Introduction to Digital logic design lecture notes

Introduction

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

2. Sequential Circuits 2
NoteNote
Most of the figures are from your Most of the figures are from your
course bookcourse book

3. Sequential Circuits 3
Sequential CircuitsSequential Circuits
CombinationalCombinational
The outputs depend only on the current input valuesThe outputs depend only on the current input values

It uses only logic gatesIt uses only logic gates
Sequential Sequential
The outputs depend on the current and past input The outputs depend on the current and past input
valuesvalues

It uses logic gates and storage elementsIt uses logic gates and storage elements

ExampleExample

Vending machineVending machine

They are referred as finite state machines since they They are referred as finite state machines since they
have a finite number of stateshave a finite number of states

4. Sequential Circuits 4
Block DiagramBlock 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

5. Sequential Circuits 5
Sequential Circuit TypesSequential Circuit Types
Synchronous Synchronous

The circuit behavior is determined by the signals The circuit behavior is determined by the signals
at discrete instants of timeat discrete instants of time

The memory elements are affected only at The memory elements are affected only at
discrete instants of timediscrete 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 pulseof a clock pulse
If memory elements use clock pulses in their If memory elements use clock pulses in their
inputs, the circuit is calledinputs, the circuit is called

Clocked sequential circuitClocked sequential circuit

6. Sequential Circuits 6
Sequential Circuit TypesSequential Circuit Types

ASynchronous ASynchronous

The circuit behavior is determined by the signals The circuit behavior is determined by the signals
at any instant of timeat any instant of time

It is also affected by the order the inputs changeIt is also affected by the order the inputs change

7. Sequential Circuits 7
ClockClock
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 pulsesbetween 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 periodclock cycle time, or period

8. Sequential Circuits 8
Flip-FlopsFlip-Flops
They are memory elementsThey are memory elements
They can store binary informationThey can store binary information

9. Sequential Circuits 9
Flip-FlopsFlip-Flops
Can keep a binary state until an input Can keep a binary state until an input
signal to switch the state is receivedsignal 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 statehow the inputs affect the binary state

10. Sequential Circuits 10
LatchesLatches

The most basic flip-flopsThe most basic flip-flops

They operate with signal levelsThey operate with signal levels

The flip-flops are constructed from The flip-flops are constructed from
latcheslatches
They are not useful for They are not useful for synchronoussynchronous
sequential circuitssequential circuits
They are useful for They are useful for asynchronousasynchronous
sequential circuitssequential circuits

11. Sequential Circuits 11
SR Latch with NORSR Latch with NOR

12. Sequential Circuits 12
SR Latch with NORSR Latch with NOR
1R 1,S avoid ,conditions normalIn
0 set to are Q' and Q undefined, 1R 1,S
statereset 1' ,0
stateset 0' ,1






QQ
QQ
resetR
setS

13. Sequential Circuits 13
SR Latch with NANDSR Latch with NAND

14. Sequential Circuits 14
SR Latch with NANDSR Latch with NAND
0R 0,S avoid ,conditions normalIn
1 set to are Q' and Q undefined, 0R 0,S
statereset 0' ,1
stateset 1' ,0






QQ
QQ
resetR
setS

15. Sequential Circuits 15
SR Latch with Control InputSR Latch with Control Input

16. Sequential Circuits 16
D LatchD Latch

17. Sequential Circuits 17
Symbols for LatchesSymbols for Latches

18. Sequential Circuits 18
NoteNote
The control input changes the state of a The control input changes the state of a
latch or flip-floplatch or flip-flop
The momentary change is called a The momentary change is called a
triggertrigger
Example: D LatchExample: D Latch

It is triggered every time the pulse goes to the It is triggered every time the pulse goes to the
logic level 1logic 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)

19. Sequential Circuits 19
How to Solve?How to Solve?
Trigger the flip-flop only during a signal Trigger the flip-flop only during a signal
transitiontransition

