Flip-flops
Chapter4
Sequential circuits
Combinational
logic
X0
Xn
Y0
Ym
Universal
combinational circuit
model
No memory units
No feedback from logic
outputs back to the inputs
Combinational
logic
System
Input
Variables
System
output
Variables
I0
In
O0
Om
S0
Sx
M0
Ex
State
Variables Excitation Variables
MX
E0
Universal
sequential circuit
model
Sequential implies that events are ordered
in time,that one event then another occurs,
separated by time.
Two types of sequential logic exist:
Synchronous sequential circuit
Synchronous sequential circuit is clocked
Asynchronous sequential circuit
Asynchronous sequential circuit is not clocked
Combinational
logic
System
Input
Variables
System
output
Variables
I0
In
O0
Om
S0
Sx
M0
Ex
State
Variables Excitation Variables
MX
E0
Set I{ I0……In }
are external
input variables
presented to
the system.
Set O{ O0……Om }
are external
output variables.
Combinational
logic
System
Input
Variables
System
output
Variables
I0
In
O0
Om
S0
Sx
M0
Ex
State
Variables
Excitation
Variables
MX
E0
Internally,the system generate the excitation
variables,E0 to Ex,and state variables,S0 to Sx.
internal output
variables
internal input
variables
The memory excitation input relationship can be written as
E = f( I,S ),Excitation E force the memory elements to
the desired state variables.
Output O is generated by the combinational logic
transform,(g),operating on input variables I and state
variables S.
O = g( I,S )
Combinational
transform
(f)
Memory
M
Combinational
logic
(g)
Input
(I) (E)
CLK
State variables
(S)
Excitation variables Output
(O)
E = f( I,S )
O = g( I,S )
The clock input is not a binary value representing
the time of day,but rather a,synchronous” train
of pulses,Synchronous memory changes its data
only at certain time intervals.
Combinational
transform
(f)
Memory
M
Combinational
logic
(g)
Input
(I) (E)
CLK
State variables
(S)
Excitation variables Output
(O)
State variables
State variable is the output of memory unit,
It is used to define the state of a
sequential machine.
State is defined by the content of memory,
Each state represent a different events.
State variables and states are related by
2x=y
x= number of State variables
y= number of States
Memory data are free to change with
time,It can be one value at time t1 and
another at time t2,
St and St+1 represent the binary
value of state variables,S,at
different times,t,
St represents the present-state (old
memory output) and St+1 represents
the next-state (new memory output),
Each state become a,present” state
after a clock pulse and will go to a
“next-state” on the next clock pulse,
The value of the next-state variables,
St+1,is determined by the present
value of the state variables,St,and the
input,I,
St+1 = f( St,I )
Machine Model
The output,O,is a function of only the
present state,St.
E = f( I,St )
St+1 = f( St,E )
O = g( St )
Moore machine
Combinational
transform
(f)
Memory
M
Combination
al logic
(g)
Input
(I) (E)
CLK
State variables
(S)
Excitation variables Output
(O)
Mealy machine
The output,O,is a function of both the
present state,St,and the input variables,I.
E = f( I,St )
St+1 = f( St,E )
O = g( I,St )
Combinational
transform
(f)
Memory
M
Combination
al logic
(g)
Input
(I) (E)
CLK
State variables
(S)
Excitation variables Output
(O)
State Diagram
A state diagram is a graphic rendition of a sequential
circuit,where individual states are represented by a
circle with an identifying symbol located inside.
Change from state to state are indicated by directed
arcs,Input conditions that cause state changes to
occur and the resulting output signals are written
adjacent to the directed arc.
State diagram graphically represent the relationships
between states,They show the input-output variable
combinations as the transitions from one state to the
next.
J1K1
Y1
J2K2
Y2
=1 1
X
&
Z
cp
Y2Y1 X/Z
0 0
1 01 1
0/0
0/0
0/0
0/1
1/1
1/0
1/0
1/0
0 1
In Mealy machine,the output is a function of both the
present state and the input variables.
