In
electronics
The field of electronics is a branch of physics and electrical engineering that deals with the emission, behaviour and effects of electrons using electronic devices. Electronics uses active devices to control electron flow by amplification ...
, a flip-flop or latch is a
circuit that has two stable states and can be used to store state information – a
bistable multivibrator. The circuit can be made to change state by
signal
In signal processing, a signal is a function that conveys information about a phenomenon. Any quantity that can vary over space or time can be used as a signal to share messages between observers. The '' IEEE Transactions on Signal Processing' ...
s applied to one or more control inputs and will have one or two outputs. It is the basic storage element in
sequential logic
In automata theory, sequential logic is a type of logic circuit whose output depends on the present value of its input signals and on the sequence of past inputs, the input history. This is in contrast to ''combinational logic'', whose output i ...
. Flip-flops and latches are fundamental building blocks of
digital electronics
Digital electronics is a field of electronics involving the study of digital signals and the engineering of devices that use or produce them. This is in contrast to analog electronics and analog signals.
Digital electronic circuits are usual ...
systems used in computers, communications, and many other types of systems.
Flip-flops and latches are used as data storage elements. A flip-flop is a device which stores a single ''
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 ...
'' (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
State may refer to:
Arts, entertainment, and media Literature
* ''State Magazine'', a monthly magazine published by the U.S. Department of State
* ''The State'' (newspaper), a daily newspaper in Columbia, South Carolina, United States
* ''Our S ...
'', and such a circuit is described as
sequential logic
In automata theory, sequential logic is a type of logic circuit whose output depends on the present value of its input signals and on the sequence of past inputs, the input history. This is in contrast to ''combinational logic'', whose output i ...
in electronics. When used in a
finite-state machine
A finite-state machine (FSM) or finite-state automaton (FSA, plural: ''automata''), finite automaton, or simply a state machine, is a mathematical model of computation. It is an abstract machine that can be in exactly one of a finite number o ...
, 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.
Flip-flops can be either level-triggered (asynchronous, transparent or opaque) or edge-triggered (
synchronous
Synchronization is the coordination of events to operate a system in unison. For example, the conductor of an orchestra keeps the orchestra synchronized or ''in time''. Systems that operate with all parts in synchrony are said to be synchronou ...
, or
clock
A clock or a timepiece is a device used to measure and indicate time. The clock is one of the oldest human inventions, meeting the need to measure intervals of time shorter than the natural units such as the day, the lunar month and t ...
ed). 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 ''transparent latches''.
Using this terminology, a level-sensitive flip-flop is called a transparent 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.
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. It was initially called the ''Eccles–Jordan trigger circuit'' and consisted of two active elements (
vacuum tube
A vacuum tube, electron tube, valve (British usage), or tube (North America), is a device that controls electric current flow in a high vacuum between electrodes to which an electric potential difference has been applied.
The type known as ...
s). The design was used in the 1943 British
Colossus codebreaking computer 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. Early flip-flops were known variously as trigger circuits or
multivibrator
A multivibrator is an electronic circuit used to implement a variety of simple two-state devices such as relaxation oscillators, timers, and flip-flops. The first multivibrator circuit, the astable multivibrator oscillator, was invented by Henri ...
s.
According to P. L. Lindley, an engineer at the US
Jet Propulsion Laboratory
The Jet Propulsion Laboratory (JPL) is a federally funded research and development center and NASA field center in the City of La Cañada Flintridge, California, United States.
Founded in the 1930s by Caltech researchers, JPL is owned by NASA an ...
, the flip-flop types detailed below (SR, D, T, JK) were first discussed in a 1954
UCLA
The University of California, Los Angeles (UCLA) is a public land-grant research university in Los Angeles, California. UCLA's academic roots were established in 1881 as a teachers college then known as the southern branch of the California ...
course on computer design by Montgomery Phister, and then appeared in his book ''Logical Design of Digital Computers.'' 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
The Hughes Aircraft Company was a major American aerospace and defense contractor founded on February 14, 1934 by Howard Hughes in Glendale, California, as a division of Hughes Tool Company. The company was known for producing, among other pro ...
