C HAPTER F IVE S YNCHRONOUS S EQUENTIAL L OGIC 1.
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CHAPTER FIVE SYNCHRONOUS SEQUENTIAL LOGIC 1
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Transcript of C HAPTER F IVE S YNCHRONOUS S EQUENTIAL L OGIC 1.
CHAPTER FIVESYNCHRONOUS
SEQUENTIAL LOGIC
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It consists of a combinational circuit to which storage elements are connected to form a feedback path.
The storage elements are devices capable of storing binary information.
The binary information stored in these elements at any given time defines the state of the sequential circuit at that time.
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SEQUENTIAL CIRCUITS
CombinationalCircuit
MemoryElements
Inputs Outputs
Synchronous
CombinationalCircuit
Flip-flops
Inputs Outputs
Clock
The outputs in a sequential circuit are a function not only of the external inputs, but also of the present state of the storage elements.
The next state of the storage elements is also a function of external inputs and the present state.
The behavior of an asynchronous sequential circuit depends upon the input signals at any instant of time and the order in which the inputs change.
A synchronous sequential circuit (clocked sequential circuit) is a system whose behavior can be defined from the knowledge of its signals at discrete instants of time.
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Synchronization is achieved by a timing device called a clock generator, which provides a clock signal having the form of a periodic train of clock pulses .
The clock signal is commonly denoted by the clk.
The clock pulses determine when computational activity will occur within the circuit, and other signals (external inputs) determine what changes will take place affecting the storage elements and the outputs.
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Storage elements that operate with signal levels (rather than signal transitions) are referred to as latches.
Those controlled by a clock transition are flip-flops.
Latches are said to be level sensitive devices.
Flip-flops are edge-sensitive devices.
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LATCHES
SR Latch (cross coupled NOR)
R
S
Q
Q
S R Q0 Q Q’
0 0 0
0
1
0
0
0 1 Q = Q0
Initial Value7
LATCHES
SR Latch
R
S
Q
Q
S R Q0 Q Q’
0 0 0 0 10 0 1
1
0
0
0
1 0 Q = Q0
Q = Q0
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LATCHES
SR Latch
R
S
Q
Q
S R Q0 Q Q’
0 0 0 0 10 0 1 1 00 1 0 0
0
1
1
0
1 Q = 0
Q = Q0
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LATCHES
SR Latch
R
S
Q
Q
S R Q0 Q Q’
0 0 0 0 10 0 1 1 00 1 0 0 10 1 11
0
1
0
0 1Q = 0
Q = Q0
Q = 0
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LATCHES
SR Latch
R
S
Q
Q
S R Q0 Q Q’
0 0 0 0 10 0 1 1 00 1 0 0 10 1 1 0 11 0 0
0
1
0
1
1 0
Q = 0
Q = Q0
Q = 1
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LATCHES
SR Latch
R
S
Q
Q
S R Q0 Q Q’
0 0 0 0 10 0 1 1 00 1 0 0 10 1 1 0 11 0 0 1 01 0 1
1
0
0
1
1 0
Q = 0
Q = Q0
Q = 1
Q = 1
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LATCHES
SR Latch
R
S
Q
Q
S R Q0 Q Q’
0 0 0 0 10 0 1 1 00 1 0 0 10 1 1 0 11 0 0 1 01 0 1 1 01 1 0
0
1
1
1
0 0
Q = 0
Q = Q0
Q = 1
Q = Q’
0
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LATCHES
SR Latch
R
S
Q
Q
S R Q0 Q Q’
0 0 0 0 10 0 1 1 00 1 0 0 10 1 1 0 11 0 0 1 01 0 1 1 01 1 0 0 01 1 1
1
0
1
1 0 0
Q = 0
Q = Q0
Q = 1
Q = Q’
0
Q = Q’
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LATCHES
SR Latch
R
S
Q
Q
S R Q
0 0 Q0
0 1 0
1 0 1
1 1 Q = Q’=0
No change
Reset
Set
Invalid
S
R
Q
Q
S R Q
0 0 Q = Q’=1
0 1 1
1 0 0
1 1 Q0
Invalid
Set
Reset
No change 15
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CONTROLLED LATCHES
SR Latch with Control Input (operates with signal level)
En S R Q
0 x x Q0
1 0 0 Q0
1 0 1 0
1 1 0 1
1 1 1 Q = Q’
No change
No change
Reset
Set
Invalid
S
R
Q
Q
S
R
C
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CONTROLLED LATCHES
D Latch (Transparent Latch)
C=En D (data) Q
0 x Q0
1 0 0
1 1 1
No change
Reset
Set
S
R
Q
Q
D
C
C
Timing Diagram
D
Q
t
Output may change
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CONTROLLED LATCHES
D Latch (D = Data)
C D Q
0 x Q0
1 0 0
1 1 1
No change
Reset
Set
C
Timing Diagram
D
Q
Output may change
S
R
Q
Q
D
C
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When latches are used for the storage elements, a serious difficulty arises. The state transitions of the latches start as soon as the clock pulse changes to the logic-1 level.
