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1
Combinational vs. Sequential
 Combinational Logic Circuit
 Output is a function only of the present
inputs.
 Does not have state information.
 Does not require memory.
 Sequential Logic Circuit (Finite State Machine)
 Output is a function of the present state and
at times present state and input.
 Has state information
 Requires memory.
 Uses Flip-Flops to implement memory.
2
Synchronous vs. Asynchronous
 Synchronous Sequential Logic Circuit
 Clocked
 All Flip-Flops use the same clock and
change state on the same triggering
edge.
 Asynchronous Sequential Logic Circuit
 No clock
 Can change state at any instance in
time.
 Faster but more complex than
synchronous sequential circuits.
3
General Models for Sequential Circuits
A sequential circuit can be divided conveniently into
two parts -- the flip-flops which serve as memory for
the circuit and the combinational logic which realizes
the input functions for the flip-flops and the output
functions.
The combinational logic may be implemented with
gates, with a ROM, or with a PLA.
4
Sequential Logic (Why) ?
°Sequential circuit has additional dimension which
is time
°Combinational logic only depends on current
input
°Sequential circuit output depends on previous
input other than current input
°More powerful than combinational logic
°Able to model condition that can’t be
accommodated by combinational logic
5
Analysis of Clocked Sequential Circuits
°Analysis of a sequential circuit consists of
obtaining a table or a diagram for the time
sequence of inputs, outputs, and internal states.
°Sequential circuit behavior is determined from the
inputs, the outputs, and the state of its flip-flops
°Boolean expressions that describe the behavior of
the sequential circuit
°Outputs and the next state are both a function of
the inputs and the present state
°A logic diagram is recognized as a clocked
sequential circuit if it includes flip-flops.
°Logic diagram may or may not include
combinational circuit gates.
6
State
°The state of a sequential circuit is a collection of
state variables whose values at any particular time
contain all the information about the past
necessary to account for the circuit’s future
behaviour.
°In the channel-selector example, the current
channel number is the current state.
°Inside the TV, this state might be stored as seven
binary state variables representing a decimal
number between 1 and 9.
°Given the current state (channel number), we can
always predict the next state as a function of the
inputs (up/down pushes).
7
D Flip-Flop with Clock input
Q(t+1) = Q.D + Q.D = D.(Q +Q) = D.1 = D
Q D Q(t+1)
0 0 0
0 1 1
1 0 0
1 1 1
8
Boolean equation for D Flip-Flop
9
Sequential Circuit Analysis
°Given sequential circuit diagram, behavioral
analysis from state table and also state diagram
°Need state equations to get flip-flop input and
output functions for circuit output other than flip-
flop (if any)
°A(t) and A(t+1) are used to represent current state
and the next state for flip-flop.
°A and A+ can also be used in order to represent
current state and the following state
10
Sequential Circuit Analysis
°Example (using D flip-flop)
State equation
Output Function
11
Sequential Circuit Analysis
°From the state equations and output function, state
table can be derived that contains all combined binary
combination for the current condition (present state)
and input
°State table
• The same as Truth Table
• Input and condition pad on the left
• Output and next condition on the right
• Combined binary combination available for current state
and input
12
Sequential Circuit Analysis
State table for circuit in Example 1
°From the state equations and output function, state table can be derived that contains all
combined binary combination for the current condition (present state) and input
°State table
• The same as Truth Table
• Input and condition pad on the left
• Output and next condition on the right
• combined binary combination available for current state and input
°M flip-flop and n input => 2m+n line
State equation Output function
13
Sequential Circuit Analysis
Other method
14
Sequential Circuit Analysis
°From the truth table, we can draw state diagram
°State diagram
• Each state is represented by circle
• Each arrow (between two circle) represent
transfer for sequential logic (i.e. line transition
in truth table)
• a/b label for each arrow where a represent
inputs and b represent output for circuit in
transition
°Each flip-flop value combination represent state.
Therefore, m flip-flop=> until 2m state.
15
Sequential Circuit Analysis
State diagram for circuit in
previous example
°Each state is represented by
circle
°Each arrow (between two
circle) represent transfer for
sequential logic (i.e. line
transition in truth table)
°a/b label for each arrow where
a represent inputs and b
represent output for circuit in
transition
16
Flip-flop Input Function
°Output of sequential circuit is a function of the
current state of the flip-flop and the input. This is
explained using algebra by circuit output function
• In previous example : y= (A+B)x’
°Circuit part that generate input to flip-flop is
represented by using Boolean equation and is known
as flip-flop input’s function
°Flip-flop input function determine next state
°From flip-flop input function and criteria table for flip-
flop, next state of the flip-flop is obtained
17
Flip-flop Input Function
°Example: circuit with JK flip flop
°2 characters are used in order to represent flip-flop
input: first character represents the flip-flop input (J
or K for JK flip-flop, S or R for SR flip-flop, D for D
flip-flop, T for T flip-flop respectively) and the
second character represents the name of the flip-
flop
18
Analysis: Example
°Given a sequential circuit with two JK flip-flop,
namely A, B and one input x
°Flip-flop input function obtained from the circuit is
°JA=B JB=x’
°KA=B.x’ JB=A’.x+A.x’
19
Analysis: Example
°Fill the state table with the above function using criteria
table for the used flip-flop
20
Analysis: Example
°Draw state diagram from the state table

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DLD Combinational vs Sequential Circuits

  • 1. 1 Combinational vs. Sequential  Combinational Logic Circuit  Output is a function only of the present inputs.  Does not have state information.  Does not require memory.  Sequential Logic Circuit (Finite State Machine)  Output is a function of the present state and at times present state and input.  Has state information  Requires memory.  Uses Flip-Flops to implement memory.
