ZeePedia Add to Favourites   |   Contact us


Digital Logic Design

<<< Previous APPLICATION OF S-R LATCH, Edge-Triggered D Flip-Flop, J-K Flip-flop Next >>>
 
img
CS302 - Digital Logic & Design
Lesson No. 23
APPLICATION OF S-R LATCH
Digital systems use switches to input values and to control the output. For example, a
keypad uses 10 switches to enter decimal numbers 0 to 9. When a switch is closed the switch
contacts physically vibrate or `bounce' before making a solid contact. The switch bounce
causes the voltage at the output of the switch to vary between logic low and high for a very
short duration before it settles to a steady state. Figure 23.1a. The variation in the voltage
causes the digital circuit to operate in an erratic manner. An S-R latch connected between the
switch and the digital circuit prevents the varying switch output from reaching the digital circuit.
Figure 23.1b.
In the figure 23.1a when the switch is moved up to connect the resistor to the ground,
the output voltage fluctuates between logic 1 and 0 for a very brief period of time when the
switch vibrates before making a solid contact. The output voltage settles to logic 0 when a
solid contact is made. The active-low input S-R latch shown in figure 23.1b prevents the output
signal from varying between logic 1 and 0. When the switch is moved from down position to up
position, the R input is set to 1 and S input is set to 0, which sets the Q output of the S-R latch
to 1. The S input varies between 0 and 1 due to switch `bounce', however the S-R latch
doesn't change its output state Q when S = 1 and R = 1.
Figure 23.1a The output of a switch connected to Logic High
+5 v
Output
S
Q
Active-low
Input
S-R
Latch
R
Q
+5 v
Figure 23.1b The switch connected through an S-R latch
224
img
CS302 - Digital Logic & Design
S
Q
R
Q
Figure 23.1c The switch connected through an S-R latch
The circuit diagram in figure 23.1c shows a burglar alarm circuit. The alarm switch is
connected to logic high connecting the S input to logic high. The alarm is activated by setting
the reset switch to ground connecting the R input to 0 volts. This sets the Q output of the latch
to 0. The switch is reset to logic high. When an intruder opens a door the alarm switch is
connected to ground or logic 0. The set input is set to logic 0, setting the Q output to logic 1
and activating the alarm. If the door is closed the alarm switch is reconnected to logic 1,
however the Q output is maintained at logic 1 and the alarm continues to sound as S=1 and
R=1 which maintains the output. The alarm can only be disabled by reconnecting the reset
switch to ground.
The S-R NAND gate based latch is available in the form of an Integrated Circuit. The
74LS279 IC has four S-R latches which can be used independently.
The Gated S-R Latch
The gated S-R latch has an enable input which has to be activated to operate the latch.
The circuit diagram of the gated S-R latch is shown. Figure 23.2. In the gated S-R circuit, the S
and R inputs are applied at the inputs of the NAND gates 1 and 2 when the enable input is set
to active-high. If the enable input is disabled by setting it to logic low the output of NAND gates
3 and 4 remains logic 1, what ever the state of S and R inputs. Thus logic 1 applied at the
inputs of NAND gates 1 and 2 keeps the Q and Q outputs to the previous state. The logic
symbol of a gated S-R latch is shown in figure 23.3. The Truth Table of the gated S-R latch is
shown in table 23.1. The timing diagram showing the operation of the gated S-R latch is
shown in figure 23.4
S
Q
EN
Q
R
Figure 23.2
Gated S-R Latch
225
img
CS302 - Digital Logic & Design
S
Q
EN
R
Q
Figure 23.3
Logic Symbol of a Gated S-R Latch
Input
Output
EN
S
R
Qt+1
0
x
x
Qt
1
0
0
Qt
1
0
1
0
1
1
0
1
1
1
1
invalid
Table 23.1
Truth-Table of a gated S-R Latch
S
R
EN
Q
Figure 23.4
Timing diagram of a gated S-R latch
The Gated D Latch
If the S and R inputs of the gated S-R latch are connected together using a NOT gate
then there is only a single input to the latch. The input is represented by D instead of S or R.
Figure 23.5. The gated D-latch can either have D set to 0 or 1, thus the four input
combinations applied at the S-R inputs of an S-R latch reduce to only two input combinations.