FLIP-FLOPS
If the inputs applied to the latches change while the clock pulse is still at the logic-1 level, the latches will respond to new values and a new output state may occur.
The new state of a latch appears at the output while the pulse is still active. This output is connected to the inputs of the latches through the combinational circuit.
The result is an unpredictable situation, since the state of the latches may keep changing for as long as the clock pulse stays at the active level. 22
Controlled latches are level-triggered
Flip-Flops are edge-triggered
It operates with signal transitions
C
CLK Positive Edge
CLK Negative Edge
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FLIP-FLOPS Master-Slave D Flip-Flop
D Latch(Master)
D
C
Q D Latch(Slave)
D
C
Q QD
CLKCLK
D
QMaster
QSlave
Looks like it is negative edge-triggered
Master Slave
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FLIP-FLOPS
Edge-Triggered D Flip-Flop
D Q
Q
D Q
Q
Positive Edge
Negative Edge 25
Q(t+1) = D
FLIP-FLOP CHARACTERISTIC EQUATIONS
Analysis / Derivation
J Q
QK
J K Q(t) Q(t+1)0 0 0 00 0 1 10 1 00 1 11 0 01 0 11 1 01 1 1
No change
Reset
Set
Toggle
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FLIP-FLOP CHARACTERISTIC EQUATIONS
Analysis / Derivation
J Q
QK
J K Q(t) Q(t+1)0 0 0 00 0 1 10 1 0 00 1 1 01 0 01 0 11 1 01 1 1
No change
Reset
Set
Toggle
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FLIP-FLOP CHARACTERISTIC EQUATIONS
Analysis / Derivation
J Q
QK
J K Q(t) Q(t+1)0 0 0 00 0 1 10 1 0 00 1 1 01 0 0 11 0 1 11 1 01 1 1
No change
Reset
Set
Toggle
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FLIP-FLOP CHARACTERISTIC EQUATIONS
Analysis / Derivation
J Q
QK
J K Q(t) Q(t+1)0 0 0 00 0 1 10 1 0 00 1 1 01 0 0 11 0 1 11 1 0 11 1 1 0
No change
Reset
Set
Toggle
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FLIP-FLOP CHARACTERISTIC EQUATIONS
Analysis / Derivation
J Q
QK
J K Q(t) Q(t+1)0 0 0 00 0 1 10 1 0 00 1 1 01 0 0 11 0 1 11 1 0 11 1 1 0
K
0 1 0 0J 1 1 0 1
Q
Q(t+1) = JQ’ + K’Q 30
FLIP-FLOPS
JK Flip-Flop
D Q
Q
Q
QCLK
J
K
J Q
QK
D = JQ’ + K’Q31
FLIP-FLOPS
T (toggle) Flip-Flop
D = TQ’ + T’Q = T Q
J Q
QK
T D Q
Q
T
D = JQ’ + K’QT Q
Q32
FLIP-FLOP CHARACTERISTIC TABLES
D Q
Q
D Q(t+1)0 01 1
Reset
Set
J K Q(t+1)0 0 Q(t)0 1 01 0 11 1 Q’(t)
No change
Reset
Set
Toggle
J Q
QK
T Q
Q
T Q(t+1)0 Q(t)1 Q’(t)
No change
Toggle33
FLIP-FLOPS WITH DIRECT INPUTS
Asynchronous Reset
D Q
Q
R
Reset
R D CLK Q(t+1)
0 x x 0
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FLIP-FLOPS WITH DIRECT INPUTS
Asynchronous Reset
D Q
Q
R
Reset
R D CLK Q(t+1)
0 x x 0
1 0 ↑ 0
1 1 ↑ 1
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