Digital Electronics
Module 2: Basic Logic Gates
PREPARED BY
Academic Services Unit
August 2012
© Applied Technology High Schools, 2012
ATE414 – Digital Electronics
Module-2: Basic Logic Gates
Module Objectives
Upon successful completion of this module, students should be able to:

Describe the operation of the AND, OR, and NOT gates.

Describe the operation of the NAND gate and the NOR gate.

Construct simple discrete circuits using the following basic gates:
AND, OR, NAND and NOR.

Use logic gates in simple applications.
Module Contents:
Topic
2
Page No.
2.1
Introduction
3
2.2
Logic States
3
2.3
Universal Logic Gates
13
2.4
Classroom Activity: Logic Gate Symbols
15
2.5
Lab Activity 1
17
2.6
Lab Activity 2
19
2.7
Lab Activity 3
21
2.8
Lab Activity 4
24
2.9
Review Exercises
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Module 2: Basic Logic Gates
ATE414 – Digital Electronics
2.1 INTRODUCTION
Logic gates are the building blocks of any digital circuit which is the building
block of modern digital systems. Therefore it is important to study the logical
operation, application, and troubleshooting of logic gates.
A Logic gate has one or more inputs and only one output; it is defined as an
electronic circuit or device which makes logical decisions. The output logical
decision is a fundamental property of a logic gate and it is a result of certain
input combinations.
The logic gates AND, OR, and NOT are referred to as Basic Logic Gates. The
basic gates combine to form more complex logic circuits called Combinational
Logic Gates. The available combinational logic gates are: NAND, NOR, XOR,
and XNOR.
2.2 Logic States
In digital systems there are only two possible states represented by two
voltage levels. The two states or voltage-levels are:

HIGH and it represents  Closed switches, Lights ON, or Logic-1

LOW and it represents  Open switches, Lights OFF, or Logic-0
Suppose the two level voltages are
+5V
HIGH
0V
LOW
+5V and 0V (Figure 1), then we
designate the two states as follows:

HIGH  +5V  Logic-1.

LOW  0V  Logic-0.
Figure 1: Logic two States
Logic State
switch
Light
Voltage Level
Binary-0
Open
OFF
LOW (0V)
Binary-1
Closed
ON
HIGH (≥+5V)
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Module 2: Basic Logic Gates
ATE414 – Digital Electronics
Basic Logic Gates
The three basic logic gates are:
1) AND
2) OR
3) NOT
2.2.1 Series Switching Circuit
Consider
the
Series
Switching
Circuit shown in Figure 2. The
series-connected switches, S1 and
S2 represent the inputs, while the
S1
S2
lamp L represents the output. This
Lamp
(L)
VDC
circuit behaves as follows:
 The light L turns ON only if the
switches
S1
AND
S2
are
CLOSED.
Figure 2: Series Switching Circuit
 The light L turns OFF if any one
of the switches is OPEN.
Series Switching Circuit Operation
INPUTS
The logical operation of a series switching circuit
OUTPUT
S1
S2
L
of Figure 2 is illustrated in Table 1 as follows:
Open
Open
OFF
 When both S1 and S2 are open  L is OFF.
Open
Closed
OFF
 When S1 is open and S2 is closed  L is OFF.
Closed
Open
OFF
 When S1 is closed and S2 is open  L is OFF.
Closed
Closed
ON
 When both S1 and S2 are closed  L is ON.
Table 1: The logical
operation of a series
switching circuit
Such a series switching circuit is also known as AND Switching Circuit
because the lamp is ON only if both, S1 AND S2 are CLOSED.
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Module 2: Basic Logic Gates
ATE414 – Digital Electronics
2.2.2 AND Logic Gate
The digital circuit which can act exactly like an AND switching circuit is
known as AND logic gate. Therefore the AND gate can be defined as a
logic device that has two or more inputs and a single output such that its
output is High only if all of its inputs are High.
Logic Symbol
The logic symbol of an AND logic gate with
two inputs (A & B) and a single output (X) is
shown in Figure 3. The AND logic gate can
A
X
AND
B
have a maximum number of 8-inputs but
Figure 3: AND logic symbol
only one output.
Logic Operation and Truth Table
The logical operation of the AND Gate is such that
INPUTS
the output is HIGH only when all of the inputs are
A
B
X
0
0
0
0
1
0
1
0
0
1
1
1
HIGH. When any one of the inputs is LOW, the
output is LOW.
We generally express the logical operation of a gate
with
a
table.
The
table
that
lists
all
input
combinations and the corresponding outputs is
called the truth table and is illustrated in Table 2.
OUTPUT
Table 2: Truth table
for 2-input AND gate
Boolean Expression
The two variables expression “X = A AND B” is called the AND Boolean
Expression and is represented in another format as follows:
X = A  B; or simply, X = A B; and they mean the following:

