Flip-flop (electronics)
From Wikipedia, the free encyclopedia
An SR latch, constructed from a pair of cross-coupled
NOR gates.
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 a fundamental building block of
digital electronics systems used in computers, communications, and many other types of systems.
Flip-flops and latches are used as data storage elements. Such data storage can be used for storage of
state, and such a circuit is described as
sequential logic. 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.
Flip-flops can be either simple (transparent or opaque) or
clocked (synchronous or edge-triggered); the simple ones are commonly called latches.
[1] The word
latch is mainly used for storage elements, while clocked devices are described as
flip-flops.
[2]
History
Flip-flop schematics from the Eccles and Jordan patent filed 1918, one
drawn as a cascade of amplifiers with a positive feedback path, and the
other as a symmetric cross-coupled pair
The first electronic flip-flop was invented in 1918 by
William Eccles and
F. W. Jordan.
[3][4] It was initially called the
Eccles–Jordan trigger circuit and consisted of two active elements (
vacuum tubes).
[5] 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.
[6][7] Early
flip-flops were known variously as trigger circuits or
multivibrators.
According to P. L. Lindley, a
JPL engineer, the flip-flop types discussed below (RS, 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.[8][9]
Lindley was at the time working at Hughes Aircraft under Dr. Eldred
Nelson, who had coined the term JK for a flip-flop which changed states
when both inputs were on. 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 Dr. 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, Dr. 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.
[10]
Implementation
Flip-flops can be either simple (transparent or asynchronous) or
clocked (synchronous); the transparent ones are commonly called latches.
[1] The word
latch is mainly used for storage elements, while clocked devices are described as
flip-flops.
[2]
Simple flip-flops can be built around a 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 to either change
or 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"
[11]),
T ("toggle"), and
JK
types are the common ones. 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,
.
Simple set-reset latches
SR NOR latch
An SR latch, constructed from a pair of cross-coupled
NOR gates (an animated picture). Red and black mean logical '1' and '0', respectively.
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 S and R 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.
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 Q. 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). In certain implementations, it could also lead to longer
ringings (damped
oscillations)
before the output settles, and thereby result in undetermined values
(errors) in high-frequency digital circuits. Although this condition is
usually avoided, it can be useful in some applications.
[citation needed]
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-latch
- Q = 0 (0,1) – referred to as an R-latch
- 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.
Characteristic: Q+ = R'Q + R'S or Q+ = R'Q + S.
[13]
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 despite the notational inconvenience of
active-low inputs.
[citation needed]
| SR latch operation |
| S |
R |
Action |
| 0 |
0 |
Restricted combination |
| 0 |
1 |
Q = 1 |
| 1 |
0 |
Q = 0 |
| 1 |
1 |
No Change |
|
Symbol for an SR NAND latch
|
JK latch
The JK latch is much less 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 when passed the restricted combination of 11. Unlike the JK
flip-flop, the 11 input combination for the SR latch is not useful
because there is no clock that directs toggling.
[14]
Gated latches and conditional transparency
Latches are designed to be
transparent. That is, input signal changes cause immediate changes in output; when several
transparent
latches follow each other, using the same clock signal, signals can
propagate through all of them at once. Alternatively, 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. 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 gated SR latch circuit diagram constructed from NOR gates.
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
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.
Gated SR latch operation
| E/C |
Action |
| 0 |
No action (keep state) |
| 1 |
The same as non-clocked SR latch |
|
Symbol for a gated SR latch
|
Gated D latch
A D-type transparent latch based on an SR NAND latch
A gated D latch based on an SR NOR 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.
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/C |
D |
|
Q |
Q |
Comment |
| 0 |
X |
Qprev |
Qprev |
No change |
| 1 |
0 |
0 |
1 |
Reset |
| 1 |
1 |
1 |
0 |
Set |
|
Symbol for a gated D latch
|
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
Earle latch uses complementary enable inputs: enable active low (E_L) and enable active high (E_H)
The classic gated latch designs have some undesirable characteristics.
[15]
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.
[16] A successful alternative is the Earle latch.
[17]
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
be merged with the last two gate levels of the circuits driving the
latch.
[clarification needed] Merging the latch function can implement the latch with no additional gate delays.
[15]
The Earle latch is hazard free.
[18] If the middle NAND gate is omitted, then one gets the
polarity hold latch, which is commonly used because it demands less logic.
[18][19] However, it is susceptible to
logic hazard. Intentionally skewing the clock signal can avoid the hazard.