. 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.
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'',
while the clocked ones are described as ''flip-flops''.
[Latches and Flip Flops](_blank)
(EE 42/100 Lecture 24 from Berkeley) ''"...Sometimes the terms flip-flop and latch are used interchangeably..."''
Simple flip-flops can be built around a single pair of cross-coupled inverting elements:
vacuum tube
A vacuum tube, electron tube, valve (British usage), or tube (North America), is a device that controls electric current flow in a high vacuum between electrodes to which an electric potential difference has been applied.
The type known as ...
s,
bipolar 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 t ...
s,
field effect transistor
The field-effect transistor (FET) is a type of transistor that uses an electric field to control the flow of current in a semiconductor. FETs (JFETs or MOSFETs) are devices with three terminals: ''source'', ''gate'', and ''drain''. FETs contro ...
s,
inverter
A power inverter, inverter or invertor is a power electronic device or circuitry that changes direct current (DC) to alternating current (AC). The resulting AC frequency obtained depends on the particular device employed. Inverters do the opp ...
s, 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
Edge or EDGE may refer to:
Technology Computing
* Edge computing, a network load-balancing system
* Edge device, an entry point to a computer network
* Adobe Edge, a graphical development application
* Microsoft Edge, a web browser developed ...
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
Drawing is a form of visual art in which an artist uses instruments to mark paper or other two-dimensional surface. Drawing instruments include graphite pencils, pen and ink, various kinds of paints, inked brushes, colored pencils, crayons, c ...
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"), 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, in terms of the input signal(s) and/or the current output,
.
Simple set-reset latches
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 or
NAND logic gates. The stored bit is present on the output marked Q.
SR NOR latch
While the R and S inputs are both low,
feedback maintains the Q and outputs in a constant state, with 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.
:
''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 = not . 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
A race condition or race hazard is the condition of an electronics, software, or other system where the system's substantive behavior is Sequential logic, dependent on the sequence or timing of other uncontrollable events. It becomes a software ...
).
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 :
:
or
Another expression is :
:
with
NAND latch
The circuit shown below is a basic NAND latch. The inputs are generally designated S and R for Set and Reset respectively. Because the NAND inputs must normally be logic 1 to avoid affecting the latching action, the inputs are considered to be inverted in this circuit (or active low).
The circuit uses feedback to "remember" and retain its logical state even after the controlling input signals have changed. When the S and R inputs are both high, feedback maintains the Q outputs to the previous state.
SR AND-OR latch
From a teaching point of view, SR latches drawn as a pair of cross-coupled components (transistors, gates, tubes, etc.) are often hard to understand for beginners. A didactically easier to understand way is to draw the latch as a single feedback loop instead of the cross-coupling. The following is an SR latch built with an
AND
or AND may refer to:
Logic, grammar, and computing
* Conjunction (grammar), connecting two words, phrases, or clauses
* Logical conjunction in mathematical logic, notated as "∧", "⋅", "&", or simple juxtaposition
* Bitwise AND, a boolea ...
gate with one
inverted input and an
OR gate. Note that the inverter is not needed for the latch functionality, but rather to make both inputs High-active.
:
Note that the SR AND-OR latch has the benefit that S = 1, R = 1 is well defined. In above version of the SR AND-OR latch it gives priority to the R signal over the S signal. If priority of S over R is needed, this can be achieved by connecting output Q to the output of the OR gate instead of the output of the AND gate.
The SR AND-OR latch is easier to understand, because both gates can be explained in isolation. When neither S or R is set, then both the OR gate and the AND gate are in "hold mode", i.e., their output is the input from the feedback loop. When input S = 1, then the output of the OR gate becomes 1, regardless of the other input from the feedback loop ("set mode"). When input R = 1 then the output of the AND gate becomes 0, regardless of the other input from the feedback loop ("reset mode"). And since the output Q is directly connected to the output of the AND gate, R has priority over S. Latches drawn as cross-coupled gates may look less intuitive, as the behaviour of one gate appears to be intertwined with the other gate.
