Download Chapter #6: Sequential Logic Design Contemporary Logic

Programmable and Steering Logic
Chapter #6: Sequential Logic Design
6-1
Chapter Overview
Programmable and Steering Logic
• Sequential Networks
Simple Circuits with Feedback
R-S Latch
J-K Flipflop
Edge-Triggered Flipflops
• Timing Methodologies
Cascading Flipflops for Proper Operation
Narrow Width Clocking vs. Multiphase Clocking
Clock Skew
• Realizing Circuits with Flipflops
Choosing a FF Type
Characteristic Equations
Conversion Among Types
• Metastability and Asynchronous Inputs
• Self-Timed Circuits
6-2
Sequential Switching Networks
X1
X2
.
.
Programmable and Steering Logic
Z1
Switching
Network
Z2
.
.
Xn
Circuits with Feedback:
Some outputs are also inputs
Zm
transistor
Combinational
Logic
Clock
State
Combinational
Logic
Traffic Light Controller is a complex
sequential logic network
Sequential logic forms basis for building
"memory" into circuits
These memory elements are primitive
sequential circuits
Lights and time
control
6-3
Sequential Switching Networks
Simple Circuits with Feedback
Programmable and Steering Logic
Primitive memory elements created from cascaded gates
Simplest gate component: inverter
Basis for commercial static RAM designs
Cross-coupled NOR gates and NAND gates also possible
"1"
Cascaded Inverters: Static Memory Cell
"0"
LD
\LD
A
Selectively break feedback path to load new
value into cell
\LD
Z
LD
6-4
Programmable and Steering Logic
Sequential Switching Networks
Inverter Chains
1
0
1
0
0
A
B
C
D
E
X
Odd # of stages leads to ring oscillator
Snapshot taken just before last inverter changes
Output high
propagating
thru this stage
duty cycle : % of time singal is high during its period
Timing Waveform:
tp = n * td
n = # inverters
Period of Repeating Waveform (tp)
Gate Delay ( td)
A (=X)
0
B
1
C
0
D
1
E
0
1
6-5
Programmable and Steering Logic
Sequential Switching Networks
Inverter Chains
Time
1
1
1
1
1
X
0
0
0
0
X
X
1
1
1
X
X
X
0
0
X
X
X
X
1
0
0
0
0
0
0
1
1
1
1
1
1
0
0
0
0
0
0
1
1
1
1
1
1
0
X
X
X
X
X
0
0
0
0
0
1
Propagation of Signals through the Inverter Chain
6-6
Programmable and Steering Logic
Sequential Switching Networks
Cross-Coupled NOR Gates
Just like cascaded inverters,
with capability to force output
to 0 (reset) or 1 (set)
R
S
R
Q
S
\Q
Timing Waveform
Reset
Hold
Set
Reset
Set
100
Race
R
S
Q
\Q
Forbidden
State
Forbidden
State
6-7
Programmable and Steering Logic
Sequential Switching Networks
State Behavior of R-S Latch
S R
Q
0 0
hold
0 1
0
1 0
1
1 1 unst able
Truth Table Summary
of R-S Latch Behavior
QQ
01
QQ
10
QQ
00
QQ
11
6-8
Programmable and Steering Logic
Sequential Logic Networks
Theoretical R-S Latch State Diagram
SR = 00, 10
SR = 00, 01
SR = 1 0
QQ
01
QQ
10
SR = 0 1
SR = 0 1
SR = 1 0
SR = 11
SR = 1 1
SR = 1 1
QQ
00
SR = 0 1
SR = 1 0
SR = 0 0
SR = 0 0, 11
QQ
11
stays for very short time
6-9
Programmable and Steering Logic
Sequential Logic Networks
Observed R-S Latch Behavior
SR = 00, 10
SR = 00, 01
SR = 1 0
QQ
01
QQ
10
SR = 0 1
SR = 0 1
SR = 1 0
SR = 11
SR = 1 1
SR = 1 1
QQ
00
SR = 0 0
SR = 0 0
Very difficult to observe R-S Latch in the 1-1 state
Ambiguously returns to state 0-1 or 1-0
A so-called "race condition"
6-10
Sequential Switching Networks
Programmable and Steering Logic
