sequential circuits. combinational circuits + storage element output depends both on previous state...
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Sequential Circuits
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• Combinational Circuits + Storage element• output depends both on previous state and input
Fig. 5-1
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Fig. 5-2
• (a): a buffer• tG the delay• the information enters the buffer at t and output at t+ tG
• the stored information only retained in buffer by tG • longer storage time is necessary in most applications
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Fig. 5-3
Use flip-flop
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•A storage element can maintain a binary state indefinitely, until directed by an input signal to switch states.•The most basic storage elements are latches.
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Fig. 5-5
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RS
RS
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RS
Fig. 5-7
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Fig. 5-8
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A change in value on the control input allows the state of a latch in a flip-flop to switch.
This change is called a trigger The trigger enable (trigger) the flip-flops See Fig. 5-3 for sequential circuits A present (original) and next (new) state occur in
flip-flop before and after the trigger, respectively The most important element in sequential circuits Can be derived from latch
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Fig. 5-9
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Fig. 5-10
•Pulse trigger •Pulse in the inputs SR will results wrong output
Initially unknown
Unknown due to R=1 S=1
Pulse input results wrong output
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Fig. 5-11
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Fig. 5-13
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Fig. 5-14
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5-4 Sequential Circuit Analysis
The output and the next state are a function of the inputs and the present state.
An example
XBAY )( Fig. 5-15
input equations
output equation
XAD
XBXAD
B
A
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State table
XADtB
XBXADtA
B
A
)1(
)1( XBAY )(
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Two-dimensional state table
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Mealy model/Moore model
Mealy model circuits Sequential circuits in which the outputs depend
on the input, as well as on the states The circuits in Fig. 5-15
Moore model circuits Sequential circuits in which the outputs depend
only on the states The circuits in Fig. 5-16
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A Moore model circuit (Fig. 5-16)
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State diagram(a): for Fig. 5-15 (b): for Fig. 5-16
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Example 5-1 States reduction
equivalent
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Example 5-1 States reduction
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Example 5-1 States reduction
equivalent
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Example 5-1 States reduction
• Reduce from 4 states, 2 flip-flops to 2 states, 1 flip-flop
• may or may not result in reduced cost
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Sequential Circuit Simulation
A simulator for the input/output of a designed circuit
Functional simulation Timing simulation