Note that the SR AND-OR latch can be transformed into the SR NOR latch using logic transformations: inverting the output of the OR gate and also the 2nd input of the AND gate and connecting the inverted Q output between these two added inverters; with the AND gate with both inputs inverted being equivalent to a NOR gate according to
De Morgan's laws
In propositional logic and Boolean algebra, De Morgan's laws, also known as De Morgan's theorem, are a pair of transformation rules that are both valid rules of inference. They are named after Augustus De Morgan, a 19th-century British math ...
.
JK latch
The JK latch is much less frequently used than the JK flip-flop. The JK latch follows the following state table:
:
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. 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.
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 latch becomes a gated SR latch (and a SR latch would transform into a gated 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, ) 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 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 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 system
In digital electronics, 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 are stored in memory devices called flip-fl ...
s that use a
two-phase clock
In electronics and especially synchronous digital circuits, a clock signal (historically also known as ''logic beat'') oscillates between a high and a low state and is used like a metronome to coordinate actions of digital circuits.
A clock sign ...
), 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
The 7400 series of integrated circuits (ICs) are a popular logic family of transistor–transistor logic (TTL) logic chips.
In 1964, Texas Instruments introduced the SN5400 series of logic chips, in a ceramic semiconductor package. A lo ...
.
The truth table below shows that when the ''e''nable/''c''lock input is 0, the D input has no effect on the output. When E/C is high, the output equals D.
File:D-Type Transparent Latch.svg, alt=Schematic diagram, A gated D latch based on an NAND latch
File:D-type Transparent Latch (NOR).svg, A gated D latch based on an SR NOR latch
File:GatedDLatch-lowres.gif, An animated gated D latch. Black and white mean logical '1' and '0', respectively.
File:Multiplexer-based latch using transmission gates.svg, A gated D latch in pass transistor logic In electronics, pass transistor logic (PTL) describes several logic families used in the design of integrated circuits. It reduces the count of transistors used to make different logic gates, by eliminating redundant transistors. Transistors are u ...
, similar to the ones in the CD4042 or the CD74HC75 integrated circuits.
Earle latch
The classic gated latch designs have some undesirable characteristics.
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. 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.
[ 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
The IBM System/360 Model 91 was announced in 1964 as a competitor to the CDC 6600. Functionally, the Model 91 ran like any other large-scale System/360, but the internal organization was the most advanced of the System/360 line, and it was the ...
for that purpose.
The Earle latch is hazard free.[
] If the middle NAND gate is omitted, then one gets the polarity hold latch, which is commonly used because it demands less logic.[
] However, it is susceptible to logic hazard
In digital logic, a hazard is an undesirable effect caused by either a deficiency in the system or external influences in both synchronous circuit, synchronous and asynchronous circuits. Logic hazards are manifestations of a problem in which cha ...
. Intentionally skewing the clock signal can avoid the hazard.[
File:SVG Earle Latch.svg, Earle latch uses complementary enable inputs: enable active low (E_L) and enable active high (E_H)
File:EarleLatch-lowres.gif, An animated Earle latch. Black and white mean logical '1' and '0', respectively.
]
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. The D flip-flop can be viewed as a memory cell, a zero-order hold
The zero-order hold (ZOH) is a mathematical model of the practical signal reconstruction done by a conventional digital-to-analog converter (DAC). That is, it describes the effect of converting a discrete-time signal to a continuous-time sign ...
, or a delay line.
Truth table:
:
(''X'' denotes a ''don't care
In digital logic, a don't-care term (abbreviated DC, historically also known as ''redundancies'', ''irrelevancies'', ''optional entries'', ''invalid combinations'', ''vacuous combinations'', ''forbidden combinations'', ''unused states'' or ''l ...