Definition of Terms
Tsu
Th
Input
Cloc k
There is a timing
"window" around the
clocking event
during which the input
must remain stable
and unchanged
in order
to be recognized
Clock:
Periodic Event, causes state of memory
element to change
rising edge, falling edge, high level, low level
Setup Time (Tsu)
Minimum time before the clocking event by
which the input must be stable
Hold Time (Th)
Minimum time after the clocking event during
which the input must remain stable
6-11
Programmable and Steering Logic
Sequential Switching Networks
Level-Sensitive Latch
Schematic:
aka Gated R-S Latch
\S
\Q
any level change
is propagated
\R
Q
\enb
Timing Diagram:
Set
Reset
6-12
Sequential Switching Networks
Programmable and Steering Logic
Latches vs. Flipflops
Input/Output Behavior of Latches and Flipflops
Type
unclocked
latch
When Inputs are Sampled
always
When Outputs are Valid
propagation delay from
input change
level
sensitive
latch
clock high
(Tsu, Th around
falling clock edge)
propagation delay from
input change
positive edge
flipflop
clock lo-to-hi transition
(Tsu, Th around
rising clock edge)
propagation delay from
rising edge of clock
negative edge
flipflop
clock hi-to-lo transition
(Tsu, Th around
falling clock edge)
propagation delay from
falling edge of clock
master/slave
flipflop
clock hi-to-lo transition
(Tsu, Th around
falling clock edge)
propagation delay from
falling edge of clock
6-13
Sequential Switching Networks
Programmable and Steering Logic
7474
D
Q
Clk
Pos itive edge-triggered
flip-flop
Edge triggered device sample inputs on the event
edge
Transparent latches sample inputs as long as the
clock is asserted
Timing Diagram:
7476
D
Q
D
C
Clk
Lev el-sens itive
latc h
Bubble here
for negative
edge triggered
device
Clk
Q
7474
Q 7476
Behavior the same unless input changes
while the clock is high
6-14
Programmable and Steering Logic
Sequential Switching Elements
Typical Timing Specifications: Flipflops vs. Latches
74LS74 Positive
Edge Triggered
D Flipflop
•
•
•
•
Setup time
Hold time
Minimum clock width
Propagation delays
(low to high, high to low,
max and typical)
D
Clk
Q
Tsu
20
ns
Th
5
ns
T su
20
ns
Th
5
ns
Tw
25
ns
Tpl h
25 ns
13 ns
T phl
40 ns
25 ns
All measurements are made from the clocking event
that is, the rising edge of the clock
6-15
Programmable and Steering Logic
Sequential Switching Networks
Typical Timing Specifications: Flipflops vs. Latches
74LS76
Transparent
Latch
D
•
•
•
•
Setup time
Hold time
Minimum Clock Width
Propagation Delays:
high to low, low to high,
maximum, typical
data to output
clock to output
Clk
Q
from clock change to output change
T su Th
20 5
ns ns
Tw
20
ns
Tplh
C» Q
27 ns
15 ns
T plh
D»Q
27 ns
15 ns
Tsu
20
ns
Th
5
ns
T phl
C» Q
25 ns
14 ns
T phl
D»Q
16 ns
7 ns
from input change to output change
Measurements from falling clock edge
or rising or falling data edge
6-16
Programmable and Steering Logic
Sequential Switching Elements
R-S Latch Revisited
Truth Table:
Next State = F(S, R, Current State)
Derived K-Map:
S
SR
00
01
11
10
0
0
0
X
1
1
1
0
X
1
Q( t )
R
Characteristic Equation:
Q+ = S + R Q t
S
R
R-S
Latch
Q+
Q
6-17
Programmable and Steering Logic
Sequential Switching Networks
J-K Flipflop
How to eliminate the forbidden state?
