04 May Latches and flip-flops are considered as sequential circuits and can act ?as data storage devices. In this discussion let’s learn about major ?differences betw
Latches and flip-flops are considered as sequential circuits and can act as data storage devices. In this discussion let's learn about major differences between latches and flipflops. We are also going to discuss major applications where flipflops are and why.
In your original post, answer the following:
- Discuss the difference between latches and flip-flops.
- Discuss the applications of flip-flops.
EET 230– Digital Systems II
Multivibrators, Latches and Flip-Flops
Outline of the lecture
2
Sequential Logic
S-R Latch
Gated S-R Latch
D- Latches
Timing Diagrams
Objective of the Lecture
After successful completion of the lecture students
will be able to:
State the difference between combinational and sequential
logic.
Describe the operations of different types of latches and
flip-flops.
Explain the operation of non-retriggerable and
retriggerable one shot.
Use logic gates to construct basic latches.
Draw the timing diagrams for S-R and D-latches.
Explain the difference between S-R latches and D-latches.
Recognize the difference between latches and flip-flops. 3
Road Traveled So Far ……….
4
Switches Logic gates Sequential Circuit
Combinational Circuit
?
What is the Sequential Circuit?
5
Can we build the circuit as shown below?
When the button is pushed: 1) Turn ‘on’ the light if
it is already ‘off’
2) Turn ‘off’ the light if it is already ‘on’
The light should change state within a second of the button press
button light
What make this circuit so different from those we have discussed before?
1. “State”, i.e., the circuit has memory
2. The input not only change output but also the ‘state’ of the circuit
3. The timing in which the state and output will be changed
6 Sequential = Stateful
(button} (light}
Off On
On Off
1 second timing
What is the Sequential Circuit?
Sequential Logic
Sequential circuit = Combinational logic + Memory Elements
Current State of A sequential Circuit: Value stored in memory
elements (value of state variables).
State transition: A change in the stored values in memory
elements thus changing the sequential circuit from one state to
another state.
7
Combinational
logic
Memory
elements
Combinational
outputs Memory outputs
Inputs
Sequential Logic
A Memory Element: A logic device that can remember a single-bit value
indefinitely, or change its value on command from its inputs.
The output Q of the memory element represents the value stored in the
memory element. This is also called the state variable of the memory
elements. A memory element can be in one of two possible states:
Q = 0 (the memory element has 0 stored), also said be in state 0.
Q =1 (the memory element has 1 stored), also said to be in state 1.
The commands to the memory element formed by its input(s) may include:
Set: Store 1 (Q=1) in the memory element.
Reset: Store 0 (Q=0) in the memory element.
Flip: Change stored value from 0 to 1 or from 1 to 0.
Hold value: Memory value does not change.
8
command Memory
element Memory Element Output:
stored single-bit value
Q
9
Sequential Circuits
The outputs of a sequential circuit depend on not only the inputs, but also the state, or the current contents of some memory
This makes things more difficult to understand, since the same inputs can yield different outputs, depending on what’s stored in memory
The memory contents can also change as the circuit runs
We’ll some need new techniques for analyzing and designing sequential circuits
Combinational circuit
Inputs
Memory
Outputs
10
Examples of Sequential Devices
Many real-life devices are sequential in nature:
Combination locks open if you enter numbers in the right
order
Elevators move up or down and open or close depending
on the buttons that are pressed on different floors and in
the elevator itself
Traffic lights may switch from red to green depending on
whether or not a car is waiting at the intersection
11
What Exactly is Memory?
A memory should have at least three properties.
1. It should be able to hold a value
2. You should be able to read the value that was saved
3. You should be able to change the value that’s saved
We’ll start with the simplest case, a one-bit memory
1. It should be able to hold a single bit, 0 or 1
2. You should be able to read the bit that was saved
3. You should be able to change the value. Since there’s only a single bit, there are only two choices: Set the bit to 1
Reset, or clear, the bit to 0
12
The Basic Idea of Storage
How can a circuit "remember" anything, when it’s just a bunch of gates that produce outputs according to the inputs?
The basic idea is to make a loop, so the circuit outputs are also inputs
Here is one initial attempt, shown with two equivalent layouts:
Does this satisfy the properties of memory?
