Lecture 8 Sequential Logic

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Lecture 8 Sequential Logic
CS147

• Prof. Sin-Min Lee
• Department of Computer Science

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Implement D Flip-flop by T Flip-flop
Q
0 1
Q
0 1
D
T
0 1
0 1
0 0
0 1
1 0
1 1
T D Q D Q D
D
T
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Implement JK Flip-flop by D Flip-flop
Q
0 1
Q
0 1
J K
J K
D
Q

• 0 1
• 0 0
• 0
• 1 1

0 0 0 1 1 1 1 0
0 0 0 1 1 1 1 0

• 0 1
• 0 0
• 0
• 1 1

0 1
0 1
D J Q K Q
Q
J
D
K
Q
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Implement JK Flip-flop by T Flip-flop
Q
Q
Q
0 1
0 1
J K
Q
J K
J K
T
Q

• 0 1
• 0 0
• 0
• 1 1

0 0 0 1 1 1 1 0
0 0 0 1 1 1 1 0

• 0 0
• 0 1
• 1
• 1 0

0 0 0 1 1 0 1 1
Q 0 1 Q
Q Q
0 1
T J Q K Q
Q
J
T
K
Q
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Implement T Flip-flop by JK Flip-flop
Q
J K
T
0 1
Q Q
0 1 1 0
0 X 1 X X 1 X
0
0 0 0 1 1 0 1 1
0 1
Q
Q
T
0 1
T
0 1
X 0 X 1
0 X 1 X
0 1
0 1
K T
J T
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Random-Access Memory

• Can read and write at any point in memory
• Implemented using D Flip-Flops
• Each row contains 16 Flip-Flops
• A Decoder

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Binary Counter

• Holds each pulse in memory
• Each pulse add another number
• Binary format
  
  

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Register

• Used to hold one item of information
• CPUs have many registers
• AX is an example in Assembly

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Clocks and Sequencers

• To perform operations a CPU often requires a
  specific sequence of sub operations
• A sequencer is used to make sure operations
  happen in correct order
• A clock is a circuit that outputs 0s and 1s at
  specific frequencies

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Real World Application

• The RAM discussed is a model for a chip that can
  actually be found in a computer
• The binary counter can be bought at
  http//www.web-tronics.com/webtronics/74hc161n.htm
  l for 45 cents each
• The Flip-Flop circuits are models of usable chips

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State Diagrams

• A state diagram
• Each state is represented by a circled vertex
• Each row of the state table is shown as directed
  arc

J
Y
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Important Rule for State Diagram

• State diagram has same situation as state table.
  Their conditions should be mutually exclusive, no
  input values should meet the condition of more
  than one arc.

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The Alarm Clock
Present state
Turn off alarm
Alarm
Weekday
Next state
On
X
Awake in bed
Yes
Asleep
Awake in bed
Off
Yes
No
Awake and up
No
Awake in bed
Asleep
No
Off
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State Diagram for The Alarm Clock (a)
Alarm
Turn off Alarm Yes
Awake in bed
Asleep
Alarm
Alarm
Alarm /\ Weekday
Alarm /\ Weekday
Awake and up
1 (Always)
( a )
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The alarm clock problem with inaction states
Present state
Alarm
Weekday
Next state
Turn off alarm
Asleep
Asleep
Off
X
No
On
Yes
X
Asleep
Awake in bed
Awake in bed
X
yes
On
Awake in bed
Off
Yes
Awake and up
No
Awake in bed
Awake in bed
Off
No
Asleep
No
X
Awake and up
X
Awake and up
No
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State Diagram for The Alarm Clock (b)
Alarm / 1
Asleep
Awake in bed
Alarm / 0
Alarm / 1
Alarm /\ Weekday / 0
Alarm /\ Weekday / 0
Awake and up
1 (Always) / 0
( b )
1 yes turn off alarm (output) 0 no turn off
alarm (output)
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State Tables for The JK Flip-Flop
Present State
J
K
Next State
Q
Y
0
0
Y
0
Y
0
1
Y
0
Y
1
0
Z
1
Y
1
1
Z
1
Z
0
0
Z
1
Z
0
1
Y
0
Z
1
0
Z
1
Z
1
1
Y
0
( a )
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Condition in Terms of J and K
J
J
K
Z
Y
Q0
Q1
K
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Mealy and Moore Machines