Idea: use output feedback to
guarantee that R and S are
never both one
J, K both one yields toggle
K
R
\Q
\Q
R-S
latc h
J
S
Q
Q
Characteristic Equation:
Q+ = Q K + Q J
6-18
Programmable and Steering Logic
Sequential Switching Networks
J-K Latch: Race Condition
Set
Reset
100
Toggle
J
K
Q
\Q
Race Condition
Race : toggle signal asserted while the output change
Toggle Correctness: Single State change per clocking event
Solution: Master/Slave Flipflop
6-19
Programmable and Steering Logic
Sequential Switching Network
Master/Slave J-K Flipflop
Master Stage
K
\Q
R
Slave Stage
\P
R
S
\Q
R-S
Latc h
R-S
Latc h
J
\Q
Q
S
P
Q
Q
Clk
Sample inputs while clock low
Sample inputs while clock high
Uses time to break feedback path from outputs to inputs!
Set
Reset
1's
Catc h
Toggle
100
J
K
Clk
P
\P
Q
\Q
Master
outputs
Correct Toggle
Operation
Slav e
outputs
6-20
Programmable and Steering Logic
Sequential Switching Networks
Edge-Triggered Flipflops
1's Catching: a 0-1-0 glitch on the J or K inputs leads to a state change!
forces designer to use hazard-free logic
Solution: edge-triggered logic
D
Negative Edge-Triggered
D flipflop
D
Hold s D when
clock g oes low
4-5 gate delays
0
R
Q
Clk=1
setup, hold times
necessary to successfully
latch the input
Q
S
0
Hold s D when
clock g oes low
D
D
holding state
Characteristic Equation:
Q+ = D
Negative edge-triggered FF
when clock is high
6-21
Programmable and Steering Logic
Sequential Switching Network
Edge-triggered Flipflops
Step-by-step analysis
D
0
D
4
3
D
R
D
D
R
Q
Clk=0
Q
5
Q
Clk=0
Q
D
D
S
D
S
2
D
D
6
D'
1
D
0
D' ° D
Negative edge-triggered FF
when clock goes high-to-low
data is latched
Negative edge-triggered FF
when clock is low
data is held
D is changed
gate 2,4,5 are holding their values
6-22
Programmable and Steering Logic
Sequential Switching Networks
Positive vs. Negative Edge Triggered Devices
100
D
Clk
Qpos
Pos itive edgetriggered FF
\ Qpos
Qneg
Negative edgetriggered FF
\ Qneg
Positive Edge Triggered
Inputs sampled on rising edge
Outputs change after rising edge
Negative Edge Triggered
Inputs sampled on falling edge
Outputs change after falling edge
Toggle Flipflop
Formed from J-K with both inputs wired together
6-23
Sequential Switching Networks
Programmable and Steering Logic
TTL Latch and Flip-Flop Components
7473 : JK Flip-Flop with active low clear
7473A : Negative Edge-Triggered JK
7474 : D Flip-Flop with clear and preset
What if you need a negative edge triggered D
Invert the clock signal into 7474
Use 7473A and wires J and K together
6-24
Timing Methodology
Programmable and Steering Logic
Overview
• Set of rules for interconnecting components and clocks
• When followed, guarantee proper operation of system
• Approach depends on building blocks used for memory elements
For systems with latches:
Narrow Width Clocking
Multiphase Clocking (e.g., Two Phase Non-Overlapping)
For systems with edge-triggered flipflops:
Single Phase Clocking
• Correct Timing:
(1) correct inputs, with respect to time, are provided to the FFs
(2) no FF changes more than once per clocking event
6-25
Programmable and Steering Logic
Timing Methodologies
Cascaded Flipflops and Setup/Hold/Propagation Delays
Shift Register
S,R are preset, preclear
New value to first stage
while second stage
obtains current value
of first stage
IN
D
Q
C Q
Q0
D
Q
Q1
C Q
CLK
100
In
Correct Operation,
assuming positive
edge triggered FF
Q0
Q1
Clk
6-26
Programmable and Steering Logic
Timing Methodologies
Cascaded Flipflops and Setup/Hold/Propagation Delays
Why this works:
• Propagation delays far exceed hold times;
Clock width constraint exceeds setup time
• This guarantees following stage will latch current value
before it is replaced by new value
• Assumes infinitely fast distribution of the clock
In
Tsu
20 ns
Tsu
20 ns
Q0
Q1
T pl h
13 ns
T pl h
13 ns
Timing constraints
guarantee proper
operation of
cascaded components
Clk
Th
5 ns
Th
5 ns
6-27
Programmable and Steering Logic
Timing Methodologies
Narrow Width Clocking versus Multiphase Clocking
Level Sensitive Latches vs. Edge Triggered Flipflops
• Latches use fewer gates to implement a memory function
• Less complex clocking with edge triggered devices
CMOS Dynamic Storage Element
Feedback path broken by two
phases of the clock
(just like master/slave idea!)