These circuits "remember" Q, because its value never changes (Similarly, Q' never changes either)
We can also "read" Q, by attaching a probe or another circuit
But we can’t change Q! There are no external inputs here, so we can’t control whether Q=1 or Q=0
13
The S-R Latch Circuit
Let’s use NOR gates instead of inverters. The SR latch below has two inputs S and R, which will let us control the outputs Q and Q'
Here Q and Q' feed back into the circuit. They’re not only outputs, they’re also inputs!
To figure out how Q and Q' change, we have to look at not only the inputs S and R, but also the current values of Q and Q':
Qnext = (R + Q'current)'
Q'next = (S + Qcurrent)'
Let’s see how different input values for S and R affect this thing
14
Storing a Value: SR = 00
What if S = 0 and R = 0?
The equations on the right reduce to:
Qnext = (0 + Q'current)' = Qcurrent
Q'next = (0 + Qcurrent)' = Q'current
So when SR = 00, then Qnext = Qcurrent
Whatever value Q has, it keeps
This is exactly what we need to store values
in the latch
Qnext = (R + Q’current)’ Q’next = (S + Qcurrent)’
15
Setting the Latch: SR = 10
What if S = 1 and R = 0?
Since S = 1, Q’next is 0, regardless of Qcurrent:
Q’next = (1 + Qcurrent)’ = 0
Then, this new value of Q’ goes into the top NOR gate, along with R = 0
Qnext = (0 + 0)’ = 1
So when SR = 10, then Q’next = 0 and Qnext = 1
This is how you set the latch to 1. The S input stands for “set”
Once Qnext becomes 1, the outputs will stop changing. This is a stable state
Qnext = (R + Q’current)’ Q’next = (S + Qcurrent)’
16
Resetting the Latch: SR = 01
What if S = 0 and R = 1?
Since R = 1, Qnext is 0, regardless of Qcurrent:
Qnext = (1 + Q’current)’ = 0
Then, this new value of Q goes into the bottom NOR gate, where S = 0
Q’next = (0 + 0)’ = 1
So when SR = 01, then Qnext = 0 and Q’next = 1
This is how you reset, or clear, the latch to 0 The R input stands for “reset”
Qnext = (R + Q’current)’ Q’next = (S + Qcurrent)’
17
SR Latches are Memories!
This little table shows that our latch provides everything we need in a memory: we can set it, reset it, and remember the current value
The output Q represents the data stored in the latch. It is sometimes called the state of the latch
We can expand the table above into a state table, which explicitly shows that the next values of Q and Q’ depend on their current values, as well as on the inputs S and R
S R Q
0 0 No change
0 1 0 (reset)
1 0 1 (set)
Inputs Current Next
S R Q Q’ Q Q’
0 0 0 1 0 1
0 0 1 0 1 0
0 1 0 1 0 1
0 1 1 0 0 1
1 0 0 1 1 0
1 0 1 0 1 0
18
SR Latches are Sequential!
Notice that for inputs SR = 00, the next value of Q could be either 0 or 1, depending on the current value of Q
So the same inputs can yield different outputs, depending on whether the latch was previously set or reset
This is very different from the combinational circuits that we’ve seen so far, where the same inputs always yield the same outputs
Inputs Current Next
S R Q Q’ Q Q’
0 0 0 1 0 1
0 0 1 0 1 0
0 1 0 1 0 1
0 1 1 0 0 1
1 0 0 1 1 0
1 0 1 0 1 0
S R Q
0 0 No change
0 1 0 (reset)
1 0 1 (set)
19
What about SR = 11?
Both Qnext and Q'next will become 0
This contradicts the assumption that Q and Q’ are always complements
Another problem is what happens if we then make S = 0 and R = 0 together
Qnext = (0 + 0)' = 1
Q’next = (0 + 0)' = 1
But these new values go back into the NOR gates, and in the next step we get:
Qnext = (0 + 1)' = 0
Q’next = (0 + 1)' = 0
The circuit enters an infinite loop, where Q and Q’ cycle between 0 and 1 forever
This is actually the worst case, but the moral is don’t ever set SR=11!
