Lecture #31 Flip-Flops, Clocks, Timing
• Last lecture:
– Finite State Machines
• This lecture:
– Digital circuits with feedback
– Clocks
– Flip-Flops
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Clocked Logic
• In the last few lectures, we have been
discussing the implementation of circuits
which can break a problem down into a
sequence of events, as contrasted with
evaluation of a single Boolean expression
(Combinatorial Logic)
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Definition: Combinatorial logic
Combinatorial logic is a set of digital gates
which produces an output based solely on
its current inputs. A combinatorial logic
circuit can be described using a truth table
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Definition: Truth table
• A Truth table is a description of a digital
circuit which is a tabulation of all possible
inputs, and the outputs which will result
from those inputs.
• Two combinatorial logic circuits are
considered logically equivalent if they have
the same truth table
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Sequential Logic
• In order to solve more complex problems
using a sequence of steps, we looked at
the concept of feedback of the output of
intermediate results back into the circuit
for additional processing. In solving the
problems caused by this, we arrived at the
finite state machine with latched and
clocked feedback.
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• In the next two lectures, we will discuss
the implementation of sequential logic,
latches, clocks, and the various problems
which can occur in dynamic digital logic
circuits.
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Memory with Cross-coupled
Gates
• Cross-coupled NOR gates
– Similar to inverter pair, with capability to force output to 0
(reset=1) or 1 (set=1)
R
Q
S
Q'
Q
R
S
• Cross-coupled NAND gates
– Similar to inverter pair, with capability to force output to 0
(reset=0) or 1 (set=0)
S'
R'
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Q
S'
R'
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Q
Q'
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Timing Behavior
Reset
Hold
R
Q
S
Q'
Set
Reset
Set
100
Race
R
S
Q
\Q
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Race condition on falling edge of
S/R
• If both set and reset are high, then the
value latched will be whichever falling
edge happens last. If this is controlled by
delays in the logic, then the outcome of
which is first might be random, erratic, or
dependent on other parameters.
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Definition: Race, or Race condition
• A Race condition is when a device's output
depends on two [or more] nearly simultaneous
events to occur, and where which signal arrives
first will change the output of the circuit. If the
race condition is so close in time, the output may
be unpredictable. When the circuit is
manufactured, slight differences can cause a
change in the operation of the circuit. A race
condition can be a logic hazard, or can result in
a random value being held in a latch.
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Definition: Glitch, Hazard
• A Glitch is a momentary output of a digital circuit of an incorrect
value
• A Static Hazard is when a single variable change at the input causes
a momentary change in the output.
• A Dynamic Hazard occurs when a change in the input causes
multiple changes in the output.
Latches can remove glitches by allowing the output to progress only
after the logic has had adequate time to stabilize on the correct
output. It is desirable to design out hazard in the logic, because the
extra transitions consume power and produce excess noise.
If Static Hazards are removed from the design, Dynamic Hazards
will not occur. If not removed by latches or Flip-Flops, timing hazards
will develop as random or intermittent circuit failures.
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Definition: Latch
• A latch is a digital circuit which will hold a
value when the level of a latching signal is
at a certain level. For example, while the
reset signal is low, the SR latch will hold
the value of Q, (and set it if Set goes high).
The alternative is to set the output only at
an rising or falling edge, which is referred
to as being edge triggered.
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Level Trigger
• A level trigger refers to the capture of a
value while a signal (clock, for example, is
high (or low). The data must be held valid
and stable during the entire time it is being
sampled
Data
Clock
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Gated R-S Latch
• Control when R and S
inputs matter
– Otherwise, the
slightest glitch on R or
S while enable is low
could cause
change in value stored
Set
R
R'
Q
enable'
Q'
S'
S
100
Reset
S'
R'
enable'
Q
Q'
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R-S latch controlled with clock
• Controlling an R-S latch with a clock
– Can't let R and S change while clock is active (allowing R and S
to pass)
– Only have half of clock period for signal changes to propagate
– Signals must be stable for the other half of clock period
R'
R
Q
clock'
S'
Q'
S
stable changing stable changing stable
R' and S'
clock
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active low
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Edge Trigger
• Edge Trigger refers to the capture of a
value at a rising or falling edge of a signal.