Table 23.2. The logic symbol of a gated D-latch is shown in figure 23.6. The timing diagram of
the operation of a D-latch is shown in figure 23.7. The Q output of the D latch is seen to be
following the D input.
226
img
CS302 - Digital Logic & Design
D
Q
3
1
EN
Q
4
2
Figure 23.5
Gated D Latch
Input
Output
Input
Output
EN
S (D)
R
Qt+1
EN
D
Qt+1
0
x
X
Qt
0
x
Qt
1
0
0
Qt
1
0
0
1
0
1
0
1
1
1
1
1
0
1
1
1
1
Invalid
Table 23.2
Truth-Table of a gated D Latch
D
Q
Gated
EN
D
Latch
Q
Figure 23.6
Logic Symbol of a Gated D Latch
D
EN
Q
Figure 23.7
Timing diagram of a gated D latch
Application of Gated D Latch
The D latch is available in the form of an Integrated Circuit. The 74LS75 has four D
latches which can be used independently. The gated D latch can be used to store binary
information. The circuit shown in figure 23.8 uses the gated D-latches connected at the input
227
img
CS302 - Digital Logic & Design
of 1-of-8 multiplexer to store a byte value (parallel). The multiplexer accesses each bit value
stored in the D-latch and routes it to the output. Thus the 8-bit (byte) parallel data is converted
into serial data.
Figure 23.8
Gated D-latch used to store parallel data
Edge-Triggered Flip-Flop
Flip-Flops are synchronous bi-stable devices, known as bi-stable multivibrators. Flip-
flops have a clock input instead of a simple enable input as discussed earlier. The output of
the flip-flop can only change when appropriate inputs are applied at the S and R inputs and a
clock signal is applied at the clock input. Flip-flops with enable inputs can change their state at
any instant when the enable input is active. Digital circuits that change their outputs when the
enable input is active are difficult to design and debug as different parts of the digital circuit
operate at different times.
In Synchronous systems, the output of all the digital circuits changes when a clock
signal is applied instead of the enable signal. The change in the state of the digital circuit
occurs either at the low-to-high or high-to-low transition of the clock signal. Since the transition
of the clock signal is for a very short a precise time intervals thus all digital parts of a Digital
system change their states simultaneously. The low to high or high to low transition of the
clock is considered to be an edge. Three different types of edge-triggered flip-flops are
generally used in digital logic circuits.
·
S-R edge-triggered flip-flop
·
D edge-triggered flip-flop
·
J-K edge-triggered flip-flop
Each flip-flop has two variations, that is, it is either positive edge-triggered or negative edge
triggered. A positive edge-triggered flip-flop changes its state on a low-to-high transition of the
clock and a negative edge-triggered flip-flop changes its state on a high-to-low transition of the
clock. The edge-detection circuit which allows a flip-flop to change its state on either the
positive or the negative transition of the clock is implemented using a simple combinational
228
img
CS302 - Digital Logic & Design
circuit. The edge detection circuit that detects the positive and the negative clock transition are
shown in figure 23.9.
CLK
CLK
CLK  PULSE
Figure 23.9a Positive clock edge detection circuit
CLK
CLK
CLK  PULSE
Figure 23.9b Timing diagram of the Positive clock edge detection circuit
CLK
CLK
CLK  PULSE
Figure 23.9c Negative clock edge detection circuit
CLK
CLK
CLK  PULSE
Figure 23.9d Timing diagram of the Negative clock edge detection circuit
Edge-Triggered S-R Flip-flop
229
img
CS302 - Digital Logic & Design
The Logic symbols of a positive edge and a negative edge triggered S-R flip-flops are
shown in figure 23.10. The truth table of the two S-R flip-flops are shown. Table 23.3. The
timing diagrams of the two S-R flip-flops are shown in figure 23.11.
