuit, is a sequential digital logic circuit which is not governed by a clock circuit or global clock signal. Instead it often uses signals that indicate completion of instructions and operations, specified by simple data transfer protocols. This type of circuit is contrasted with synchronous circuits, in which changes to the signal values in the circuit are triggered by repetitive pulses called a clock signal. Most digital devices today use synchronous circuits. However asynchronous circuits have the potential to be faster, and may also have advantages in lower power consumption, lower electromagnetic interference, and better modularity in large systems. Asynchronous circuits are an active area of research in digital logic design.

The DIMS system is an asynchronous design methodology making the least possible timing assumptions. Assuming only the quasi-delay-insensitive delay model the generated designs need little if any timing hazard testing. The basis for DIMS is the use of two wires to represent each bit of data. This is known as a dual-rail data encoding. Parts of the system communicate using the early four-phase asynchronous protocol.

The Muller C-element is a small digital block widely used in design of asynchronous circuits and systems. It has been specified formally in 1955 by David E. Muller and first used in ILLIAC II computer. In terms of the theory of lattices, the C-element is a semimodular distributive circuit, whose operation in time is described by a Hasse diagram. The C-element is closely related to the rendezvous and join elements, where an input is not allowed to change twice in succession. In some cases, when relations between delays are known, the C-element can be realized as a sum-of-product (SOP) circuit ,. Earlier techniques for implementing the C-element include Schmidt trigger, Eccles-Jordan flip-flop and last moving point flip-flop.

Metastability in electronics is the ability of a digital electronics system to persist for an unbounded time in an unstable equilibrium or metastable state. In digital logic circuits, a digital signal is required to be within certain voltage or current limits to represent a '0' or '1' logic level for correct circuit operation; if the signal is within a forbidden intermediate range it may cause faulty behavior in logic gates the signal is applied to. In metastable states, the circuit may be unable to settle into a stable '0' or '1' logic level within the time required for proper circuit operation. As a result, the circuit can act in unpredictable ways, and may lead to a system failure, sometimes referred to as a "glitch". Metastability is an instance of Buridan's paradox.

In digital electronic design a clock domain crossing (CDC), or simply clock crossing, is the traversal of a signal in a synchronous digital circuit from one clock domain into another. If a signal does not assert long enough and is not registered, it may appear asynchronous on the incoming clock boundary.

A frequency divider, also called a clock divider or scaler or prescaler, is a circuit that takes an input signal of a frequency, , and generates an output signal of a frequency:

The memory cell is the fundamental building block of computer memory. The memory cell is an electronic circuit that stores one bit of binary information and it must be set to store a logic 1 and reset to store a logic 0. Its value is maintained/stored until it is changed by the set/reset process. The value in the memory cell can be accessed by reading it.

Low Power flip-flops are flip-flops that are designed for low-power electronics, such as smartphones and notebooks. A flip-flop, or latch, is a circuit that has two stable states and can be used to store state information.

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