For example, the data from a memory
might be held valid and sampled at a rising
edge of a clock
Data
Clock
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Definition: Flip-Flop
• A flip flop is a digital circuit which will
capture a value at a rising (or falling) edge,
and will hold that value. It will only change
the value held at an edge, and will not
pass on transitions from the inputs while
the clock or latch signal is either high or
low.
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Cascading Latches
• Connect output of one latch to input of another
• How to stop changes from racing through chain?
– Need to control flow of data from one latch to the next
– Advance from one latch per clock period
– Must worry about logic between latches (arrows) that is too fast
R
R
Q'
R
Q'
S
S
Q
S
Q
clock
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Master-Slave Structure
• Break flow by alternating clocks (like an air-lock)
– Use positive clock to latch inputs into one R-S latch
– Use negative clock to change outputs with another R-S latch
• View pair as one basic unit
– master-slave flip-flop
– twice as much logic
– output changes a few gate delays after the falling edge of clock
but does not affect any cascaded flip-flops
slave stage
master stage
R
R
Q'
S
S
Q
P'
P
R
Q'
S
Q
CLK
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The 1s Catching Problem
• In first R-S stage of master-slave FF
– 0-1-0 glitch on R or S while clock is high "caught" by master
stage
– Leads to constraints on logic to be hazard-free
slave stage
master stage
Set
S
R
CLK
P
P'
Q
Q'
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Reset
1s
catch
R
R
Q'
S
S
Q
P'
P
R
Q'
S
Q
CLK
Master
Outputs
Slave
Outputs
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D Flip-Flop
• Make S and R complements of each other
– Eliminates 1s catching problem
– Can't just hold previous value (must have new value ready every
clock period)
– Value of D just before clock goes low is what is stored in flip-flop
– Can make R-S flip-flop by adding logic to make D = S + R' Q
– The value at the output (Q, Q’) only changes based on the value
of the falling edge of the clock of the master stage
slave stage
master stage
D
R
Q'
S
Q
P'
P
CLK
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R
Q'
Q'
S
Q
Q
10 gates
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Edge triggering
• The proceeding slide showed how a flip
flop could be designed by using two
latches which are cascaded in a masterslave relationship.
• Another way of creating an edge triggered
flip flop is to use logic with feedback, as in
the following slide.
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Edge-Triggered Flip-Flops
• More efficient solution: only 6 gates
– sensitive to inputs only near edge of clock signal (not while high)
holds D' when
clock goes low
R
Q
Clk=1
S
Q’
holds D when
clock goes low
D
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negative edge-triggered D
flip-flop (D-FF)
4-5 gate delays
must respect setup and hold time
constraints to successfully
capture input
characteristic equation
Q(t+1) = D
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Edge-Triggered Flip-Flops
(cont’d)
D’
• Step-by-step analysis
D’
D
D
D’
D’
R
R
Q
Q
Clk=0
Clk=0
S
S
D
D
new D
D
D’
D’
new D  old D
when clock goes high-to-low
data is latched
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when clock is low
data is held
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Edge-Triggered Flip-Flops
(cont’d)
• Positive edge-triggered
– Inputs sampled on rising edge; outputs change after rising edge
• Negative edge-triggered flip-flops
– Inputs sampled on falling edge; outputs change after falling edge
100
D
CLK
Qpos
positive edge-triggered FF
Qpos'
Qneg
negative edge-triggered FF
Qneg'
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Timing Methodologies
• Rules for interconnecting components and clocks
– Guarantee proper operation of system when strictly followed
• Approach depends on building blocks used for memory
elements
– Focus on systems with edge-triggered flip-flops
• Found in programmable logic devices
– Many custom integrated circuits focus on level-sensitive latches
• Basic rules for correct timing:
– (1) Correct inputs, with respect to time, are provided to the flip-flops
– (2) No flip-flop changes state more than once per clocking event