[19]
D flip-flop
D flip-flop symbol
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.
[20][21] The D flip-flop can be viewed as a memory cell, a
zero-order hold, or a
delay line.
[citation needed]
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:
-
-
| Inputs |
Outputs |
| S |
R |
D |
> |
Q |
Q' |
| 0 |
1 |
X |
X |
0 |
1 |
| 1 |
0 |
X |
X |
1 |
0 |
| 1 |
1 |
X |
X |
1 |
1 |
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
A positive-edge-triggered D flip-flop
This circuit
[22] 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 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 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.
A master–slave D flip-flop. It responds on the falling edge of the
enable input (usually a clock)
An implementation of a master–slave D flip-flop that is triggered on the rising edge of the clock
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 |
A CMOS IC implementation of a "true single-phase edge-triggered flip-flop with reset"
Edge-triggered dynamic D storage element
An efficient functional alternative to a D flip-flop can be made with
dynamic circuits 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
A circuit symbol for a T-type 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:
| T flip-flop operation[23] |
| Characteristic table |
Excitation table |
 |
|
 |
Comment |
|
|
|
Comment |
| 0 |
0 |
0 |
hold state (no clk) |
0 |
0 |
0 |
No change |
| 0 |
1 |
1 |
hold state (no clk) |
1 |
1 |
0 |
No change |
| 1 |
0 |
1 |
toggle |
0 |
1 |
1 |
Complement |
| 1 |
1 |
0 |
toggle |
1 |
0 |
1 |
Complement |
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 D flip-flop (T input and Q
previous is connected to the D input through an XOR gate).
JK flip-flop
A circuit symbol for a positive-edge-triggered JK flip-flop
JK flip-flop timing diagram
The JK flip-flop augments the behavior of the SR flip-flop (J=Set,
K=Reset) by interpreting the S = R = 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 does NOT result in a D flip-flop, but
rather, will hold 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:
and the corresponding truth table is:
| JK flip-flop operation[23] |
| Characteristic table |
Excitation table |
| J |
K |
Comment |
Qnext |
Q |
J |
K |
Comment |
Qnext |
|
| 0 |
0 |
hold state |
Q |
0 |
0 |
X |
No Change |
0 |
| 0 |
1 |
reset |
0 |
0 |
1 |
X |
Set |
1 |
| 1 |
0 |
set |
1 |
1 |
X |
1 |
Reset |
0 |
| 1 |
1 |
toggle |
Q |
1 |
X |
0 |
No Change |
1 |
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.
[24]
Timing considerations
Setup, hold, recovery, removal times
Flip-flop setup, hold and clock-to-output timing parameters
Setup time is the minimum amount of time the data signal should be held steady
before the clock event so that the data are reliably sampled by the clock. This applies to synchronous input signals to the flip-flop.
Hold time is the minimum amount of time the data signal should be held steady
after the clock event so that the data are reliably sampled. This applies to synchronous input signals to the flip-flop.
Synchronous signals (like Data) should be held steady from the set-up
time to the hold time, where both times are relative to the clock
signal.
Recovery time is like setup time for asynchronous ports (set,
reset). It is the time available between the asynchronous signals going
inactive and the active clock edge.
Removal time is like hold time for asynchronous ports (set,
reset). It is the time between active clock edge and asynchronous signal
going inactive.
[25]
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 asynchronous signal will be
applied, but in that case it is also possible that a very short glitch
may 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
TTL 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.
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 (t
su) and the
hold time (t
h)
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.
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.
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 we make the device,
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.
Propagation delay
Another important timing value for a flip-flop is the clock-to-output delay (common symbol in data sheets: t
CO) or
propagation delay (t
P), which is the time a flip-flop takes to change its output after the clock edge. The time for a high-to-low transition (t
PHL) is sometimes different from the time for a low-to-high transition (t
PLH).
When cascading flip-flops which share the same clock (as in a
shift register), it is important to ensure that the t
CO of a preceding flip-flop is longer than the hold time (t
h)
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 t
CO and t
h
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 t
su + t
h.
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.
[26]
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.
[27]
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.
[28]
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.
[29] In addition, a multiple-valued clock can also be used, leading to new possible clock transitions.
[30]
The 555 timer is capable of being used in astable and monostable
circuits. In an astable circuit, the output voltage alternates between
VCC and 0 volts on
a continual basis.
By selecting values for R1, R2 and C we can determine the period/frequency and the duty cycle.