S
S
Q
Q
S-R
S-R
CLK
CLK
Flip-Flop
Flip-Flop
R
R
Q
Q
Figure 23.10 Logic Symbol of Positive and Negative edge triggered S-R flip-flops
Input
Output
Input
Output
CLK
S
R
Qt+1
CLK
S
R
Qt+1
0
x
x
Qt
0
X
X
Qt
1
x
x
Qt
1
X
X
Qt
0
0
Qt
0
0
Qt
0
1
0
0
1
0
1
0
1
1
0
1
1
1
invalid
1
1
invalid
Table 23.3
Truth-Table of Positive and Negative Edge triggered S-R flip-flops
S
R
CLK
Q
Figure 23.11a Timing diagram of a Positive Edge triggered S-R flip-flop
230
img
CS302 - Digital Logic & Design
S
R
CLK
Q
Figure 23.11b Timing diagram of a Negative Edge triggered S-R flip-flop
Edge-Triggered D Flip-flop
The Logic symbols of a positive edge and a negative edge triggered D flip-flops are
shown in figure 23.12. The truth table of the two D flip-flops are shown. Table 23.4. The timing
diagrams of the two D flip-flops are shown in figure 23.13.
Q
Q
D
D
D
D
CLK
CLK
Flip-Flop
Flip-Flop
Q
Q
Figure 23.12 Logic Symbol of Positive and Negative edge triggered D flip-flops
Input
Output
Input
Output
CLK
D
Qt+1
CLK
D
Qt+1
0
X
Qt
0
X
Qt
1
X
Qt
1
X
Qt
0
0
0
0
1
1
1
1
Table 23.4
Truth-Table of Positive and Negative Edge triggered D flip-flops
231
img
CS302 - Digital Logic & Design
D
CLK
Q
Figure 23.13a Timing diagram of a Positive Edge triggered D flip-flop
D
CLK
Q
Figure 23.13b Timing diagram of a Negative Edge triggered D flip-flop
Edge-Triggered J-K Flip-flop
The J-K flip-flop is widely used in digital circuits. Its operation is similar to that of the S-
R flip-flop except that the J-K flip-flop doesn't have an invalid state, instead it toggles its state.
The circuit diagram of a J-K edge-triggered flip-flop is shown in figure 23.14
J
Q
3
1
CLK
Q
4
2
K
Figure 23.14 Edge-triggered J-K flip-flop
Consider the Q and Q output of the J-K flip-flop set to 1 and 0 respectively and 0 and 1
respectively. Four set of inputs are applied at J and K, the effect on the outputs is as follows.
232
img
CS302 - Digital Logic & Design
J = 0 and K =0
With Q=1 and Q =0, on a clock transition the outputs of NAND gates 3 and 4 are set to
logic 1. With logic 1 value at the inputs of NAND gates 1 and 2 the output Q and Q remains
unchanged. With Q=0 and Q =1, on a clock transition the outputs of the NAND gates 3 and 4
are set to logic 1. With logic 1 value at the inputs of NAND gates 1 and 2 the output Q and Q
remains unchanged.
Thus when J=0 and K=0 the previous state is maintained and there is no change in the
output.
J = 0 and K =1
With Q=1 and Q =0, on a clock transition the output of NAND gate 3 is set to logic 1.
The output of the NAND gate 4 is set to 0 as all three of its inputs are at logic 1. The logic 1
and 0 at the inputs of the NAND gates 3 and 4 respectively resets the Q output to 0 and Q to
1. With Q=0 and Q =1, on a clock transition the output of NAND gate 3 is set to logic 1. The
output of the NAND gate 4 is also set to 1 as the input of the NAND gate 4 is connected to
Q=0. The logic 1 and 1 at the inputs of the NAND gates 3 and 4 respectively retains the Q and
Q to 0 and 1 respectively.
Thus when J=0 and K=1 the J-K flip-flop irrespective of its earlier state is rest to state
Q=0 and Q =1.
J = 1 and K =0
With Q=1 and Q =0, on a clock transition the output of NAND gate 4 is set to logic 1.
The output of the NAND gate 3 is also set to 1 as its input connected to Q is at logic 0. Thus
inputs 1 and 1 at inputs of NAND gates 1 and 2 retain the Q and Q output to 1 and 0
respectively. With Q=0 and Q =1, on a clock transition the output of NAND gate 4 is set to
logic 1. The output of the NAND gate 3 is set to 0 as all its input are at logic 1. Thus inputs 0
and 1 at inputs of NAND gates 1 and 2 sets the flip-flop to Q=1 and Q =0.
Thus when J=1 and K=0 the J-K flip-flop irrespective of its output state is set to state
Q=1 and Q =0.