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Timing Methodologies (cont’d)
• Definition of terms
– clock: periodic event, causes state of memory element to
change; can be rising or falling edge, or high or low level
– setup time: minimum time before the clocking event by which the
input must be stable (Tsu)
– hold time: minimum time after the clocking event until which the
input must remain stable (Th)
Tsu Th
data
D Q
D Q
input
clock
there is a timing "window"
around the clocking event
during which the input must
remain
stable and unchanged
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in order to be recognized
clock
stable changing
data
clock
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Comparison of Latches and
Flip-Flops
D Q
CLK
positive
edge-triggered
flip-flop
D
CLK
Qedge
D Q
G
Qlatch
CLK
transparent
(level-sensitive)
latch
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behavior is the same unless input changes
while the clock is high
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Comparison of Latches and
Flip-Flops (cont’d)
Type
When inputs are sampled When output is valid
unclocked
latch
always
propagation delay from input change
level-sensitive
latch
clock high
(Tsu/Th around falling
edge of clock)
propagation delay from input change
or clock edge (whichever is later)
master-slave
flip-flop
clock high
(Tsu/Th around falling
edge of clock)
propagation delay from falling edge
of clock
negative
clock hi-to-lo transition propagation delay from falling edge
edge-triggered (Tsu/Th around falling of clock
flip-flop
edge of clock)
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Typical Timing Specifications
• Positive edge-triggered D flip-flop
– Setup and hold times
– Minimum clock width
– Propagation delays (low to high, high to low, max and typical)
D
CLK
Q
Tsu Th
20ns 5ns
Tsu
20ns
Th
5ns
Tw 25ns
Tplh
25ns
13ns
Tphl
40ns
25ns
all measurements are made from the clocking event that is,
the rising edge of the clock
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Definition: Metastability
• Metastability is a condition in which a latch
or a Flip-Flop is exactly balanced between
the logic high and logic low states. This
can be caused by an asynchronous data
signal input to a clocked Flip Flop. The
resulting output may stay undefined for
some time.
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Cascading Edge-triggered Flip-Flops
• Shift register
– New value goes into first stage
– While previous value of first stage goes into second stage
– Consider setup/hold/propagation delays (prop must be > hold)
IN
D Q
Q0
D Q
Q1
OUT
CLK
100
IN
Q0
Q1
CLK
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Cascading Edge-triggered FlipFlops (cont’d)
• Why this works
– Propagation delays exceed hold times
– Clock width constraint exceeds setup time
– This guarantees following stage will latch current value before it
changes to new value
In
Q0
Tsu
4ns
Tsu
4ns
Tp
3ns
Q1
Tp
3ns
assumes infinitely fast
distribution of the clock
CLK
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timing constraints
guarantee proper
operation of
cascaded components
Th
2ns
Th
2ns
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Clock Skew
• The problem
– Correct behavior assumes next state of all storage elements
determined by all storage elements at the same time
– tThis is difficult in high-performance systems because time for
clock to arrive at flip-flop is comparable to delays through logic
– Effect of skew on cascaded flip-flops:
In
Q0
100
Q1
CLK1 is a delayed
version of CLK0
CLK0
CLK1
original state: IN = 0, Q0 = 1, Q1 = 1
due to skew, next state becomes: Q0 = 0, Q1 = 0, and not Q0 = 0, Q1 = 1
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Summary of Latches and FlipFlops
• Development of D-Flip-Flop
– Level-sensitive used in custom integrated circuits
• can be made with 4 switches
– Edge-triggered used in programmable logic devices
– Good choice for data storage register
• Historically J-K Flip Flop was popular but now never used
– Similar to R-S but with 1-1 being used to toggle output (complement state)
– Can always be implemented using D-FF
• Preset and clear inputs are highly desirable on flip-flops
– Used at start-up or to reset system to a known state
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