Transcript Chapter 6:Synchronous Sequential Circuits

Chapter 5
Synchronous
Sequential
Circuits
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Logic Circuits- Review
Logic Circuits
Combinational
Circuits
•Consists of logic gates
whose outputs are
determined from the current
combination of inputs.
•Performs an operation that
can be specified by a set of
Boolean functions.
Sequential
Circuits
•Employ storage elements in
addition to logic gates.
•Outputs are a function of the
inputs and the state of the
storage elements.
•Output depend on present
value of input + past input.
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Overview
 Storage
Elements and Analysis
 Introduction to sequential circuits
 Types of sequential circuits
 Storage elements
 Latches
 Flip-flops
 Sequential
 State
circuit analysis
tables
 State diagrams
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Introduction to Sequential Circuits
Inputs
A
Sequential
circuit contains:


Storage
Elements
Storage elements:
Latches or Flip-Flops
Combinatorial Logic:
 Implements
Combinational
Logic
State
a multiple-output
switching function
 Inputs are signals from the outside.
 Outputs are signals to the outside.
 Other inputs, State or Present State,
are signals from storage elements.
 The remaining outputs, Next State are
inputs to storage elements.
Next
State
Outputs
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Introduction to Sequential Circuits
Inputs
Outputs
Combinational
Logic
Storage
Elements
State
Sequential Logic
Output function
Outputs = g(Inputs, State)
Next state function
Next State = f(Inputs, State)
Next
State
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Types of Sequential Circuits



Depends on the times at which:
 storage elements observe their inputs, and
 storage elements change their state
Synchronous
 Behavior defined from knowledge of its signals at discrete
instances of time
 Storage elements observe inputs and can change state
only in relation to a timing signal (clock pulses from a clock)
Asynchronous
 Behavior defined from knowledge of inputs at any instant
of time and the order in continuous time in which inputs
change
 If clock just regarded as another input, all circuits are
asynchronous!
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5.3 Storage Elements :Latches
 Storage
elements
 Maintain
a binary state (0 or 1) indefinitely as
long as power is delivered to the circuit
 Switch states (01 or 10) when directed by
an input signal
 Most
basic storage element
 Used mainly to construct Flip-Flops
 Asynchronous storage circuit
 Types of latches:



SR Latches
S`R` Latches
D Latches
X=X
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Basic (NOR) S – R Latch
 Cross-coupling
S – R Latch:
two NOR gates gives the
Graphic Symbol
R (reset)
S
Q
R
Q
S (set)
Q
Q
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Basic (NOR)
S – R Latch
S
R
Q t+1
0
0
Q t+1=Q
No change
0
1
Reset to 0
1
0
Set to 1
1
1
undefined
S
R
Q
Q t+1
Q’ t+1
0
0
0
Q t+1=Q =0
1
0
0
1
1
0
0
1
0
0
1
0
1
1
0
1
1
0
0
1
0
1
0
1
1
0
1
1
0
Undefined
‫؟‬
1
1
1
undefined
‫؟‬
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Basic (NAND) Ś – Ŕ Latch
 “Cross-Coupling”
the Ś -Ŕ Latch:
Graphic Symbol
S
Q
R
Q
two NAND gates gives
S (set)
R (reset)
Q
Q
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Basic (NAND)
Ś – Ŕ Latch
S
R
Q t+1
0
0
Undefined
0
1
Reset to 1
1
0
Set to 0
1
1
Q t+1=Q
No change
S
R
Q
Q t+1
Q’ t+1
0
0
0
?
?
0
0
1
?
?
0
1
0
1
0
0
1
1
1
0
1
0
0
0
1
1
0
1
0
1
1
1
0
0
1
1
1
1
1
0
Clocked S - R Latch

Adding two NAND
gates to the basic
Ś - Ŕ NAND latch
gives the clocked
S – R latch:
S`
S
Q
1
C
1


