This document provides an overview of sequential circuits. It defines sequential circuits as circuits whose outputs depend on current and past input values, unlike combinational circuits whose outputs only depend on current inputs. It describes the main types of sequential circuits as synchronous (controlled by a clock) and asynchronous. Common memory elements for sequential circuits called flip-flops are introduced, including SR, D, J-K, and T flip-flops. The use of state tables and state diagrams to analyze sequential circuits is covered. Procedures for reducing states, assigning binary codes to states, and designing sequential circuits using flip-flops are also outlined. An example of designing a circuit to detect three or more consecutive 1s in an input bit string
3. Sequential Circuits 3
Sequential Circuits
Combinational
The outputs depend only on the current input
values
It uses only logic gates
Sequential
The outputs depend on the current and past input
values
It uses logic gates and storage elements
Example
Vending machine
They are referred as finite state machines since
they have a finite number of states
4. Sequential Circuits 4
Block Diagram
Memory elements can store binary
information
This information at any given time determines
the state of the circuit at that time
5. Sequential Circuits 5
Sequential Circuit Types
Synchronous
The circuit behavior is determined by the signals
at discrete instants of time
The memory elements are affected only at
discrete instants of time
A clock is used for synchronization
Memory elements are affected only with the
arrival of a clock pulse
If memory elements use clock pulses in their
inputs, the circuit is called
Clocked sequential circuit
6. Sequential Circuits 6
Sequential Circuit Types
ASynchronous
The circuit behavior is determined by the signals
at any instant of time
It is also affected by the order the inputs change
7. Sequential Circuits 7
Clock
It emits a series of pulses with a
precise pulse width and precise
interval between consecutive pulses
Timing interval between the
corresponding edges of two
consecutive pulses is known as the
clock cycle time, or period
9. Sequential Circuits 9
Flip-Flops
Can keep a binary state until an input
signal to switch the state is received
There are different types of flip-flops
depending on the number of inputs
and how the inputs affect the binary
state
10. Sequential Circuits 10
Latches
The most basic flip-flops
They operate with signal levels
The flip-flops are constructed from
latches
They are not useful for synchronous
sequential circuits
They are useful for asynchronous
sequential circuits
12. Sequential Circuits 12
SR Latch with NOR
1
R
1,
S
avoid
,
conditions
normal
In
0
set to
are
Q'
and
Q
undefined,
1
R
1,
S
state
reset
1
'
,
0
state
set
0
'
,
1
Q
Q
Q
Q
reset
R
set
S
14. Sequential Circuits 14
SR Latch with NAND
0
R
0,
S
avoid
,
conditions
normal
In
1
set to
are
Q'
and
Q
undefined,
0
R
0,
S
state
reset
0
'
,
1
state
set
1
'
,
0
Q
Q
Q
Q
reset
R
set
S
18. Sequential Circuits 18
Note
The control input changes the state of
a latch or flip-flop
The momentary change is called a
trigger
Example: D Latch
It is triggered every time the pulse goes to the
logic level 1
As long as the pulse remains at the logic level 1,
the change in the data (D) directly affects the
output (Q)
THIS MAY BE A BIG PROBLEM since the state of
the latch may keep changing depending on the
input (may be coming from a combinational logic
network)
26. Sequential Circuits 26
Direct Inputs
You can use asynchronous inputs to
put a flip-flop to a specific state
regardless of the clock
You can clear the content of a flip-flop
The content is changed to zero (0)
This is called clear or direct reset
This is particularly useful when the power is off
The state of the flip-flop is set to unknown
28. Sequential Circuits 28
State Equations
'
)
(
'
)
1
(
)
1
(
)
(
'
)
(
)
(
)
(
)
(
)
(
'
)
1
(
)
(
)
(
)
(
)
(
)
1
(
x
B
A
y
x
A
t
B
Bx
Ax
t
A
t
x
t
B
t
A
t
y
t
x
t
A
t
B
t
x
t
B
t
x
t
A
t
A
A state equation shows
the next state as a
function of the current
state and inputs
32. Sequential Circuits 32
State Reduction
Reduce the number of states but keep
the input-output requirements
Reducing the number of states may
reduce the number of flip-flops
If there are n flip-flops, there are 2^n states
If you have two circuits that produce
the same output sequence for any
given input sequence, the two circuits
are equivalent
They may replace each other
33. Sequential Circuits 33
State Reduction Example
Find the states for which the
next states and outputs are
the same
36. Sequential Circuits 36
State Assignment
You need to assign binary values for
each state so that they can be
implemented
You need to use enough number of
bits to cover all the states
38. Sequential Circuits 38
Design Procedure
Derive a state diagram
Reduce the number of states
Assign binary values to the states
Obtain binary coded state table
Choose the type of flip-flop to be used
Derive simplified flip-flop input
equations and output equations
Draw the logic diagram
39. Sequential Circuits 39
Example
Design a circuit (with D flip-flops) that
detects three or more consecutive 1’s in a
string of bits coming through an input line
40. Sequential Circuits 40
Example (Cont.)
7
,
6
)
,
,
(
7
,
5
,
1
)
,
,
(
)
1
(
7
,
5
,
3
)
,
,
(
)
1
(
x
B
A
y
x
B
A
D
t
B
x
B
A
D
t
A
B
A
43. Sequential Circuits 43
Example
Design a circuit (with JK flip-flops) that
detects three or more consecutive 1’s in a
string of bits coming through an input line