Introduction to Digital logic design lecture notes

Sequential Circuits 1
DIGITAL LOGIC DESIGN
by
Dr. Fenghui Yao
Tennessee State University
Department of Computer Science
Nashville, TN

Note
Note
 Most of the figures are from your
Most of the figures are from your
course book
course book

Sequential Circuits
Sequential Circuits
 Combinational
Combinational
 The outputs depend only on the current input values
The outputs depend only on the current input values
 It uses only logic gates
It uses only logic gates
 Sequential
Sequential
 The outputs depend on the current and past input
The outputs depend on the current and past input
values
values
 It uses logic gates and storage elements
It uses logic gates and storage elements
 Example
Example
 Vending machine
Vending machine
 They are referred as finite state machines since they
They are referred as finite state machines since they
have a finite number of states
have a finite number of states

Block Diagram
Block Diagram
 Memory elements can store binary
Memory elements can store binary
information
information
 This information at any given time determines the
This information at any given time determines the
state of the circuit at that time
state of the circuit at that time

Sequential Circuit Types
 Synchronous
Synchronous
 The circuit behavior is determined by the signals
The circuit behavior is determined by the signals
at discrete instants of time
at discrete instants of time
 The memory elements are affected only at
The memory elements are affected only at
discrete instants of time
discrete instants of time
 A clock is used for synchronization
A clock is used for synchronization
 Memory elements are affected only with the arrival
Memory elements are affected only with the arrival
of a clock pulse
of a clock pulse
 If memory elements use clock pulses in their
If memory elements use clock pulses in their
inputs, the circuit is called
inputs, the circuit is called
 Clocked sequential circuit
Clocked sequential circuit

 ASynchronous
ASynchronous
 The circuit behavior is determined by the signals
The circuit behavior is determined by the signals
at any instant of time
at any instant of time
 It is also affected by the order the inputs change
It is also affected by the order the inputs change

Clock
Clock
 It emits a series of pulses with a
It emits a series of pulses with a
precise pulse width and precise interval
precise pulse width and precise interval
between consecutive pulses
between consecutive pulses
 Timing interval between the
Timing interval between the
corresponding edges of two
corresponding edges of two
consecutive pulses is known as the
consecutive pulses is known as the
clock cycle time, or period
clock cycle time, or period

Flip-Flops
Flip-Flops
 They are memory elements
They are memory elements
 They can store binary information
They can store binary information

Flip-Flops
Flip-Flops
 Can keep a binary state until an input
Can keep a binary state until an input
signal to switch the state is received
signal to switch the state is received
 There are different types of flip-flops
There are different types of flip-flops
depending on the number of inputs and
depending on the number of inputs and
how the inputs affect the binary state
how the inputs affect the binary state

Latches
Latches
 The most basic flip-flops
The most basic flip-flops
 They operate with signal levels
They operate with signal levels
 The flip-flops are constructed from
The flip-flops are constructed from
latches
latches
 They are not useful for
They are not useful for synchronous
synchronous
sequential circuits
sequential circuits
 They are useful for
They are useful for asynchronous
asynchronous
sequential circuits
sequential circuits

SR Latch with NOR
SR Latch with NOR

SR Latch with NOR
SR Latch with NOR
1
R
1,
S
avoid
,
conditions
normal
In
0
set to
are
Q'
and
Q
undefined,
1
R
1,
S
state
reset
1
'
,
0
state
set
0
'
,
1













Q
Q
Q
Q
reset
R
set
S

SR Latch with NAND
SR Latch with NAND

SR Latch with NAND
SR Latch with NAND
0
R
0,
S
avoid
,
conditions
normal
In
1
set to
are
Q'
and
Q
undefined,
0
R
0,
S
state
reset
0
'
,
1
state
set
1
'
,
0













Q
Q
Q
Q
reset
R
set
S

SR Latch with Control Input
SR Latch with Control Input

D Latch
D Latch

Symbols for Latches
Symbols for Latches

Note
Note
 The control input changes the state of a
The control input changes the state of a
latch or flip-flop
latch or flip-flop
 The momentary change is called a
The momentary change is called a
trigger
trigger
 Example: D Latch
Example: D Latch
 It is triggered every time the pulse goes to the
It is triggered every time the pulse goes to the
logic level 1
logic level 1
 As long as the pulse remains at the logic level 1,
As long as the pulse remains at the logic level 1,
the change in the data (D) directly affects the
the change in the data (D) directly affects the
output (Q)
output (Q)
 THIS MAY BE A BIG PROBLEM since the state of
THIS MAY BE A BIG PROBLEM since the state of
the latch may keep changing depending on the
the latch may keep changing depending on the
input (may be coming from a combinational logic
input (may be coming from a combinational logic
network)
network)

How to Solve?
How to Solve?
 Trigger the flip-flop only during a signal
Trigger the flip-flop only during a signal
transition
transition

Edge-Triggered D Flip-Flop
Edge-Triggered D Flip-Flop

Characteristics of D Flip-
Characteristics of D Flip-
Flop
Flop
D
t
Q 
 )
1
(

Edge-Triggered J-K Flip-Flop
Edge-Triggered J-K Flip-Flop
Q
K
JQ
t
Q '
'
)
1
( 


How???????