5
If A = High AND B = High then X = High. Otherwise X = Low.
Module 2: Basic Logic Gates
ATE414 – Digital Electronics
2.2.3 Number of Input Combinations
The number of all possible combinations 0f 1 and 0 values for n-inputs is
given by 2n.
Example-1:
a) For 2-input logic gate  Number of input-combinations = 2n = 22 = 4.
b) For 3-input logic gate  Number of input-combinations = 2n = 23 = 8.
Exercise-1:
Table
3a illustrates the
truth
table
Switches
Output
S1
S2
S3
Lamp
OFF
OFF
OFF
OFF
series switching circuit.
OFF
OFF
ON
OFF
a) Rewrite this truth table
OFF
ON
OFF
OFF
in terms of 0's and 1's.
OFF
ON
ON
OFF
b) Draw the AND symbol
ON
OFF
OFF
OFF
switching
ON
OFF
ON
OFF
circuit which represent
ON
ON
OFF
OFF
ON
ON
ON
ON
and
the
the
truth
of
2-inputs
tables
Table (3a and 3b).
6
of
Table 3a: Truth Table
for the series switching
circuit
Module 2: Basic Logic Gates
Input
A
B
Output
C
X
Table 3b: Truth
Table in terms of 0's
and 1's
ATE414 – Digital Electronics
c) Write the Boolean expression for a 3-input AND gate.
d) Find the number of input-combinations for a 4-input logic gate.
Conduct Lab Activity 1.
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2.2.4 Parallel Switching Circuit
Consider
the
Parallel
Switching
Circuit shown in Figure 4. The
Parallel-connected
switches,
S1
S1
and S2 represent the inputs, while
the lamp L represents the output.
S2
Lamp
L
VDC
This circuit behaves as follows:
 If either, S1 OR S2 OR both are
CLOSED, then L turns ON.
 The light turns OFF if both the
switches are OPENED.
Figure 4: Parallel Switching Circuit
Parallel Switching Circuit Operation
The logical operation of a Parallel switching
circuit of Figure 4 is illustrated in Table 4 and can
be explained as follows:
 When both S1 and S2 are open  L is OFF.
 When S1 is open and S2 is closed  L is ON.
 When S1 is closed and S2 is open  L is ON.
 When both A and B are closed  L is ON.
INPUTS
OUTPUT
S1
S2
L
Open
Open
OFF
Open
Closed
ON
Closed
Open
ON
Closed
Closed
ON
Table 4: The logical
operation of a parallel
switching circuit
Such a parallel switching circuit is also known as OR Switching Circuit
because the lamp is ON if S1 OR S2 OR both are CLOSED.
2.2.5 OR Logic Gate
The digital circuit which can act exactly like an OR switching circuit is known
as OR logic gate. Therefore the OR gate can be defined as a logic device
that has two or more inputs and a single output such that its output is High
if any one of its inputs is High.
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ATE414 – Digital Electronics
Logic Symbol
The logic symbol of an OR logic gate with
two inputs (A & B) and a single output (X)
is shown in Figure 5. The OR logic gate can
have a maximum number of 8-inputs but
only one output.
A
X
OR
B
Figure 5: OR logic symbol
Logic Operation and Truth Table
The logic operation of the OR Gate is such that the
INPUTS
OUTPUT
output is HIGH when any one of the inputs is
A
B
X
HIGH. When all the inputs are LOW, the output is
0
0
0
LOW.
0
1
1
The truth table of an OR gate is shown in Table 5;
1
0
1
it illustrates all the inputs combinations and the
1
1
1
corresponding outputs.
Table 5: Truth table
for 2-inputs OR gate
OR Boolean Expression
The two variables expression “X = A OR B” is called the OR Boolean
expression and is represented by a + between the variables as follows:

X = A + B; and it means the following:

If either, A OR B = High, OR A = B = High, then X = High.

If both are Low (A = B = 0), then X = Low.
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Module 2: Basic Logic Gates
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Exercise-2:
Switches
Output
6a illustrates the
S1
S2
S3
Lamp
truth table of a 3-input
OFF
OFF
OFF
OFF
parallel switching circuit.
OFF
OFF
ON
ON
OFF
ON
OFF
ON
OFF
ON
ON
ON
ON
OFF
OFF
ON
ON
OFF
ON
ON
circuit that represents
ON
ON
OFF
ON
Table 6a.
ON
ON
ON
ON
Table
a) Rewrite this truth table
in terms of 0's and 1's.
b) Draw
the
switching
Table 6a: Truth Table
for parallel switching
circuit
c) Write the Boolean expression for a 3-input OR gate.
Conduct Lab Activity 2.
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Module 2: Basic Logic Gates
Input
A
B
Output
C
X
Table 6b: Truth
Table in terms of 0's
and 1's
ATE414 – Digital Electronics
2.2.6 Inverter Switching Circuit
Consider the Inverter Circuit shown
in Figure 6. The Parallel-connected
switch S in series with a resistor R,
R
represents the inputs, while the lamp
L represents the output. This circuit
behaves as follows:
VDC
S
Lamp
L
 If S is CLOSED, all the current will
flow through R and the lamp L will
turn OFF.
 The lamp L turns ON if the switch
Figure 6: Inverter Circuit
S is OPENED.
Inverter Circuit Operation
The logical operation of an inverter circuit of
Figure 6 is illustrated in Table 7 as follows:
 When S is open  L is ON.
 When S is closed  L is OFF.
INPUTS
OUTPUT
S
L
Open
ON
Closed
OFF
Table 7: The logical
operation of an inverter
circuit
Such an Inverting Switching circuit is also known as NOT Circuit because
the lamp is ON if S is NOT closed.
2.2.7 NOT Logic Gate
The digital circuit which can act exactly like a NOT switching circuit is known
as NOT logic gate. Therefore, the NOT gate can be defined as a logic
device that has one input and a single output such that its output is HIGH if
its input is LOW.
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Module 2: Basic Logic Gates
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Logic Symbol
The logic symbol of a NOT logic gate is
shown in Figure 7. The NOT gate, unlike
A
X
other gates, has only one input.
Figure 7: NOT logic symbol
Boolean Expression
The Logical expression “X = NOT A” is called the NOT Boolean expression
and is represented by a bar over the variables as follows:
 X = A ; and it means the following:
 where A is the complement or the inverse of A;
 A is read “A bar” or “Not A”;
 so if A = 1, then X = A = 0; and if A = 0, then X = A = 1.
Timing Diagram
The timing diagram which represents Table 7 is in shown in Figure 8. The
output waveform is exactly opposite to the input (inverted) at each point.
1
Input (A) 
0
1
 (X) Output
0
Figure 8: NOT gate operation
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Module 2: Basic Logic Gates
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2.3 Universal Logic Gates
2.3.1 The NAND Gate
The NAND gate is a very popular logic gate and is called a universal gate;
because it can be used to construct all basic gates or any combination of
these gates.
Logic Symbol
The term NAND is a short form of NOT-AND and means an AND function
with inverted output. A standard logic symbol for a two-input NAND gate
and its equivalent to an AND gate followed by a NOT gate (inverter), are
shown in Figures 9 and 10, with the inputs labeled A and B and the output
labeled X. The bubble indicate an inverted output.
A
AND
A
Q
NOT
X
B
Figure 9: NAND Equivalent Logic Circuit