An input-output statement
is written adjacent to each
directed arc,
D2
Y2 Y2’
D1
Y1 Y1’
X
Z
CP
10/1
00/0
11/0
01/0
0
1
1
0
0 01
1
Moore machine notation,where the output is
depend only on the present state,represent
the output variable inside the state circle.
A state diagram is somewhat analogous to the
programmer’s flowchart,The states can be viewed as
tasks or operations and the directed arcs,indicating
input conditions,as conditional statements.
The addition of one input variable double the number
of possible next state transitions,
With large numbers of input variables,it is
convenient to indicate only the asserted conditions
that cause state or output variable changes,The
unspecified input variable combinational are
assumed to leave the state machine in its present
state.
State Table
State table are tabular forms of diagrams,The
purpose of the state table is to indicate the state
transitions.
The present state column list all of the possible
state in the machine,A series of next state
columns exist,one from each combination.
Transition table takes the state table one step
further,
The state diagram represent states using
symbol or names,whereas the transition table
assign specific state variable values to each
state.
J1K1
Y1
J2K2
Y2
=1 1
X
&
Z
cp Present
state
Next state/output
Y2 Y1
Y2t+1 Y1t+1/Z
0
0
1
1
0
1
0
1
1
0
1
0
0
1
1
0
X = 0 X = 1
/0
/0
/0
/1
1
0
1
0
1
0
0
1
/0
/1
/0
/0
Present
state
Next state/output
X = 0 X = 1
A
B
C
D
/0
/0
/0
/1
B
C
D
A
/0
/1
/0
/0
D
A
B
C
A,B,C,D
are states
Y2,y1 are
state variables
D2
Y2 Y2’
D1
Y1 Y1’
X
Z
CP
Present
state
Next state
Y2 Y1
Y2t+1Y1t+1
0
0
1
1
0
1
0
1
0
1
0
0
0
1
0
1
X=0 X=1
1
1
1
1
0
0
0
0
Output
Z
0
0
1
0
Chapter4
Sequential circuits
Combinational
logic
X0
Xn
Y0
Ym
Universal
combinational circuit
model
No memory units
No feedback from logic
outputs back to the inputs
Combinational
logic
System
Input
Variables
System
output
Variables
I0
In
O0
Om
S0
Sx
M0
Ex
State
Variables Excitation Variables
MX
E0
Universal
sequential circuit
model
Sequential implies that events are ordered
in time,that one event then another occurs,
separated by time.
Two types of sequential logic exist:
Synchronous sequential circuit
Synchronous sequential circuit is clocked
Asynchronous sequential circuit
Asynchronous sequential circuit is not clocked
Combinational
logic
System
Input
Variables
System
output
Variables
I0
In
O0
Om
S0
Sx
M0
Ex
State
Variables Excitation Variables
MX
E0
Set I{ I0……In }
are external
input variables
presented to
the system.
Set O{ O0……Om }
are external
output variables.
Combinational
logic
System
Input
Variables
System
output
Variables
I0
In
O0
Om
S0
Sx
M0
Ex
State
Variables
Excitation
Variables
MX
E0
Internally,the system generate the excitation
variables,E0 to Ex,and state variables,S0 to Sx.
internal output
variables
internal input
variables
The memory excitation input relationship can be written as
E = f( I,S ),Excitation E force the memory elements to
the desired state variables.
Output O is generated by the combinational logic
transform,(g),operating on input variables I and state
variables S.
O = g( I,S )
Combinational
transform
(f)
Memory
M
Combinational
logic
(g)
Input
(I) (E)
CLK
State variables
(S)
Excitation variables Output
(O)
E = f( I,S )
O = g( I,S )
The clock input is not a binary value representing
the time of day,but rather a,synchronous” train
of pulses,Synchronous memory changes its data
only at certain time intervals.
Combinational
transform
(f)
Memory
M
Combinational
logic
(g)
Input
(I) (E)
CLK
State variables
(S)
Excitation variables Output
(O)
State variables
State variable is the output of memory unit,
It is used to define the state of a
sequential machine.