\Clk2
\(LD • Clk1)
A
LD•Clk1
Clk2
Z
8 transistors to implement memory function
but requires two clock signals constrained
to be non-overlapping
Edge-triggered D-FF: 6 gates (5 x 2-input, 1 x 3-input) = 26 transistors!
6-28
Programmable and Steering Logic
Timing Methodologies
Narrow Width Clocking for Systems with Latches for State
Generic Block Diagram
for Clocked Sequential
System
Combinational
logic
state implemented by
latches or edge-triggered FFs
S
t
a
t
e
Cloc k
Two-sided Constraints:
must be careful of very fast signals as well as very slow signals!
Clock Width < fastest propagation through comb. logic
plus latch prop delay
Clock Period > slowest propagation through comb. logic
(rising edge to rising edge)
6-29
Programmable and Steering Logic
Timing Methodologies
Two Phase Non-Overlapped Clocking
Clock Waveforms:
must never overlap!
1
2
only worry about slow signals
1 /1
2 /2
Embedding CMOS storage
element into Clocked Sequential
Logic
Combinational
Logic 1
Combinational
Logic 2
Note that Combinational Logic
can be partitioned into two
pieces
C/L1: inputs latched and stable
by end of phase 1; compute
between phases, latch outputs
by end of phase 2
C/L2: just the reverse
6-30
Programmable and Steering Logic
Timing Methodologies
Generating Two-Phase Non-Overlapping Clocks
Clk
phase1
Single reference clock (or crystal)
Phase 1 high while clock is low
Phase 2 high while clock is high
phase2
Phase X cannot go high until
phase Y goes low!
Use all positive or all negative edge triggered F/F
single phase clock
100
Clk
Phase 1
Phase 2
Non-overlap time can be increased by increasing the delay on
the feedback path
6-31
Programmable and Steering Logic
Timing Methodologies
The Problem of Clock Skew
Correct behavior assumes next state of all storage elements
determined by all storage elements at the same time
Not possible in real systems!
• logical clock driven from more than one physical circuit with
timing behavior
• different wire delay to different points in the circuit
Effect of Skew on Cascaded Flipflops:
FF0 samples IN
In
Q0
FF1 samples Q0
100
CLK2 is a delayed
version of CLK1
Q1
Clk1
Clk2
Original State: Q0 = 1, Q1 = 1, In = 0
Because of skew, next state becomes: Q0 = 0, Q1 = 0,
not Q0 = 0, Q1 = 1
6-32
Timing Methodologies
Programmable and Steering Logic
Design Strategies for Minimizing Clock Skew
Typical propagation delays for LS FFs: 13 ns
Need substantial clock delay (on the order of 13 ns) for skew to
be a problem in this relatively slow technology
Nevertheless, the following are good design practices:
• distribute clock signals in general direction of data flows
• wire carrying the clock between two communicating components
should be as short as possible
• for multiphase clocked systems, distribute all clocks in similar
wire paths; this minimizes the possibility of overlap
• for the non-overlap clock generate, use the phase feedback
signals from the furthest point in the circuit to which the clock
is distributed; this guarantees that the phase is seen as low
everywhere before it allows the next phase to go high
6-33
Realing Circuits with Different Kinds of FFs
Programmable and Steering Logic
Choosing a Flipflop
R-S Clocked Latch:
used as storage element in narrow width clocked systems
its use is not recommended!
however, fundamental building block of other flipflop types
J-K Flipflop:
versatile building block
can be used to implement D and T FFs
usually requires least amount of logic to implement (In,Q,Q+)
but has two inputs with increased wiring complexity
because of 1's catching, never use master/slave J-K FFs
edge-triggered varieties exist
D Flipflop:
minimizes wires, much preferred in VLSI technologies
simplest design technique
best choice for storage registers
T Flipflops:
don't really exist, constructed from J-K FFs
usually best choice for implementing counters
Preset and Clear inputs highly desirable!!