J = 1 and K =1
With Q=1 and Q =0, on a clock transition the output of the NAND gates 3 and 4 depend
on the outputs Q and Q . The output of NAND gate 3 is set to 1 as Q is connected to its input.
The output of NAND gate 4 is set to 0 as all its inputs including Q is at logic 1. A logic 1 and 0
at the input of gates 1 and 2 toggles the outputs Q and Q from logic 1 and 0 to 0 and 1
233
img
CS302 - Digital Logic & Design
respectively. With Q=0 and Q =1, on a clock transition the output of NAND gate 3 is set to 0 as
Q and the output of NAND gate 4 is set to 1. A logic 0 and 1 at the input toggles the outputs Q
and Q from logic 0 and 1 to 1 and 0 respectively.
In summary when J-K inputs are both set to logic 0, the output remains unchanged. At
J=0 and K=1 the J-K flip-flop is reset to Q=0 and Q =1. At J=1 and K=0 the flip-flop is set to
Q=1 and Q =0. With J=1 and K=1 the output toggles from the previous state. The truth tables
of the positive and negative edge triggered J-K flip-flops are shown in table 23.5. The logic
symbols of the J-K flip-flops are shown in figure 23.15. The timing diagrams of the J-K flip-
flops are shown in figure 23.16.
Input
Output
Input
Output
CLK
J
K
Qt+1
CLK
J
K
Qt+1
0
x
X
Qt
0
x
x
Qt
1
x
X
Qt
1
x
x
Qt
0
0
Qt
0
0
Qt
0
1
0
0
1
0
1
0
1
1
0
1
1
1
1
1
Qt
Qt
Table 23.5
Truth-Table of Positive and Negative Edge triggered J-K flip-flops
J
J
Q
Q
J-K
J-K
CLK
CLK
Flip-Flop
Flip-Flop
K
K
Q
Q
Figure 23.15 Logic Symbol of Positive and Negative edge triggered J-K flip-flops
234
img
CS302 - Digital Logic & Design
J
K
CLK
Q
Figure 23.16a Timing diagram of a Positive Edge triggered J-K flip-flop
J
K
CLK
Q
Figure 23.16b Timing diagram of a Negative Edge triggered J-K flip-flop
Asynchronous Preset and Clear Inputs
The S-R, J-K and D inputs are known as synchronous inputs because the outputs
change when appropriate input values are applied at the inputs and a clock signal is applied at
the clock input. If there is no clock transition then the inputs have no effect on the output.
Digital circuits require that the flip-flops be set or reset to some initial state before a new set of
inputs is applied for changing the output. The flip-flops are set-reset to some initial state by
using asynchronous inputs known as Preset and Clear inputs. Since these inputs change the
output to a known logic level independently of the clock signal therefore these inputs are
known as asynchronous inputs. The circuit diagram of a J-K flip-flop with Preset and Set
Asynchronous inputs is shown in figure 23.17. The asynchronous inputs override the
synchronous inputs thus to operate the flip-flop in the synchronous mode the asynchronous
inputs have to be disabled. To preset the flip-flop to Q=1 and Q =0 the PRE input is set to 0
which sets the Q output to 1 and the output of NAND gate 4 to 1. The CLR input is set to 1
235
img
CS302 - Digital Logic & Design
which sets the Q output to 0 as all three inputs of the NAND gate 2 are set to 1. The flip-flop
is cleared to Q=0 and Q =1 by setting the PRE input is set to 1 and the CLR input is to 0. The
CLR input set to 0 sets Q =1 it also sets the output of NAND gate 3 to 1. The PRE input set to
1 sets the output Q to 0. When the PRE and the CLR inputs are used inputs J and K have no
effect on the operation of the flip-flop. To use the flip-flop with synchronous inputs J-K, the
PRE and the CLR inputs are set to logic 1. Setting PRE and the CLR to logic 0 is not
allowed.
PRE
J
Q
3
1
CLK
Q
4
2
K
CLR
Figure 23.17 J-K flip-flop with Asynchronous Preset and Clear inputs
Figure 23.18 shows the logic symbol of a J-K edge-triggered flip-flop with synchronous and
asynchronous inputs.