Qnext = (R + Q’current)’ Q’next = (S + Qcurrent)’
0
0
0
0
0
0
1
1
20
Converting a NOR S-R to an NAND S-R
Active High NOR
Gate Implementation Push Bubbles
(DeMorgan’s) Rearrange
Bubbles Convert
from Bubbles
to Active Low
Signal Names
S
R Q
Q
≡
S
R Q
Q S
R Q
Q
≡
Q
Q
≡
S
R
21
S’R’ Latch
There are several varieties of latches
You can use NAND instead of NOR gates to get a S’R’ latch
The input signals for the NAND latch are the complement of the signals for the NOR latch, hence the name S’R’ latch
You can derive this table by writing equations for the outputs in terms of the inputs and the current state, just as we did for the SR latch
S’ R’ Q
1 1 No change
1 0 0 (reset)
0 1 1 (set)
0 0 Avoid!
22
An SR Latch with a Control Input
Here is an SR latch with a control input C
Notice the hierarchical design! The dotted blue box is the S’R’ latch from the previous slide
The additional NAND gates are simply used to generate the correct inputs for the S’R’ latch
The control input acts just like an enable. Latch can only change when C = 1, all other times the circuit remains in the same state no matter what values are on the S and R inputs
C S R S’ R’ Q
0 x x 1 1 No change
1 0 0 1 1 No change
1 0 1 1 0 0 (reset)
1 1 0 0 1 1 (set)
1 1 1 0 0 Avoid!
SR Latch with Enable input
23
SR Latch with Enable input
25
D Latch
The D latch is designed to eliminate the undefined state of the SR latch by ensuring that the S and R inputs are never high at the same time
A D latch is based on an S'R' latch. The additional gates generate the S' and R' signals, based on inputs D ("Data") and C ("Control")
When C = 0, S' and R' are both 1, so the state Q does not change
When C = 1, the latch output Q will equal the input D
No more messing with one input for set and another input for reset!
Also, this latch has no "bad" input combinations to avoid. Any of the four possible assignments to C and D are valid
C D Q
0 x No change
1 0 0
1 1 1
D Latch
D Latch
S R Q
0 0 No change
0 1 0 (reset)
1 0 1 (set)
Inputs Current Next
S R Q Q’ Q Q’
0 0 0 1 0 1
0 0 1 0 1 0
0 1 0 1 0 1
0 1 1 0 0 1
1 0 0 1 1 0
1 0 1 0 1 0S’ R’ Q
1 1 No change
1 0 0 (reset)
0 1 1 (set)
0 0 Avoid!
C S R S’ R’ Q
0 x x 1 1 No change
1 0 0 1 1 No change
1 0 1 1 0 0 (reset)
1 1 0 0 1 1 (set)
1 1 1 0 0 Avoid!
C D Q
0 x No change
1 0 0
1 1 1
Latch Timing Diagram Practice
32
Latch Timing Diagram Practice
33
Latch Timing Diagram Practice
34
Latch Timing Diagram Practice
35
Latch Timing Diagram Practice
36
Latch Timing Diagram Practice
37
Summary
38
Sequential Logic
S-R Latch
Gated S-R Latch
D- Latches
Timing Diagrams
,
EET 230– Digital Systems II
Multivibrators, Latches and Flip-
Flops
2
Outline of the lecture
Edge – Triggered S-R Flip-Flop
Method of Edge – Triggering
Edge – Triggered D Flip-Flop
Edge – Triggered J-K Flip-Flop
Asynchronous Preset and Clear Inputs
Flip-Flop Operating Characteristics
Flip-Flop Applications
Objective of the Lecture
After successful completion of the lecture students
will be able to:
Explain the operations of S-R, D and J-K flip-flops
Draw the timing diagram for S-R, D and J-K flip-flops
Understand the significance of propagation delay.