6-34
Programmable and Steering Logic
Realizing Circuits with Different Kinds of Flipflops
Characteristic Equations
R-S:
Q+ = S + R Q
D:
Q+ = D
Derived from the K-maps
for Q+ = (Inputs, Q)
J-K:
Q+ = J Q + K Q
T:
Q+ = T Q + T Q
E.g., J=K=0, then Q+ = Q
J=1, K=0, then Q+ = 1
J=0, K=1, then Q+ = 0
J=1, K=1, then Q+ = Q
Implementing One FF in Terms of Another
D
J
C
K
Q
Q
K
Q
D implemented with J-K
J
D
Q
C
Q
J-K implemented with D
6-35
Programmable and Steering Logic
Realizing Circuits with Different Kinds of Flipflops
Design Procedure
Excitation Tables: What are the necessary inputs to cause a
particular kind of change in state?
Q Q+
0 0
0 1
1 0
1 1
R
X
0
1
0
S
0
1
0
X
J K
0 X
1 X
X 1
X 0
T
0
1
1
0
D
0
1
0
1
D
0
1
0
0
1
1
0
1
Q
Implementing D FF with a J-K FF:
1) Start with K-map of Q+ = (D, Q)
2) Create K-maps for J and K with same inputs (D, Q)
Q+ = D
3) Fill in K-maps with appropriate values for J and K
to cause the same state changes as in the original K-map
D
E.g., D = Q= 0, Q+ = 0
then J = 0, K = X
0
1
0
0
1
1
X
X
Q
J= D
D
0
1
0
X
X
1
1
0
Q
K=D
6-36
Programmable and Steering Logic
Realizing Circuits with Different Kinds of Flipflops
Design Procedure (Continued)
Implementing J-K FF with a D FF:
1) K-Map of Q+ = F(J, K, Q)
2,3) Revised K-map using D's excitation table
its the same! that is why design procedure with D FF is simple!
J
JK
Q
0
1
00 01 11
10
0
0
1
1
1
0
0
1
K
Q+ = D = JQ + KQ
Resulting equation is the combinational logic input to D
to cause same behavior as J-K FF. Of course it is identical
to the characteristic equation for a J-K FF.
6-37
Metastability and Asynchronous Inputs
Programmable and Steering Logic
Terms and Definitions
Clocked synchronous circuits
• common reference signal called the clock
• state of the circuit changes in relation to this clock signal
Asynchronous circuits
• inputs, state, and outputs sampled or changed independent
of a common reference signal
R-S latch is asynchronous, J-K master/slave FF is synchronous
Synchronous inputs
• active only when the clock edge or level is active
Asynchronous inputs
• take effect immediately, without consideration of the clock
Compare R, S inputs of clocked transparent latch vs. plain latch
(level sensitive)
6-38
Metastability and Asynchronous Inputs
Programmable and Steering Logic
Asynchronous Inputs Are Dangerous!
Since they take effect immediately, glitches can be disastrous
Synchronous inputs are greatly preferred!
But sometimes, asynchronous inputs cannot be avoided
e.g., reset signal, memory wait signal
6-39
Metastability and Asynchronous Outputs
Handling Asynchronous Inputs
Programmable and Steering Logic
Clocked
Synchronous
System
Async
Input
D
Q
Synchronizer
Q0
Async
Input
D
Q
D
Q
Clock
Clock
D
Q
Q1
Clock
Q0
D
Q
Q1
Clock
Never allow asynchronous inputs to be fanned out to more than
one FF within the synchronous system
6-40
Metastability and Asynchronous Inputs
What Can Go Wrong
Programmable and Steering Logic
Setup time violation!
In
Q0
In is asynchronous
Fans out to D0 and D1
One FF catches the
signal, one does not
Q1
Clk
impossible state might
be reached!
Single FF that receives the asynchronous signal is a synchronizer
6-41
Metastability and Asynchronous Inputs
Synchronizer Failure
In
D
Q
?