PRE
J
Q
J-K
CLK
Flip-Flop
K
Q
CLR
Figure 23.18 Logic Symbol of a J-K flip-flop with Asynchronous inputs
The truth table of a J-K flip-flop with Asynchronous inputs is shown in table 23.4. The timing
diagram describes the effect of asynchronous inputs on the operation of the flip-flop. Figure
23.10
236
img
CS302 - Digital Logic & Design
Input
Output
Qt+1
CLR
PRE
0
0
Invalid
0
1
1
1
0
0
1
1
Clocked operation
Table 23.4
Truth table of J-K flip-flop with Asynchronous inputs
J
K
PRE
CLR
CLK
Q
Figure 23.10 Timing diagram of a J-K flip-flop with Preset and Clear inputs
The 74HC74 Dual Positive-Edge triggered D flip-flop
The edge-triggered D flip-flop with asynchronous inputs is available as an Integrated
Circuit. The 74HC74 has dual D-flip-flops with independent clock inputs, synchronous and
asynchronous inputs.
The 74HC112 Dual Positive-Edge triggered J-K flip-flop
The edge-triggered D flip-flop with asynchronous inputs is available as an Integrated
Circuit. The 74HC112 has dual J-K-flip-flops with independent clock inputs, synchronous and
asynchronous inputs.
Master-Slave Flip-Flops
Master-Slave flip-flops have become obsolete and are being replaced by edge-
triggered flip-flops. Master-Slave flips have two stages each stage works in one half of the
237
img
CS302 - Digital Logic & Design
clock signal. The inputs are applied in the first half of the clock signal. The outputs do not
change until the second half of the clock signal. As mentioned earlier the use of edge-triggered
flip-flip is to synchronize the operation of a digital circuit with a common clock signal. The
master-slave setup also allows digital circuits to operate in synchronization with a common
clock signal. The circuit diagram of the master-slave J-K flip-flop is shown in figure 23.11. The
Master-Slave flip-flop is composed of two parts the Master and the Slave. Both the Master and
the Slave are Gated S-R flip-flops. The Master-Slave flip-flop is not synchronised with the
clock positive or negative transition, rather it known as a pulse triggered flip-flop as it operates
at the positive and negative clock cycles.
Consider that the J-K inputs of the flip-flop are set at 1 and 0 respectively. The outputs
Q and Q are initially set at 1 and 0 respectively. During the positive half of the clock gates 3
and 4 are both enabled by the clock signal. The output of gate 3 is set to 1 due to the Q
output set at 0. Similarly the output of gate 4 is also set at 1 due to the K input set at 0. The
outputs of gates 1 and 2 remain unchanged as the inputs to gates 1 and 2 are both logic 1.
Assume the outputs of gates 1 and 2 to be 1 and 0 respectively. During the positive half cycle,
the clock input to gates 7 and 8 is inverted therefore both the gates are disabled and their
output is set to logic 1. With logic 1 at the inputs of gates 5 and 6 the output Q and Q remains
unchanged throughout the positive half of the clock cycle. During the negative half of the clock
cycle the Master flip-flop is disabled and the output of the Master flip-flop remains fixed during
the negative half cycle. The Slave flip-flop is enabled and the 1 and 0 outputs of the Master
flip-flop set the Q and Q output to 1 and 0 respectively.
J
Q
3
1
7
5
CLK
Q
4
2
8
6
K
MASTER
SLAVE
Figure 23.11 Master-Slave flip-flop
Initially, if the Q and Q outputs are 0 and 1 respectively, setting the J and K inputs to 1
and 0 respectively sets the output to 1 and 0 respectively. During the positive half of the clock
the Master flip-flop is enabled, the output of gate 3 is set to 0 as the J, Q and CLK inputs are
all at logic 1. The output of gate 4 is set to 1 as the K input is logic 0. These inputs set the
output of the Master flip-flop at gates 1 and 2 to logic 1 and 0 respectively. During the negative
half of the clock cycle the Slave flip-flop is enabled the output Q and Q are set to logic 1 and 0
respectively.
The truth-table of the master-slave flip-flop is shown in table 23.5. The timing diagram
of the master-slave flip-flop is shown in figure 23.12.