State is defined by the content of memory,
Each state represent a different events.
State variables and states are related by
2x=y
x= number of State variables
y= number of States
Memory data are free to change with
time,It can be one value at time t1 and
another at time t2,
St and St+1 represent the binary
value of state variables,S,at
different times,t,
St represents the present-state (old
memory output) and St+1 represents
the next-state (new memory output),
Each state become a,present” state
after a clock pulse and will go to a
“next-state” on the next clock pulse,
The value of the next-state variables,
St+1,is determined by the present
value of the state variables,St,and the
input,I,
St+1 = f( St,I )
Machine Model
The output,O,is a function of only the
present state,St.
E = f( I,St )
St+1 = f( St,E )
O = g( St )
Moore machine
Combinational
transform
(f)
Memory
M
Combination
al logic
(g)
Input
(I) (E)
CLK
State variables
(S)
Excitation variables Output
(O)
Mealy machine
The output,O,is a function of both the
present state,St,and the input variables,I.
E = f( I,St )
St+1 = f( St,E )
O = g( I,St )
Combinational
transform
(f)
Memory
M
Combination
al logic
(g)
Input
(I) (E)
CLK
State variables
(S)
Excitation variables Output
(O)
State Diagram
A state diagram is a graphic rendition of a sequential
circuit,where individual states are represented by a
circle with an identifying symbol located inside.
Change from state to state are indicated by directed
arcs,Input conditions that cause state changes to
occur and the resulting output signals are written
adjacent to the directed arc.
State diagram graphically represent the relationships
between states,They show the input-output variable
combinations as the transitions from one state to the
next.
J1K1
Y1
J2K2
Y2
=1 1
X
&
Z
cp
Y2Y1 X/Z
0 0
1 01 1
0/0
0/0
0/0
0/1
1/1
1/0
1/0
1/0
0 1
In Mealy machine,the output is a function of both the
present state and the input variables.
An input-output statement
is written adjacent to each
directed arc,
D2
Y2 Y2’
D1
Y1 Y1’
X
Z
CP
10/1
00/0
11/0
01/0
0
1
1
0
0 01
1
Moore machine notation,where the output is
depend only on the present state,represent
the output variable inside the state circle.
A state diagram is somewhat analogous to the
programmer’s flowchart,The states can be viewed as
tasks or operations and the directed arcs,indicating
input conditions,as conditional statements.
The addition of one input variable double the number
of possible next state transitions,
With large numbers of input variables,it is
convenient to indicate only the asserted conditions
that cause state or output variable changes,The
unspecified input variable combinational are
assumed to leave the state machine in its present
state.
State Table
State table are tabular forms of diagrams,The
purpose of the state table is to indicate the state
transitions.
The present state column list all of the possible
state in the machine,A series of next state
columns exist,one from each combination.
Transition table takes the state table one step
further,
The state diagram represent states using
symbol or names,whereas the transition table
assign specific state variable values to each
state.
J1K1
Y1
J2K2
Y2
=1 1
X
&
Z
cp Present
state
Next state/output
Y2 Y1
Y2t+1 Y1t+1/Z
0
0
1
1
0
1
0
1
1
0
1
0
0
1
1
0
X = 0 X = 1
/0
/0
/0
/1
1
0
1
0
1
0
0
1
/0
/1
/0
/0
Present
state
Next state/output
X = 0 X = 1
A
B
C
D
/0
/0
/0
/1
B
C
D
A
/0
/1
/0
/0
D
A
B
C
A,B,C,D
are states
Y2,y1 are
state variables
D2
Y2 Y2’
D1
Y1 Y1’
X
Z
CP
Present
state
Next state
Y2 Y1
Y2t+1Y1t+1
0
0
1
1
0
1
0
1
0
1
0
0
0
1
0
1
X=0 X=1
1
1
1
1
0
0
0
0
Output
Z
0
0
1
0