Programmable and Steering Logic
When FF input changes close to clock edge, the FF may
enter the metastable state: neither a logic 0 nor a logic 1
It may stay in this state an indefinate amount of time,
although this is not likely in real circuits
Logic 1
Logic 0
Time
Small, but non-zero probability
that the FF output will get stuck
in an in-between state
Oscilloscope Traces Demonstrating
Synchronizer Failure and Eventual
Decay to Steady State
6-42
Programmable and Steering Logic
Metastability and Asynchronous Inputs
Solutions to Synchronizer Failure
• reset the entire clock
• the probability of failure can never be reduced to 0, but it can be reduced
• slow down the system clock
this gives the synchronizer more time to decay into a steady state
synchronizer failure becomes a big problem for very high speed
systems
• use fastest possible logic in the synchronizer
this makes for a very sharp "peak" upon which to balance
S or AS TTL D-FFs are recommended
• cascade two synchronizers
• use timing strategy that is independent of the speed
Asynchronous
Input
D
Q
D
Synchronized
Input
Q
Clk
Synchronous System
6-43
Self-Timed and Speed Independent Circuits
Limits of Synchronous Systems
Programmable and Steering Logic
Fully synchronous not possible for very large systems
because of problems of clock skew
Partition system into components that are locally clocked
These communicate using "speed independent" protocols
Clocked
Subsystem
Communications
Signals
Clocked
Subsystem
Request/Acknowledgement Signaling
Reques t
S2
S1
requester
client
mas ter
Data Flow
Acknow ledgement
provider
server
slav e
6-44
Self-Timed and Speed Independent Circuits
Synchronous Signaling
Programmable and Steering Logic
Req
Data
Ac k
Clk
Master issues read request; Slave produces data and acks back
Req
Data
Wait
Clk
Alternative Synchronous Scheme:
Slave issues WAIT signal if it cannot satisfy request in one
clock cycle
6-45
Self-Timed and Speed Independent Circuits Programmable and Steering Logic
Asynchronous/Speed Independent Signaling
Communicate information by signal levels rather than edges!
No clock signal
4 Cycle Signaling/Return to Zero Signaling
Req
Data
Ac k
(1) master raises request
slave performs request
(3) master latches data
acks by lowering request
(2) slave "done" by raising
acknowledge
(4) slave resets self by lowing
acknowledge signal
6-46
Self-Timed and Speed Independent Circuits
Programmable and Steering Logic
Alternative: 2 cycle signaling
Non-Return-to-Zero
Req
Data
Ac k
(1) master raises request
slave services request
(2) slave indicates that it is
done by raising acknowledge
Next request indicated by low level of request
Requires additional state in master and slave
to remember previous setting or request/acknowledge
4 Cycle Signaling is more foolproof
6-47
Self-Timed and Speed Independent Circuits Programmable and Steering Logic
Self-Timed Circuits
Determine on their own when a given request has been serviced
No internal clocks
Usually accomplished by modeling worse case delay within
self-timed component
Input
Combinational
logic
Req
Output
Ac k
Delay
Models worst case delay
e.g., if combinational logic is 5 gate levels deep,
delay line between request in and ack out is
also 5 levels deep
6-48
Practical Matters
Programmable and Steering Logic
Debouncing Switches
bouncing : when a switch is flipped from one terminal to another
it does not make a clean, solid contact
solution : debouncing a switch
initial setup
6-49
Practical Matters
Programmable and Steering Logic
• Debouncing a switch
6-50
Practical Matters
Programmable and Steering Logic
• 555 programmable timer
6-51
Practical Matters
Programmable and Steering Logic
• Free-running clock frequency of 555 timer
6-52
Chapter Summary
Programmable and Steering Logic
• Fundamental Building Block of Circuits with State: latch and flipflop
• R-S Latch, J-K master/slave Flipflop, Edge-triggered D Flipflop
• Clocking Methodologies:
For latches: Narrow width clocking vs. Multiphase Non-overlapped
Narrow width clocking and two sided timing constraints
Two phase clocking and single sided timing constraints
For FFs: Single phase clocking with edge triggered flipflops
Cascaded FFs work because propagation delays exceed hold times
Beware of Clock Skew
• Asynchronous Inputs and Their Dangers
Synchronizer Failure: What it is and how to minimize its impact
• Speed Independent Circuits
Asynchronous Signaling Conventions: 4 and 2 Cycle Handshakes
Self-Timed Circuits
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