238
img
CS302 - Digital Logic & Design
Input
Output
CLK
J
K
Qt+1
Pulse
0
0
Qt
Pulse
0
1
0
Pulse
1
0
1
Pulse
1
1
Qt
Table 23.5
Truth table of the Master-Slave J-K flip-flop
J
K
CLK
Q
Figure 23.12 Timing diagram of a Master Slave J-K flip-flop
Flip-Flop Operating Characteristics
The performance of the flip-flop is specified by several operating characteristics
mentioned in the data sheets of the flip-flops. The important operating characteristics are
·  Propagation Delay
·  Set-up Time
·  Hold Time
·  Maximum Clock frequency
·  Pulse width
·  Power Dissipation
Propagation Delay
The propagation delay time is the interval of time when the input is applied and the
output changes. Four different types of Propagation Delays are measured.
1. Propagtaion Delay tPLH measured with respect to the triggering edge of the clock to the
low-to-high transition of the output. Figure 23.13. On a positive or negative clock transition
the flip-flop changes its output state. The Propagation Delay is measured at 50% transition
239
img
CS302 - Digital Logic & Design
mark on the triggering edge of the clock and the 50% mark on the low-to-high transition of
the output that occurs due to the clock transition.
Figure 23.13 Propagation Delay, clock to low-to-high transition of the output
2. Propagtaion Delay tPHL measured with respect to the triggering edge of the clock to the
high-to-low transition of the output. Figure 23.14. On a positive or negative clock transition
the flip-flop changes its output state. The Propagation Delay is measured at 50% transition
mark on the triggering edge of the clock and the 50% mark on the high-to-low transition of
the output that occurs due to the clock transition.
3. Propagtaion Delay tPLH measured with respect to the leading edge of the preset input to the
low-to-high transition of the output. Figure 23.15. On a high-to-low transition of the preset
signal the flip-flop changes its output state to logic high. The Propagation Delay is
measured at 50% transition mark on the triggering edge of the preset signal and the 50%
mark on the low-to-high transition of the output that occurs due to the preset signal.
Figure 23.14 Propagation Delay, clock to high-to-low transition of the output
240
img
CS302 - Digital Logic & Design
Figure 23.15 Propagation Delay, preset to low-to-high transition of the output
4. Propagtaion Delay tPHL measured with respect to the leading edge of the clear input to the
high-to-low transition of the output. Figure 23.16. On a high-to-low transition of the clear
signal the flip-flop changes its output state to logic low. The Propagation Delay is
measured at 50% transition mark on the triggering edge of the clear signal and the 50%
mark on the high-to-low transition of the output that occurs due to the preset signal.
Figure 23.16 Propagation Delay, clear to high-to-low transition of the output
Set-up Time
When a clock transition occurs at the clock input of a flip-flop the output of the flip-flop
is set to a new state based on the inputs. For the flip-flop to change its output to a new state at
the clock transition, the input should be stable. The minimum time required for the input logic
levels to remain stable before the clock transition occurs is known as the Set-up time. Figure
23.17.
241
img
CS302 - Digital Logic & Design
Figure 23.17 Set-up time for a D flip-flop
Hold Time
The input signal maintained at the flip-flop input has to be maintained for a minimum
time after the clock transition for the flip-flop to reliably clock in the input signal. The minimum
time for which the input signal has to be maintained at the input is the Hold time of the flip-flop.
Figure 23.18
Figure 23.18 Hold time for a D flip-flop
Maximum Clock Frequency
A flip-flop can be operated at a certain clock frequency. If the clock frequency is
increased beyond a certain limit the flip-flop will be unable to respond to the fast changing
clock transitions, therefore the flip-flop will be unable to function. The maximum clock
frequency fmax is the highest rate at which the flip-flop operates reliably.
Pulse Width
A flip-flop uses the clock, preset and clear inputs for its operation. Each signal has to
be of a specified duration for correct operation of the flip-flop. The manufacturer specifies the
minimum pulse width tw for each of the three signals. The clock signal is specified by minimum
high time and minimum low time.
Power Dissipation
A flip-flop consumes power during its operation. The power consumed by a flip-flop is
defined by P = Vcc x Icc. The flip-flop is connected to +5 volts and it draws 5 mA of current
during its operation, therefore the power dissipation of the flip-flop is 25 mW.