Has a time sequence R
behavior similar to the
basic S-R latch except that
the S and R inputs are only
observed when the line C is
high.
C means “control” or
“clock”.
Q
R`
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D Latch(Transparent Latch)
 Adding
an inverter to the S-R Latch,
gives the D Latch:
 Note that there are no “indeterminate”
states!
The graphic symbol for a
D Latch is:
D
Q
D
Q
Q
C
Q
C
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D Latch(Transparent Latch)
D
Q t+1
0
0
1
1
Q D
0 0
0 1
1 0
1 1
Q(t+1)
0
1
0
1
Chapter 5: Sequential Circuits
5.4: Flip-Flops
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Flip-Flops
 The
latch timing problem
 Master-slave flip-flop
 Edge-triggered flip-flop
 Other flip-flops
- JK flip-flop
- T flip-flop
The Latch Timing Problem

In a sequential circuit, paths may exist through
combinational logic:
From one storage element to another
 From a storage element back to the same storage
element



The combinational logic between a latch output
and a latch input may be as simple as an
interconnect
For a clocked D-latch, the output Q depends on the
input D whenever the clock input C has value 1
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The Latch Timing Problem
(continued)

Consider the following circuit:

Suppose that initially Y = 0.
Clock
D
Q
C
Q
Clock
Y




As long as C = 1, the value of Y continues to change!
The changes are based on the delay present on the
loop through the connection from Y back to Y.
This behavior is clearly unacceptable.
Desired behavior: Y changes only once per clock pulse
Y
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The Latch Timing Problem
(continued)
A
solution to the latch timing problem is to
break the closed path from Y to Y within
the storage element
 The commonly-used, path-breaking
solutions replace the clocked D-latch
with:


a master-slave flip-flop
an edge-triggered flip-flop
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Master-Slave Flip-Flop
Master





D
D
C
C
Slave
Y
D
Q
C
Consists of two clocked
D latches in series
with the clock on the
second latch inverted
What happened when c=1?
The data from D input is transferred to the master .
The slave is disabled .
Any change in the input change the master output ( Y ) but
can’t effect the slave output .
Q
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Master
 What
D
D
C
C
Slave
Y
happened
when C=0?
 The master is disabled .
 The slave is enable.
 The value of ( Y ) is
transferred to the slave as input .
 The output ( Q ) is equal ( Y ) .
Conclusion:
The output of the F.F. can change only during
the transition of clock from 1 to 0 or at
Trigger .
D
C
Q
Q
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Timing
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Timing
A
trigger: The state of a latch or flip-flop is
switched by a change of the control input.
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Graphic Symbols
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Graphic Symbols
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Other flip-flops
•
•
•
Other F-Fs can be built using D F-F
There are four operation on a F-F
- set to 1
- Reset to 0
- toggle ( complement ) of Q
- nothing
There are tow F-F
- JK F-F
- T F-F
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JK Flip-Flops
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JK Flip-Flops
D = JQ’ + K’Q
J
K
Q t+1
0
0
No change
Q t+1 = Q
0
1
Reset to 0
1
0
Set to 1
1
1
Complement
Q t+1= Q’
T Flip-Flops
T Flip-Flops
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T Flip-Flops
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Characteristic Table
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Characteristic Table
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Characteristic Equations
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State Equation
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State Equation
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Analysis
 This
circuit consist of :
 2 D F-F A and B
 Input x
 Output Y
 Qt+1 = D
 A= D A
B = DB
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State Table
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State Diagram
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Input / output
state
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Analysis
1 D F-F ( A )
 2 Input X , Y
 Qt+1 = D
D=AXy

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Analysis
2 JK F-F (A , B)
 Input x
 Q t+1 = JQ’ + K’Q

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Analysis
2
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T F-F ( A, B )
 1 input X
 1 output Y
 Qt+1 = T  Q
 The input equations are
T_A = BX
T_B = X
 The out put equation is
Y = AB
 The characteristic equations are :
At+1 = T_A  A
= BX  A
= BX(A’) + (BX)’A
= A’BX + AB’ + AX’
Bt+1 = X  B
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