Digital Design: Sequential Circuits for Registers and Counters Part - IV

Chapter 8

Sequential Circuits for Registers and Counters

Ch16L4- "Digital Principles and Design", Raj Kamal, Pearson Education, 2006 2

Lesson 4

RING AND JOHNSON RING AND JOHNSON COUNTERS COUNTERS


• Ring Counter•• Johnson Counter Johnson Counter •• Odd Sequencer Switch tail Odd Sequencer Switch tail

(Twisted Ring) Johnson counter(Twisted Ring) Johnson counter•• Even Sequencer Switch tail Even Sequencer Switch tail

(Twisted Ring) Johnson counter(Twisted Ring) Johnson counter

Outline


4-bit Ring Counter

D FFD FFD D FFD FF

Each flip flop has output delay tp of and ring output and input delays by tp of one D-FF

QA

Q

CLR

Clock input CLK

After tp

D D DQB

QDQC

PR PR PR

PR = 1

Serial in = 1


Ring Counter First Cycle after CLR

Inputs CLR = 1, Outputs

CLK Sequence = Qn+1(A) Qn+1(B) Qn+1(C) Qn+1(D)

Qn+1 means next state after nth clock input and after a delay of tp at successive FFs. Delay = 4×tp at Qn+1(D) on each transition

↓ 0 0 0 0 1

↓ 1 0 0 1 0↓ 2 0 1 0 0↓ 3 1 0 0 0


Ring Counter Second Cycle




↓ 0 0 0 0 1

↓ 1 0 0 1 0↓ 2 0 1 0 0↓ 3 1 0 0 0


State Diagram of Ring CounterS00001

S0

0010

S0

0100

S0

0100


Ring Counting

• When CLR = 0, all FFs are cleared (Q = 0) except right most, which sets to 1.

• When CLR = 1, ring counting starts. On next clock edge, the QD = 1 left shifts to QCand since QA = 0 and connects to serial input at DD, QA = 0 and QC = 1. In next transition, QB = 1 and QC = 0; and so 1 rotates in ring form..


Ring Counter Sequences

• Ring counter has 4 sequences: 0001, 0010, 0100, 1000, 0000


• Ring Counters•• Johnson Counter Johnson Counter •• Odd Sequencer Switch tail Odd Sequencer Switch tail



Outline


4-bit Johnson Counter

D FFD FFD D FFD FF

Each flip flop has output delay tp of and ring output and input delays by tp of one D-FF

QA

Q

CLR

Clock input CLK

After tp

D D DQB

QDQC

PR PR PR

PR = 1

Serial in = 1


Output Sequences

OE

To CLR

QAY3

To CLR

QB

QC

QD

Y2

Y1

Y0


State Diagram of Johnson CounterS00001

S1

0011

S6

1000

S7

0000

S2

0111

S5

1100

S3

1111

S4

1110


Johnson Counter First Cycle after CLR




↓ 0 0 0 0 1

↓ 1 0 0 1 1↓ 2 0 1 1 1↓ 3 1 1 1 1


Johnson Counter First Cycle



Qn+1 means next state after nth clock input and after a delay of tp at successive FFs. Delay = 4 ×tp at Qn+1(D) on each transition

↓ 4 1 1 1 0

↓ 5 1 1 0 0↓ 6 1 9 0 0↓ 7 0 0 0 0


Johnson Counter QA is given as input to rightmost place instead of QD input in case of ring counter.

• When CLR = 0, all Qs and Ds of FFs = 0 cleared except the DD input at right most FF which sets to 1, as it connects QA.

• When CLR = 1, Johnson counting starts. On the clock edge, the QD = 1 left shifts to QCand since QA = 1 and connects to serial input at DD, QA = 1, QA = 1 and QC = 1.