'' 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. Setting S = R = 0 makes the flip-flop behave as described above. Here is the truth table for the other possible S and R configurations:
:
These flip-flops are very useful, as they form the basis for shift registers
A shift register is a type of digital circuit using a cascade of flip-flops where the output of one flip-flop is connected to the input of the next. They share a single clock signal, which causes the data stored in the system to shift from one lo ...
, 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 consists of two stages implemented by 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 latch by inverting the data input signal (both the circuits split the single D signal in two complementary and 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 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 master latch controls the slave latch's output value Q and forces the slave latch to hold its value whenever the slave latch is enabled, as the slave latch always copies its new value from the master latch and changes its value only in response to a change in the value of the master latch and clock signal.
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.
Removing the leftmost inverter in the circuit creates a D-type flip-flop that strobes on the ''falling edge'' of a clock signal. This has a truth table like this:
:
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:
: (expanding the XOR operator)
and can be described in a 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 ...
:
:
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 counter
Counter may refer to:
Mathematics and computing
* Counter machine, a subclass of register machines
* Counter (digital), an electronic device, mechanical device, or computer program for counting
* Loop counter, the variable that controls the iter ...
s. 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 (input J will act as input D). 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:
:
and the corresponding truth table is:
:
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. 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.
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
In chemistry and physics, metastability denotes an intermediate energetic state within a dynamical system other than the system's state of least energy.
A ball resting in a hollow on a slope is a simple example of metastability. If the ball i ...
, 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.
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
Propagation delay is the time duration taken for a signal to reach its destination. It can relate to networking, electronics or physics. ''Hold time'' is the minimum interval required for the logic level to remain on the input after triggering ed ...
(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
A shift register is a type of digital circuit using a cascade of flip-flops where the output of one flip-flop is connected to the input of the next. They share a single clock signal, which causes the data stored in the system to shift from one loc ...
), 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
In logic, a three-valued logic (also trinary logic, trivalent, ternary, or trilean, sometimes abbreviated 3VL) is any of several many-valued logic systems in which there are three truth values indicating ''true'', ''false'' and some indeterminat ...
, such an element may be referred to as a ''flip-flap-flop''.
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
In digital circuits and machine learning, a one-hot is a group of bits among which the legal combinations of values are only those with a single high (1) bit and all the others low (0). A similar implementation in which all bits are '1' except ...
(respectively ''one-cold'') representation. The construction is similar to a conventional cross-coupled flip-flop; each output, when high, inhibits all the other outputs. 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.
Another generalization of the conventional flip-flop is a memory element for multi-valued logic
Many-valued logic (also multi- or multiple-valued logic) refers to a propositional calculus in which there are more than two truth values. Traditionally, in Aristotle's logical calculus, there were only two possible values (i.e., "true" and "false ...
. In this case the memory element retains exactly one of the logic states until the control inputs induce a change. In addition, a multiple-valued clock can also be used, leading to new possible clock transitions.[
]
See also
* Latching relay
A relay
Electromechanical relay schematic showing a control coil, four pairs of normally open and one pair of normally closed contacts
An automotive-style miniature relay with the dust cover taken off
A relay is an electrically operated switch ...
* Positive feedback
Positive feedback (exacerbating feedback, self-reinforcing feedback) is a process that occurs in a feedback loop which exacerbates the effects of a small disturbance. That is, the effects of a perturbation on a system include an increase in th ...
* Pulse transition detector
* Static random-access memory
Static random-access memory (static RAM or SRAM) is a type of random-access memory (RAM) that uses latching circuitry (flip-flop) to store each bit. SRAM is volatile memory; data is lost when power is removed.
The term ''static'' differe ...
* Sample and hold
In electronics, a sample and hold (also known as sample and follow) circuit is an analog device that samples (captures, takes) the voltage of a continuously varying analog signal and holds (locks, freezes) its value at a constant level for ...
, analog latch
* Schmitt trigger
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 ...
References
External links
FlipFlop Hierarchy
, shows interactive flipflop circuits.
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{{DEFAULTSORT:Flip-Flop (Electronics)
Computer-related introductions in 1918
Digital electronics
Electronic engineering
Digital systems
Logic gates
Computer memory