X
NAND
B
Figure 10: NAND Logic
Symbol
Logic Operation and Truth Table
The logical operation of the NAND gate is such
that a LOW output occurs only when all inputs are
HIGH. When any of the inputs are LOW, the output
will be HIGH. The truth table illustrating the logical
AND
NOT
A
B
Q
X= Q
0
0
0
1
0
1
0
1
1
0
0
1
operation of a two inputs NAND gate for all input
1
1
1
0
combinations is shown in Table 8.
Table 8: Truth table
for NAND gate
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Module 2: Basic Logic Gates
ATE414 – Digital Electronics
Boolean Expression
The Boolean expression for a two input NAND gate is given by “ X  A  B ”.
By referring to Figure 9 we can explain the NAND Function as follows:

Q = A  B; but X  Q ;

then X  A  B , and read as:

X = NOT (A AND B) or (A B bar)
Conduct Lab Activity 3.
2.3.2 The NOR Gate
The NOR gate, like the NAND gate, is a very useful logic gate because of its
universal properties which can be used to construct all basic gates or any
combination of these gates.
Logic Symbol
The term NOR is a short form of NOT-OR and is equivalent to an OR
function with inverted output. The standard logic symbol for a two-inputs
NOR gate, and its equivalent to an OR gate followed by a NOT gate
(inverter), are shown in Figures 11 and 12 respectively, with the inputs
labeled A and B and the output labeled X. The bubble indicates an inverted
output.
A
Q
OR
NOT
X
B
Figure 11: NOR Equivalent Logic
Circuit
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Module 2: Basic Logic Gates
A

NOR
X
B
Figure 12: NOR Logic Symbol
ATE414 – Digital Electronics
Logical Operation and Truth Table
The logical operation of the NOR gate is such that
OR
NOT
A
B
Q
X= Q
0
0
0
1
0
1
1
0
1
0
1
0
operation of a two input NOR gate for all input
1
1
1
0
combinations is shown in Table 9.
Table 9: Truth table
for NOR gate
a LOW output occurs when any of its inputs are
HIGH. Only when all inputs are LOW, the output
will be HIGH. The truth table illustrating the logical
Boolean Expression
The Boolean expression for a two input NOR gate is given by “ X  A  B ”. By
referring to Figure 11, we can explain the NOR Function as follows:

Q = A + B; but X  Q ;

then, X  A  B and read as:

X = NOT (A + B) or [(A + B) bar]
Conduct Lab Activity 4.
2.4 Classroom Activity: Logic Gate Symbols
The IEEE standard provides two different types of symbols for logic gates.
a) Distinctive-shape symbols: These are the symbols used in this module
since they represent the most commonly used symbols.
b) Rectangular-shape symbols: Where all the gates use the same shape,
along with an internal label to identify the type of gate.
Complete the table below based on what you have learned in this
module. Use the internet to search for rectangular-shape symbols for
the different logic gates.
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Module 2: Basic Logic Gates
ATE414 – Digital Electronics
Gate
Distinctive-shape
AND
OR
NOT
NAND
NOR
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Module 2: Basic Logic Gates
Rectangular-shape
ATE414 – Digital Electronics
2.5 Lab Activity 1:
OBJECTIVES:
EQUIPMENT
To verify the truth table of the AND
 Logic Tutor LT345 Mk2
gate.
 Power Supply 5V
PROCEDURE
a) Make the connections as shown in the patching diagram of Figure 13.
To clearly understand these connections shown, the circuit is redrawn in
Figure 14.
b) Switch the dip switches A and B (ON/OFF) to form the combination
given in Table 10.
Figure 13: Patching Diagram (AND-gate Circuit)
+5VDC
0VDC
ON OFF
LP1
A
X
AND
ON OFF
B
Figure 14: Logic Circuit of AND gate
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Module 2: Basic Logic Gates
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OBSERVATIONS
For each switching combination of A and B note
the corresponding output state of (LP1) in Table
10.
Switches
A
B
OFF
OFF
OFF
ON
ON
OFF
ON
ON
Output
LP1
Table 10: LP1 State
RESULT

