1 Sequential Circuits –Digital circuits that use memory elements as part of their operation –Characterized by feedback path –Outputs depend not only on.

1

Sequential Circuits• Sequential Circuits

– Digital circuits that use memory elements as part of their operation

– Characterized by feedback path– Outputs depend not only on its current inputs but

also on the past sequence of inputs, possibly arbitrarily far back in time

• Examples– Counters– Parallel-to-Serial conversion of byte data

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Sequential Circuits

• State of Circuit– Binary information stored in the memory

elements determines the “state” of the circuit– Output and next state is determined by input

signals and current state of circuit

Q

Q

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Sequential Circuits

• 2 Major Types of Circuits• Asynchronous

– Inputs may change at any time– Complicated and maybe unstable because of

feedback

• Synchronous– Input change is only effected at certain times

determined by a master clock (pulse or edge detection) or master-slave operation

Q

Q

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Asynchronous Sequential Circuits

Latch• Temporary storage device that has two stable states• Normally has two inputs • Two complementary outputs available: Q and Q’• When the latch is set to a certain state it retains its

state unless the inputs are changed to set the latch to a new state

• A latch serves as a memory element which is able to retain the information stored in it

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S-R (Set-Reset) Latch

1

2 Q

QR

S

Input Output

S R Qt+1

0 0 Qt

0 1 0

1 0 1

1 1 Invalid

NOR gate based

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S-R (Set-Reset) LatchTruth table

Characteristic EquationQt+1 = S + R’Q; SR = 0

Q S R Qt+1

0 0 0 0

0 0 1 0

0 1 0 1

0 1 1 Invalid

1 0 0 1

1 0 1 0

1 1 0 1

1 1 1 Invalid

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S-R (Set-Reset) Latch

Input Output

S’ R’ Qt+1

1 1 Qt

1 0 0

0 1 1

0 0 Invalid

NAND gate based

1

2 Q

S

R

Q

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S-R (Set-Reset) Latch

Standard Logic Symbols

Active-highInput

S-RLatch

Q

QS

R

Active-lowInput

S-RLatch

Q

QS

R

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S-R (Set-Reset) Latch

Timing diagram of active-low input latch

S

R

Q

t1 t2 t3 t4 t5 t6 t7 t8 t9 t10 t11 t12

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S-R (Set-Reset) Latch

Timing diagram of active-high input latch

S

R

Q

t1 t2 t3 t4 t5 t6 t7 t8 t9 t10 t11 t12

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S-R Latch Apps - Burglar Alarm

Active-lowInput

S-RLatch

Q

QS

R

+5 v

Alarm

Reset switch

Alarm switch

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Synchronous Sequential Circuits• Latches

– Asynchronous circuits– Outputs are transparent to inputs

• Gated or Clocked Latches– Synchronous circuits b/c clock or enable input dictates when

inputs are latched onto outputs– May still have both transparent and latched operation if inputs

change while clock is active• Flip Flops

– Flip-Flops are synchronous bi-stable devices, known as bi-stable multivibrators

– The output of the flip-flop can only change once by the applied inputs upon application of clock input

– Edge Triggered or Master Slave

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S-R Gated Latch– Adds a clock (control) input gated to an S-R latch– S/R inputs are passed on to the latch portion

synchronised by the clock pulse– Also called Clocked S-R Latch

1

2 Q

S

R

Q3

4

CK

GatedS-R

Latch

Q

QS

R

ENCK

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S-R Gated LatchTruth table

Characteristic EquationQt+1 = S + R’Q; SR = 0

Q S R Qt+1

0 0 0 0

0 0 1 0

0 1 0 1

0 1 1 Invalid

1 0 0 1

1 0 1 0

1 1 0 1

1 1 1 Invalid

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S-R Gated Latch Timing

S

R

Q

t1 t2 t3 t6t5

CK

t8t7t4

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D Gated Latch

1

2 Q

D Q3

4

ENCK

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D Gated LatchTruth table

Characteristic EquationQt+1 = D

Q D Qt+1

0 0 0

0 1 1

1 0 0

1 1 1

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D Gated Latch Apps

I01

I11

1I2

0I3

YEN

0

74X151

I40

I51

0I6

1I7

A0

A1

A2

C2

Counter

clock C1

C0

Serial Transmission

Line

D QEND QEND QEND QEND QEND QEND QEND QEN

1

1

1

0

0

1

0

1

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D Gated Latch Timing

D

Q

t1 t2 t3 t4 t5 t6 t7 t8 t9

CLK

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Latches - Transparency Problem