Set-up time and hold time in logic circuits
Explain methods of triggering flip-flops
Apply flip-flops in basic applications such as square wave
generation and frequency division
3
4
Edge Triggered Flip-Flops
An edge triggered flip-flop changes state either at the
positive edge (rising edge) or a the negative edge (falling
edge) of the clock pulse
Its sensitive to inputs only at this transition of the clock
There are 3 types of edge triggered flips: S-R, D, and J-K
Each flip-flop can be either positive edge triggered (no
bubble at the C input) or negative edge triggered (bubble at
the C input)
5
Edge Triggered Flip-Flops
Edge-triggered flip-flop logic symbols (top: positive edge-triggered; bottom: negative edge-triggered)
The dynamic input indicator means the flip flop changes state only on the edge of a clock pulse
6
A Method of Edge Triggering
The S-R flip-flop differs from the gated S-R latch only in that it has a pulse transition detector
This circuit produces a very short duration spike on either the positive- going transition or the negative-going transition of each clock pulse
The circuit uses a AND gate as the input thereby providing a delay in nanoseconds
The inverter is used to handle both positive and negative edge triggering because of the inversion process
The Enable in this case is called the Clock (CLK) S
R
Q
Q'
pulse transition detector
CLK
A simplified logic diagram for an edge-triggered S-R flip flop
7
Edge Detection Circuits
8
Edge Triggered S-R Flip-Flop
The S and R inputs of the S-R flip-flop are called synchronous inputs because data on these inputs are transferred to the flip-flop’s output only on the triggering edge of the clock pulse
When the S is HIGH and R is LOW, the Output goes HIGH on the triggering edge of the clock pulse – flip flop is SET
When the S is LOW and R is HIGH, the Output goes LOW on the triggering edge of the clock pulse – flip flop is RESET
When both S and R are LOW, the output does not change from its previous state
An invalid condition exists when both S and R are HIGH
S
R
Q
Q'
pulse transition detector
CLK
9
Operation of a positive edge-triggered S-R flip-flop
Note: The operation and truth table for a negative edge-triggered flip-flop are the same as those for a positive except that the falling edge of the clock pulse is the triggering edge
S R Q Q* Operation
0 0 Q Q Hold
1 0 1 0 Set (Q → 1)
0 1 0 1 Reset (Q → 0)
1 1 X X Not Allowed
Positive Edge Triggered S-R Flip-Flop Timing Diagram
S R Q Q* Operation
0 0 Q Q Hold
1 0 1 0 Set (Q → 1)
0 1 0 1 Reset (Q → 0)
1 1 X X Not Allowed
Positive Edge Triggered S-R Flip-Flop Timing Diagram
12
Positive Edge Triggered S-R Flip-Flop Timing Diagram
Edge Triggered S-R Flip-Flop Timing Diagram
14
The Edge Triggered D Flip-Flop
The D flip-flop is useful when a single bit (1 or 0) is to be stored
The addition of an inverter to an S-R flip flop creates a basic D Flip- Flop
The flip-flop only has 1 input in addition to the clock
If there is a HIGH on the D when a clock pulse is applied, the flip flop will set and the HIGH on the D input is stored by the flip-flop on the triggering edge of the clock pulse
If there is a LOW on the D when the clock pulse is applied, the flip flop will reset and the LOW on the D input is stored by the flip-flop on the triggering edge of the clock pulse
In a SET state the flip-flop is storing a 1, and the RESET state is storing a 0
A positive edge-triggered D Flip-Flop formed with an S-R flip-flop and an inverter
15
The Positive Edge Triggered D Flip-Flop Timing Diagram
Note: From the above timing diagram, it's called a D flip-flop because it delays the signal. The output is just the input delayed until the next active clock transition
Q*0 0 1 1
D Q C
0 0 0 1 1 0 1 1
Set 0
Set 1
The Positive Edge Triggered D Flip-Flop Timing Diagram
Edge Triggered D Flip-Flop Timing Diagram
18
The Edge Triggered J-K Flip-Flop
The J-K Flip-Flop is versatile and is a widely used type of
flip flop
The J and K designations for the inputs have no know
significance except that they adjacent letters in the alphabet
The function of the J-K flip flop is identical to that of the S-R
flip-flop in the SET, RESET and no change conditions of
operation
The difference is that the J-K flip-flop has no invalid state as
does the S-R flip-flops
19
The Negative Edge Triggered J-K Flip-Flop Timing Diagram
Q*
0
1
0
0
1
1
1
0
J K Q C
0 0 0
0 0 1
0 1 0
0 1 1
1 0 0
1 0 1
1 1 0
1 1 1 Toggle
Hold
Reset
Set
Q*
0
1
0
0
1
1
1
0
J K Q C
0 0 0
0 0 1
0 1 0
0 1 1
1 0 0
1 0 1
1 1 0
1 1 1 Toggle
Hold
Reset
Set
Edge Triggered J-K Flip-Flop Timing Diagram
Edge Triggered J-K Flip-Flop Timing Diagram
24
Asynchronous Preset and Clear Inputs
The S-R, D and J-K inputs just discussed are called synchronous inputs because data on these inputs are transferred to the flip-flop’s output only on the triggering edge of the clock pulse → data is transferred synchronously with clock
Most IC flip flops also have asynchronous inputs
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