20. Sequential Circuits 20
Edge-Triggered D Flip-FlopEdge-Triggered D Flip-Flop

21. Sequential Circuits 21
Characteristics of D Flip-Characteristics of D Flip-
Flop Flop
DtQ )1(

22. Sequential Circuits 22
Edge-Triggered J-K Flip-FlopEdge-Triggered J-K Flip-Flop
QKJQtQ '')1( 
How???????

23. Sequential Circuits 23
Excitation TableExcitation Table

24. Sequential Circuits 24
Edge-Triggered T Flip-FlopEdge-Triggered T Flip-Flop
QTTQQTtQ '')1( 
)(' 1
)( 0
)1(
tQ
tQ
tQT 

25. Sequential Circuits 25
Excitation TableExcitation Table

26. Sequential Circuits 26
Direct InputsDirect 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 clockregardless of the clock
You can clear the content of a flip-flopYou 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 resetThis is called clear or direct reset

This is particularly useful when the power is offThis is particularly useful when the power is off

The state of the flip-flop is set to unknownThe state of the flip-flop is set to unknown

27. Sequential Circuits 27
D Flip-Flop with D Flip-Flop with
Asynchronous ResetAsynchronous Reset

28. Sequential Circuits 28
State Equations State Equations
 
')(
')1(
)1(
)(')()()(
)()(')1(
)()()()()1(
xBAy
xAtB
BxAxtA
txtBtAty
txtAtB
txtBtxtAtA






A state equation shows
the next state as a
function of the current
state and inputs

29. Sequential Circuits 29
State TableState Table

30. Sequential Circuits 30
State DiagramState Diagram

31. Sequential Circuits 31
Analysis with D Flip-FlopsAnalysis with D Flip-Flops
yxAtA
yxAD
A


)1(

32. Sequential Circuits 32
State ReductionState Reduction
Reduce the number of states but keep Reduce the number of states but keep
the input-output requirementsthe input-output requirements
Reducing the number of states may Reducing the number of states may
reduce the number of flip-flopsreduce the number of flip-flops

If there are If there are n n flip-flops, there are 2^flip-flops, there are 2^nn 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 equivalentare equivalent

They may replace each otherThey may replace each other

33. Sequential Circuits 33
State Reduction ExampleState Reduction Example
Find the states for which the
next states and outputs are
the same

34. Sequential Circuits 34
Example (Cont.)Example (Cont.)
In the next
state, g is
replaced with e
In the next
state, f is
replaced with d

35. Sequential Circuits 35
Example (Cont.)Example (Cont.)

36. Sequential Circuits 36
State AssignmentState 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
implementedimplemented
You need to use enough number of bits You need to use enough number of bits
to cover all the statesto cover all the states

37. Sequential Circuits 37
State AssignmentsState Assignments

38. Sequential Circuits 38
Design ProcedureDesign Procedure
Derive a state diagramDerive a state diagram
Reduce the number of statesReduce the number of states
Assign binary values to the statesAssign binary values to the states
Obtain binary coded state tableObtain binary coded state table
Choose the type of flip-flop to be usedChoose the type of flip-flop to be used
Derive simplified flip-flop input Derive simplified flip-flop input
equations and output equationsequations and output equations
Draw the logic diagramDraw the logic diagram

39. Sequential Circuits 39
ExampleExample

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 detects three or more consecutive 1’s in a
string of bits coming through an input linestring of bits coming through an input line

40. Sequential Circuits 40
Example (Cont.)Example (Cont.)








7,6),,(
7,5,1),,()1(
7,5,3),,()1(
xBAy
xBADtB
xBADtA
B
A

41. Sequential Circuits 41
Example (Cont.)Example (Cont.)

42. Sequential Circuits 42
Example (Cont.)Example (Cont.)

43. Sequential Circuits 43
ExampleExample

Design a circuit (with JK flip-flops) that Design a circuit (with JK flip-flops) that
detects three or more consecutive 1’s in a detects three or more consecutive 1’s in a
string of bits coming through an input linestring of bits coming through an input line

44. Sequential Circuits 44
Example (Cont.)Example (Cont.)

45. Sequential Circuits 45
Example (Cont.)Example (Cont.)

46. Sequential Circuits 46
Example (Cont.)Example (Cont.)

47. Sequential Circuits 47
Study ProblemsStudy Problems
Course Book Chapter – 5 ProblemsCourse Book Chapter – 5 Problems

5 – 35 – 3

5 – 55 – 5
5 – 65 – 6

5 – 75 – 7

5 – 105 – 10
5 – 125 – 12

5 – 135 – 13

5 – 195 – 19

48. Sequential Circuits 48
QuestionsQuestions