Johnson CounterIn next cycle, QA = 0 so 0 rotates in

ring form in second half cycle• Johnson counter has 8 sequences:

0001, 0011, 0111, 1111, 1110, 1100, 1000, 0000


• Ring Counters•• Johnson Counter Johnson Counter •• Odd Sequencer Switch tail Odd Sequencer Switch tail



Outline


4-bit Twisted Tail Odd Sequencer Johnson Counter

D FFD FFD D FFD FF

QA

Q

CLR

Clock input CLK

After tp

D D D QB

QDQC

PR PR PR

PR = 1

Serial in = 1

QB

QA


Odd SequencerOdd Sequencer Johnson Counter

•• Odd SequencerOdd Sequencer Johnson counter has 7 sequences: 0001, 0011, 0111, 1111, 1110, 1100, 1000,

• The 0000 sequence does not exist, as QAand QB are given as input after AND operation to rightmost place instead of QD input in case of ring counter. Therefore, as soon as sequence QAQBQCQD 1000 switches to 0000, the QA and QB become 1 and thus AND gives the input DD = 1. On next clock, the sequence of output is 0001 in place of 0000.


State Diagram of (2n –1) Sequencer (n =4) Johnson Counter

S00001

S1

0011

S6

1000

S2

0111

S5

1100

S3

1111

S4

1110


Johnson Counter Twisted Tail First Cycle after CLR




↓ 0 0 0 0 1

↓ 1 0 0 1 1↓ 2 0 1 1 1↓ 3 1 1 1 1


Johnson Counter Twisted Tail First Cycle




↓ 4 1 1 1 0

↓ 5 1 1 0 0↓ 6 1 9 0 0↓ 0 Repeat 0 0 0 1


• Ring Counters•• Johnson Counter Johnson Counter • Odd Sequencer Switch tail

(Twisted Ring) Johnson counter•• Even Sequencer Switch tail Even Sequencer Switch tail


Outline


4-bit Twisted Tail Even Sequencer Johnson Counter

D FFD FFD D FFD FF

QA

Q

CLR

Clock input CLK

After tp

D D D QB

QDQC

PR PR PR

PR = 1

Serial in = 1

QB

QA

QB

QA


Even SequencerEven Sequencer Johnson Counter

•• Even SequencerEven Sequencer Johnson counter has 6 sequences: 0001, 0011, 0111, 1110, 1100, 1000,

• The 1111 and 0000 sequence do not exist, as QA and QB ,and QA and QBare given as inputs after two AND operations to rightmost place instead of QD input in case of ring counter.


Even SequencerEven Sequencer Johnson Counter

• Therefore, as soon as sequence QAQBQCQD 1000 switches to 0000 or 0111 switches to 1100 the QA and QB become 1 and thus AND gives the input DD = 1. On next clock, the sequence of output is 0001 in place of 0000. Similarly as soon as the QA and QB become 1 other AND gives the input DD = 0.


State Diagram of (2n –2) Sequencer (n =4) Johnson Counter

S00001

S1

0011

S6

1000

S2

0111

S5

1100

S4

1110


Johnson Counter Twisted Tail First Cycle after CLR




↓ 0 0 0 0 1

↓ 1 0 0 1 1↓ 2 0 1 1 1


Johnson Counter Twisted Tail First Cycle




↓ 3 1 1 1 0

↓ 4 1 1 0 0↓ 5 1 0 0 0↓ 0 Repeat 0 0 0 1


Summary


We learnt • Ring counter has n-sequences rotating when

n-bit shift register is used with last end Q FF output connected to first end D input of FF

• Johnson counter has 2n-sequences rotating when n-bit shift register is used with last end QA at FF output connected to first end D input of FF


We learnt • Johnson counter twisted has (2n–1) sequences

rotating when n-bit shift register is used with last two QA and QB ANDed and connected to first end D input of FF

• Johnson counter twisted has (2n–2) sequences rotating when n-bit shift register is used with last two QA and QB ANDed and connected through OR gate to first end D input of FF and also last two QA and QB NANDed and connected through OR gate to first end D input of FF


End of Lesson 4

RING AND JOHNSON RING AND JOHNSON COUNTERS COUNTERS


THANK YOUTHANK YOU

Digital Design: Sequential Circuits for Registers and Counters Part - IV

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Transcript of Digital Design: Sequential Circuits for Registers and Counters Part - IV