  • 2. 2 Synchronous vs. Asynchronous  Synchronous Sequential Logic Circuit  Clocked  All Flip-Flops use the same clock and change state on the same triggering edge.  Asynchronous Sequential Logic Circuit  No clock  Can change state at any instance in time.  Faster but more complex than synchronous sequential circuits.
  • 3. 3 General Models for Sequential Circuits A sequential circuit can be divided conveniently into two parts -- the flip-flops which serve as memory for the circuit and the combinational logic which realizes the input functions for the flip-flops and the output functions. The combinational logic may be implemented with gates, with a ROM, or with a PLA.
  • 4. 4 Sequential Logic (Why) ? °Sequential circuit has additional dimension which is time °Combinational logic only depends on current input °Sequential circuit output depends on previous input other than current input °More powerful than combinational logic °Able to model condition that can’t be accommodated by combinational logic
  • 5. 5 Analysis of Clocked Sequential Circuits °Analysis of a sequential circuit consists of obtaining a table or a diagram for the time sequence of inputs, outputs, and internal states. °Sequential circuit behavior is determined from the inputs, the outputs, and the state of its flip-flops °Boolean expressions that describe the behavior of the sequential circuit °Outputs and the next state are both a function of the inputs and the present state °A logic diagram is recognized as a clocked sequential circuit if it includes flip-flops. °Logic diagram may or may not include combinational circuit gates.
  • 6. 6 State °The state of a sequential circuit is a collection of state variables whose values at any particular time contain all the information about the past necessary to account for the circuit’s future behaviour. °In the channel-selector example, the current channel number is the current state. °Inside the TV, this state might be stored as seven binary state variables representing a decimal number between 1 and 9. °Given the current state (channel number), we can always predict the next state as a function of the inputs (up/down pushes).
  • 7. 7 D Flip-Flop with Clock input Q(t+1) = Q.D + Q.D = D.(Q +Q) = D.1 = D Q D Q(t+1) 0 0 0 0 1 1 1 0 0 1 1 1
  • 9. 9 Sequential Circuit Analysis °Given sequential circuit diagram, behavioral analysis from state table and also state diagram °Need state equations to get flip-flop input and output functions for circuit output other than flip- flop (if any) °A(t) and A(t+1) are used to represent current state and the next state for flip-flop. °A and A+ can also be used in order to represent current state and the following state
  • 10. 10 Sequential Circuit Analysis °Example (using D flip-flop) State equation Output Function
  • 11. 11 Sequential Circuit Analysis °From the state equations and output function, state table can be derived that contains all combined binary combination for the current condition (present state) and input °State table • The same as Truth Table • Input and condition pad on the left • Output and next condition on the right • Combined binary combination available for current state and input
  • 12. 12 Sequential Circuit Analysis State table for circuit in Example 1 °From the state equations and output function, state table can be derived that contains all combined binary combination for the current condition (present state) and input °State table • The same as Truth Table • Input and condition pad on the left • Output and next condition on the right • combined binary combination available for current state and input °M flip-flop and n input => 2m+n line State equation Output function
  • 14. 14 Sequential Circuit Analysis °From the truth table, we can draw state diagram °State diagram • Each state is represented by circle • Each arrow (between two circle) represent transfer for sequential logic (i.e. line transition in truth table) • a/b label for each arrow where a represent inputs and b represent output for circuit in transition °Each flip-flop value combination represent state. Therefore, m flip-flop=> until 2m state.
  • 15. 15 Sequential Circuit Analysis State diagram for circuit in previous example °Each state is represented by circle °Each arrow (between two circle) represent transfer for sequential logic (i.e. line transition in truth table) °a/b label for each arrow where a represent inputs and b represent output for circuit in transition
  • 16. 16 Flip-flop Input Function °Output of sequential circuit is a function of the current state of the flip-flop and the input. This is explained using algebra by circuit output function • In previous example : y= (A+B)x’ °Circuit part that generate input to flip-flop is represented by using Boolean equation and is known as flip-flop input’s function °Flip-flop input function determine next state °From flip-flop input function and criteria table for flip- flop, next state of the flip-flop is obtained
  • 17. 17 Flip-flop Input Function °Example: circuit with JK flip flop °2 characters are used in order to represent flip-flop input: first character represents the flip-flop input (J or K for JK flip-flop, S or R for SR flip-flop, D for D flip-flop, T for T flip-flop respectively) and the second character represents the name of the flip- flop
  • 18. 18 Analysis: Example °Given a sequential circuit with two JK flip-flop, namely A, B and one input x °Flip-flop input function obtained from the circuit is °JA=B JB=x’ °KA=B.x’ JB=A’.x+A.x’
  • 19. 19 Analysis: Example °Fill the state table with the above function using criteria table for the used flip-flop
  • 20. 20 Analysis: Example °Draw state diagram from the state table