• A finite state machine can represent outputs in
  one of two ways
• Moore Machines
• Mealy Machines

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Moore Machines

• Moore Machines
• Associates its outputs with the states.
• Output values depend only on the state and not on
  the transitions.
• It requires less hardware to produce the output
  values
• It is well suited for representing the control
  units of microprocessors and cpu.

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State Diagram for The Alarm Clock (a)
Alarm
Turn off Alarm Yes
Awake in bed
Asleep
Alarm
Alarm
Alarm /\ Weekday
Alarm /\ Weekday
Awake and up
1 (Always)
Moore Machine
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Mealy Machines

• Mealy Machines
• Associates outputs with the transitions.
• It depends on both its state and its input values

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State Diagram for The Alarm Clock (b)
Alarm / 1
Asleep
Awake in bed
Alarm / 0
Alarm / 1
Alarm /\ Weekday / 0
Alarm /\ Weekday / 0
Awake and up
1 (Always) / 0
Mealy Machine
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Designing State Diagrams

• Counter
• String Checker
• Toll Booth

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Modulo 6 Counter

• A modulo 6 counter is a 3-bit counter that counts
  through the sequence.
• 000 001 010 011 100 101 000
• 0 1 2 3 4 5 0
• Unlike a regular 3-bit counter
• 110(6) and 111(7) do not count

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State Table for The Modulo 6 Counter
Present State
Next State
C
V2 V1 V0
U
S0
0
S0
1
0 0 0
S0
1
S1
0
0 0 1
S1
0
S1
0
0 0 1

S1
1

S2
0
0 1 0
S2
0
S2
0
0 1 0
S2
1
S3
0
0 1 1
S3
0
S3
0
0 1 1
S3
0

1 0 0
1
S4
S4
0
S4
0
1 0 0
S4
1
S5
0
1 0 1
S5
0
S5
0
1 0 1
S5
1
S0
1
0 0 0
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State Diagram for The Modulo 6 Counter (Mealy)
0 / 1000
0 / 0001
0 / 0010
S0
S1
S2
1 / 0001
1 / 0010
1 / 1000
1 / 0011
S5
S4
S3
1 / 0101
1 / 0100
0 / 0101
0 / 0011
0 / 0100
( a ) Mealy
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State Diagram for The Modulo 6 Counter (Moore)
C0 V0010
C1 V 000
C0 V010
S0
S1
U
U
S2
U
U
U
U
U
S5
S4
S3
U
U
U
U
C0 V011
C0 V100
C0 V101
( b ) Moore
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String Checker

• A String Checker inputs a string of
• bits, one bits per clock cycle.
• It checks bits 1,2, and 2, then 2,3,and 4 and so
  forever

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State Table For String Checker
Present State
L
Next State
M
0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1
S0 S1 S2 S3 S4 S5 S6 S7 S0 S1 S2 S3 S4 S5 S6 S7
0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0
S0 S0 S1 S1 S2 S2 S3 S3 S4 S4 S5 S5 S6 S6 S7 S7
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State Diagrams for the String Checker ( Mealy)
0/0
S5
S4
S6
1/0
0/0
0/1
0/1
0/0
1/0
S7
0/1
S0
1/0
0/0
1/0
0/0
1/0
1/0
S3
S1
S2
0/0
1/0
Mealy
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State Diagrams for the String Checker (Moore)
I
M0
M1
M0
I
S6
S5
S4
I
I
I
I
S7
I
S0
I
I
I
I
I
M0
M0
I
I
S3
S2
S1
I
M0
M0
M0
I
Moore