242
img
CS302 - Digital Logic & Design
A digital circuit is made of a number of gates, functional units and flip-flops. The total
power requirement of each device should be known so that an appropriate dc power source is
used to supply power to the digital circuit.
243
Table of Contents:
  1. AN OVERVIEW & NUMBER SYSTEMS
  2. Binary to Decimal to Binary conversion, Binary Arithmetic, 1’s & 2’s complement
  3. Range of Numbers and Overflow, Floating-Point, Hexadecimal Numbers
  4. Octal Numbers, Octal to Binary Decimal to Octal Conversion
  5. LOGIC GATES: AND Gate, OR Gate, NOT Gate, NAND Gate
  6. AND OR NAND XOR XNOR Gate Implementation and Applications
  7. DC Supply Voltage, TTL Logic Levels, Noise Margin, Power Dissipation
  8. Boolean Addition, Multiplication, Commutative Law, Associative Law, Distributive Law, Demorgan’s Theorems
  9. Simplification of Boolean Expression, Standard POS form, Minterms and Maxterms
  10. KARNAUGH MAP, Mapping a non-standard SOP Expression
  11. Converting between POS and SOP using the K-map
  12. COMPARATOR: Quine-McCluskey Simplification Method
  13. ODD-PRIME NUMBER DETECTOR, Combinational Circuit Implementation
  14. IMPLEMENTATION OF AN ODD-PARITY GENERATOR CIRCUIT
  15. BCD ADDER: 2-digit BCD Adder, A 4-bit Adder Subtracter Unit
  16. 16-BIT ALU, MSI 4-bit Comparator, Decoders
  17. BCD to 7-Segment Decoder, Decimal-to-BCD Encoder
  18. 2-INPUT 4-BIT MULTIPLEXER, 8, 16-Input Multiplexer, Logic Function Generator
  19. Applications of Demultiplexer, PROM, PLA, PAL, GAL
  20. OLMC Combinational Mode, Tri-State Buffers, The GAL16V8, Introduction to ABEL
  21. OLMC for GAL16V8, Tri-state Buffer and OLMC output pin
  22. Implementation of Quad MUX, Latches and Flip-Flops
  23. APPLICATION OF S-R LATCH, Edge-Triggered D Flip-Flop, J-K Flip-flop
  24. Data Storage using D-flip-flop, Synchronizing Asynchronous inputs using D flip-flop
  25. Dual Positive-Edge triggered D flip-flop, J-K flip-flop, Master-Slave Flip-Flops
  26. THE 555 TIMER: Race Conditions, Asynchronous, Ripple Counters
  27. Down Counter with truncated sequence, 4-bit Synchronous Decade Counter
  28. Mod-n Synchronous Counter, Cascading Counters, Up-Down Counter
  29. Integrated Circuit Up Down Decade Counter Design and Applications
  30. DIGITAL CLOCK: Clocked Synchronous State Machines
  31. NEXT-STATE TABLE: Flip-flop Transition Table, Karnaugh Maps
  32. D FLIP-FLOP BASED IMPLEMENTATION
  33. Moore Machine State Diagram, Mealy Machine State Diagram, Karnaugh Maps
  34. SHIFT REGISTERS: Serial In/Shift Left,Right/Serial Out Operation
  35. APPLICATIONS OF SHIFT REGISTERS: Serial-to-Parallel Converter
  36. Elevator Control System: Elevator State Diagram, State Table, Input and Output Signals, Input Latches
  37. Traffic Signal Control System: Switching of Traffic Lights, Inputs and Outputs, State Machine
  38. Traffic Signal Control System: EQUATION DEFINITION
  39. Memory Organization, Capacity, Density, Signals and Basic Operations, Read, Write, Address, data Signals
  40. Memory Read, Write Cycle, Synchronous Burst SRAM, Dynamic RAM
  41. Burst, Distributed Refresh, Types of DRAMs, ROM Read-Only Memory, Mask ROM
  42. First In-First Out (FIFO) Memory
  43. LAST IN-FIRST OUT (LIFO) MEMORY
  44. THE LOGIC BLOCK: Analogue to Digital Conversion, Logic Element, Look-Up Table
  45. SUCCESSIVE –APPROXIMATION ANALOGUE TO DIGITAL CONVERTER