Rewrite your observation in Table 11 using 1’s
and 0’s format.

Switches
A
B
Output
X (LP1)
Note that (OFF  0) while (ON  1).
Table 11: LP1 State
VERIFICATION
Compare Table 11 with the truth table of AND gate and note your remarks.
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Module 2: Basic Logic Gates
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2.6 Lab Activity 2:
OBJECTIVES:
EQUIPMENT
To verify the truth table of the OR
 Logic Tutor LT345 Mk2
gate.
 Power Supply 5V
PROCEDURE
a) Make the connections as shown in the patching diagram of Figure 15.
To clearly understand these connections, the circuit is redrawn in Figure
16.
b) Switch the dip switches A and B (ON/OFF) to form the combination
given in Table 12.
Figure 15: Patching Diagram (OR-gate Circuit)
+5VDC
0VDC
ON OFF
LP1
A
X
OR
ON OFF
B
Figure 16: Logic Circuit of OR gate
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Module 2: Basic Logic Gates
ATE414 – Digital Electronics
OBSERVATIONS
For each switching combination of A and B note
the corresponding output state of (LP1) in Table
12.
Switches
A
B
OFF
OFF
OFF
ON
ON
OFF
ON
ON
Output
LP1
Table 12: LP1 State
RESULT

Rewrite your observation in Table 13 using 1’s
and 0’s format.

Switches
A
B
Output
X (LP1)
Note that (OFF  0) while (ON  1).
Table 13: LP1 State
VERIFICATION
Compare Table 13 with the truth table of OR gate and note your remarks.
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Module 2: Basic Logic Gates
ATE414 – Digital Electronics
2.7 Lab Activity 3:
OBJECTIVES:
EQUIPMENT
To verify the truth table of NAND gate.
 Logic Tutor LT345 Mk2
 Power Supply 5V
PROCEDURE
a) Make the connections as shown in the patching diagram of Figure 17.
To clearly understand these connections, the circuit is redrawn in Figure
18.
b) Switch the dip switches A and B (ON/OFF) to form the combination
given in Table 14.
PATCHING DIAGRAM
Figure 17: Patching Diagram (NAND-gate Circuit)
+5VDC
0VDC
ON OFF
A
ON OFF
B
ON OFF
C
ON OFF
D
LP1
NAND
Figure 18: Logic Circuit of NAND gate
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Module 2: Basic Logic Gates
X
ATE414 – Digital Electronics
OBSERVATIONS
A
B
C
OFF
OFF
OFF
B note the corresponding output state of
OFF
OFF
ON
(LP1) in Table 14.
OFF
ON
OFF
OFF
ON
ON
ON
OFF
OFF
ON
OFF
ON
ON
ON
OFF
ON
ON
ON
OFF
OFF
OFF
OFF
OFF
ON
OFF
ON
OFF
OFF
ON
ON
ON
OFF
OFF
ON
OFF
ON
ON
ON
OFF
ON
ON
ON
For each switching combination of A and
LP1
Table 14: LP1 State
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Module 2: Basic Logic Gates
ATE414 – Digital Electronics
RESULT

Rewrite your observation in Table
A
B
C
X (LP1)
15 using 1’s and 0’s format.