Excitation Table
Excitation Table

Edge-Triggered T Flip-Flop
Edge-Triggered T Flip-Flop
Q
T
TQ
Q
T
t
Q '
'
)
1
( 




)
(
'
1
)
(
0
)
1
(
t
Q
t
Q
t
Q
T 

Excitation Table
Excitation Table

Direct Inputs
Direct Inputs
 You can use asynchronous inputs to
You can use asynchronous inputs to
put a flip-flop to a specific state
put a flip-flop to a specific state
regardless of the clock
regardless of the clock
 You can clear the content of a flip-flop
You can clear the content of a flip-flop
 The content is changed to zero (0)
The content is changed to zero (0)
 This is called clear or direct reset
This is called clear or direct reset
 This is particularly useful when the power is off
This is particularly useful when the power is off
 The state of the flip-flop is set to unknown
The state of the flip-flop is set to unknown

D Flip-Flop with
D Flip-Flop with
Asynchronous Reset
Asynchronous Reset

State Equations
State Equations
 
'
)
(
'
)
1
(
)
1
(
)
(
'
)
(
)
(
)
(
)
(
)
(
'
)
1
(
)
(
)
(
)
(
)
(
)
1
(
x
B
A
y
x
A
t
B
Bx
Ax
t
A
t
x
t
B
t
A
t
y
t
x
t
A
t
B
t
x
t
B
t
x
t
A
t
A














A state equation shows
the next state as a
function of the current
state and inputs

State Table
State Table

State Diagram
State Diagram

Analysis with D Flip-Flops
Analysis with D Flip-Flops
y
x
A
t
A
y
x
A
DA







)
1
(

State Reduction
State Reduction
 Reduce the number of states but keep
Reduce the number of states but keep
the input-output requirements
the input-output requirements
 Reducing the number of states may
Reducing the number of states may
reduce the number of flip-flops
reduce the number of flip-flops
 If there are
If there are n
n flip-flops, there are 2^
flip-flops, there are 2^n
n states
states
 If you have two circuits that produce
If you have two circuits that produce
the same output sequence for any
the same output sequence for any
given input sequence, the two circuits
given input sequence, the two circuits
are equivalent
are equivalent
 They may replace each other
They may replace each other

State Reduction Example
State Reduction Example
Find the states for which the
next states and outputs are
the same

Example (Cont.)
Example (Cont.)
In the next
state, g is
replaced with e
In the next
state, f is
replaced with d

Example (Cont.)
Example (Cont.)

State Assignment
State Assignment
 You need to assign binary values for
You need to assign binary values for
each state so that they can be
each state so that they can be
implemented
implemented
 You need to use enough number of bits
You need to use enough number of bits
to cover all the states
to cover all the states

State Assignments
State Assignments

Design Procedure
Design Procedure
 Derive a state diagram
Derive a state diagram
 Reduce the number of states
Reduce the number of states
 Assign binary values to the states
Assign binary values to the states
 Obtain binary coded state table
Obtain binary coded state table
 Choose the type of flip-flop to be used
Choose the type of flip-flop to be used
 Derive simplified flip-flop input
Derive simplified flip-flop input
equations and output equations
equations and output equations
 Draw the logic diagram
Draw the logic diagram

Example
Example
 Design a circuit (with D flip-flops) that
Design a circuit (with D flip-flops) that
detects three or more consecutive 1’s in a
string of bits coming through an input line

Example (Cont.)
Example (Cont.)
 
 
 










7
,
6
)
,
,
(
7
,
5
,
1
)
,
,
(
)
1
(
7
,
5
,
3
)
,
,
(
)
1
(
x
B
A
y
x
B
A
D
t
B
x
B
A
D
t
A
B
A

Example (Cont.)
Example (Cont.)

Example
Example
 Design a circuit (with JK flip-flops) that
Design a circuit (with JK flip-flops) that

Example (Cont.)
Example (Cont.)

Study Problems
Study Problems
 Course Book Chapter – 5 Problems
Course Book Chapter – 5 Problems
 5 – 3
5 – 3
 5 – 5
5 – 5
 5 – 6
5 – 6
 5 – 7
5 – 7
 5 – 10
5 – 10
 5 – 12
5 – 12
 5 – 13
5 – 13
 5 – 19
5 – 19

Questions
Questions

Introduction to Digital logic design lecture notes

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