• What’s transparency?– Output follows input instantaneously –

tunneling– Behavior depicted in latches

• The transparency problem– If output is fed back, circuit may become

unstable

• The solution?– Master Slave or Edge Triggered FF

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Transparency Problem

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Transparency Problem

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Master Slave Flip Flop

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Master Slave Flip Flop

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S-R Master Slave Flip Flop

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Master Slave Flip Flops Summary• Have two stages – Master and Slave• Each stage works in one half of the clock signal• Inputs are applied in the first half of the clock signal• Outputs do not change until the second half of the clock

signal• Allows digital circuits to operate in synchronization with a

common clock signal• Inherently slow throughput• Mostly obsoleteBetter Solution:• Edge Triggered flip-flops• An edge-triggered flip-flop ignores the pulse while it is at

a constant level and triggers only during a transition of the clock signal - faster

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D Flip-Flop Apps – Registers

Q

QSET

CLR

D

Q

QSET

CLR

D

Q

QSET

CLR

D

Q

QSET

CLR

D

D0

D1

D2

D3

Q0

Q1

Q2

Q3

CLK

Con

nect

ed to

inpu

ts o

f Mul

tiple

xer

D0

D1

D2

D3

Q0

Q1

Q2

Q3

CLK

t1

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Edge Triggered J-K Flip Flop

1

2 Q

J

K

Q3

4

CLK

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Edge Triggered J-K Flip Flop

tQ

J-KFlip-Flop

J

K

CLK

Q

Q

J-KFlip-Flop

J

K

CLK

Q

Q

Input Output

CLK J K Qt+1

0 X X Qt

1 X X Qt

↑ 0 0 Qt

↑ 0 1 0

↑ 1 0 1

↑ 1 1 Qt’

Input Output

CLK J K Qt+1

0 X X Qt

1 X X Qt

↓ 0 0 Qt

↓ 0 1 0

↓ 1 0 1

↓ 1 1 Qt’

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T Flip FlopTruth table

Characteristic EquationQt+1 = TQ’ + T’Q

Q T Qt+1

0 0 0

0 1 1

1 0 1

1 1 0

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T Flip Flop

T

Q

t1 t2 t3 t4 t5 t6 t7 t8 t9

CLK

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Flip-Flop Operating Characteristics

• Performance specified by several operating characteristics provided in the data sheets of FF’s

• The important operating characteristics are:– Propagation Delay

– Set-up Time

– Hold Time

– Maximum Clock frequency

– Pulse Width

– Power Dissipation

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Flip Flop Logic Symbols Summary

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Qt+1 = S + R’Q; SR = 0

Qt+1 = D

Qt+1 = JQ’ + K’Q

Qt+1 = TQ’ + T’Q

Flip Flop Characteristic Equations

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Flip Flop Excitation Tables

Qt Qt+1 S R

0 0 0 X

0 1 1 0

1 0 0 1

1 1 X 0

Qt Qt+1 J K

0 0 0 X

0 1 1 X

1 0 X 1

1 1 X 0

Qt Qt+1 D

0 0 0

0 1 1

1 0 0

1 1 1

Qt Qt+1 T

0 0 0

0 1 1

1 0 1

1 1 0

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Flip Flop Usage Guide

Type of Application Preferred FF

Transfer of data

(e.g. shift registers)RS or D

Complementation

(e.g. binary counters)T

Above or any other

general applicationJK