Note that (OFF  0) while (ON  1).
Table 15: LP1 State
VERIFICATION
Compare Table 15 with the truth table of OR gate and note your remarks.
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Module 2: Basic Logic Gates
ATE414 – Digital Electronics
2.8 Lab Activity 4:
OBJECTIVES:
EQUIPMENT
To verify the truth table of the NOR-
 Logic Tutor LT345 Mk2
gate.
 Power Supply 5V
PROCEDURE
a) Make the connections as shown in the patching diagram of Figure 19.
To clearly understand these connections, the circuit is redrawn in Figure
20.
b) Switch the dip switches A and B (ON/OFF) to form the combination
given in Table 16.
PATCHING DIAGRAM
Figure 19: Patching Diagram (NOR-gate Circuit)
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Module 2: Basic Logic Gates
ATE414 – Digital Electronics
+5VDC
0VDC
ON OFF
A
ON OFF
B
ON OFF
C
ON OFF
D
LP1
X
NOR
Figure 20: Logic Circuit of NOR gate
OBSERVATIONS
For each switching combination of A and
B note the corresponding output state of
(LP1) in Table 16.
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Module 2: Basic Logic Gates
A
OFF
OFF
OFF
OFF
ON
ON
ON
ON
OFF
OFF
OFF
OFF
ON
ON
ON
ON
B
C
LP1
OFF
OFF
OFF
ON
ON
OFF
ON
ON
OFF
OFF
OFF
ON
ON
OFF
ON
ON
OFF
OFF
OFF
ON
ON
OFF
ON
ON
OFF
OFF
OFF
ON
ON
OFF
ON
ON
Table 16: LP1 State
ATE414 – Digital Electronics
RESULT

Rewrite your observation in Table
A
B
C
X (LP1)
17 using 1’s and 0’s format.

Note that (OFF  0) while (ON  1).
Table 17: LP1 State
VERIFICATION
Compare Table10 with the truth table of NOR gate and note your remarks.
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Module 2: Basic Logic Gates
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2.9 Review Exercises
1) Complete the AND logic table and symbol seen below.
2) Complete the OR logic table and symbol seen below.
3) Complete the INVERTER logic table and symbol seen below.
4) What is the function of an INVERTER GATE?
…………………………………………………………………………………………………………………………
5) Complete the NAND logic table and symbol seen below.
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Module 2: Basic Logic Gates
ATE414 – Digital Electronics
6) How does the NAND gate differ from an AND gate?
…………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………
7) Complete the NOR logic table and symbol seen below.
8) How does the NOR gate differ from an OR gate?
…………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………
9) From the Truth Tables of all gates we note that for n inputs, there are 2n
combinations of inputs. Fill in the missing answers below:
if we have 1 input, there are 21 combinations, ____ combinations.
if we have 2 inputs, there are ___ combinations, 4 combinations.
if we have ___ inputs, there are 24 combinations, ____ combinations.
if we have ___ inputs, there are 26 combinations, 64 combinations.
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10) From the following three circuits, draw the truth tables and explain what
happens when you change the state of the input.
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ATE414 – Digital Electronics
11) A car manufacturing firm wants to introduce a Seat Belt Alarm. When the
engine is on and the Seat belt is not properly in place, an alarm is
sounded. Produce a logic circuit to represent this situation.
12) For the circuit shown below write the input states and the Boolean
expression.
A
B
Inputs
Inputs
Boolean
Expression
Boolean
Expression
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13) A student is given a merit certificate if he gets a pass in all subjects or
obtains an overall average of 60 in his annual exam.
a) Draw a logic circuit that would allow a computer to decide which student
should get a merit certificate.
b) Produce the truth table for this circuit.
a)
b)
14) Determine the outputs of the following example logic circuits using their
truth table and function.
a) ……………………………………………
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Module 2: Basic Logic Gates
b) ……………………………………………
ATE414 – Digital Electronics
15) Determine the output when the LDR is in darkness, and then when exposed to
light.
…………………………………………………………………………………………………………………………
16) For the 4-input gate shown in the figure below, determine the output.
…………………………………………………………………………………………………………………………
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Module 2: Basic Logic Gates