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1. CSC-103 1

2. Outcome of this chapter
 Knowledge about logic gates, their expression, input
and output.
 Know how to draw circuits for Boolean expression.
 Know how to express a circuit through Boolean
expression.
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CSC-103

3. Boolean Algebra
 Boolean algebra is the mathematics of Boolean logic,
where statements are evaluated to be either true or
false.
 It is extremely important in computer sciences, such
as programming, database querying and computer
engineering, as electrical signals at the most basic
level are translated to and from binary (true/false,
1/0, on/off, closed/open, etc).
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4. Logic Gate
 A logic gate is an elementary building block of a digital
circuit.
 A Logic Gate in an electronic sense makes a ‘logical’
decision based upon a set of rules, and if the
appropriate conditions are met then the gate is
opened, and an output signal is produced.
 Most logic gates have two inputs and one output.
 At any given moment, every terminal is in one of the
two binary conditions low (0) or high (1), represented
by different voltage levels.
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5. Truth Table
 A truth table shows how a
logic circuit's output responds
to various combinations of
the inputs, using logic 1 for
true and logic 0 for false.
 All permutations of the
inputs are listed on the left,
and the output of the circuit
is listed on the right.
 The desired output can be
achieved by a combination of
logic gates.
Inputs Output
B
A
Q
0
0
0
0
1
0
1
0
0
1
1
1
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6. Logic Gates
Fundamental Logic Gates:
 AND gate
 OR gate
 NOT gate
Universal Logic Gates:
 NAND gate
 NOR gate
Special Logic Gates:
 XNOR gate
 XOR gate
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7. The AND gate
2 input AND gate:
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A
B
Q
Inputs Output
B A Q
0 0 0
0 1 0
1 0 0
1 1 1
The truth table for the 2
input AND gate
Symbol for a 2 input
AND gate
Q=A.B
Boolean expression for a 2
input AND gate
3 input AND gate:
A
B
Q
C
Inputs Output
C B A Q
0 0 0 0
0 0 1 0
0 1 0 0
0 1 1 0
1 0 0 0
1 0 1 0
1 1 0 0
1 1 1 1
Symbol for a 3 input
AND gate
The truth table for the 3
input AND gate
Q=A.B.C
Boolean expression for a 3
input AND gate
CSC-103

8. The OR gate
2 input OR gate:
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Inputs Output
B A Q
0 0 0
0 1 1
1 0 1
1 1 1
The truth table for the 2
input OR gate
Symbol for a 2 input
OR gate
Q = A + B
Boolean expression for a 2
input OR gate
3 input OR gate:
Inputs Output
C B A Q
0 0 0 0
0 0 1 1
0 1 0 1
0 1 1 1
1 0 0 1
1 0 1 1
1 1 0 1
1 1 1 1
Symbol for a 3 input
OR gate
The truth table for the 3
input OR gate
Q = A + B + C
Boolean expression for a 3
input OR gate
CSC-103

9. The NOT gate
Symbol for a NOT gate :
9
The truth table for the 2
input OR gate
Truth Table for NOT gate
A = A’
Boolean expression for NOT
gate
Input Output
A Q
0 1
1 0
This is the simplest form of logic
gate and has only 1 input and 1
output.
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10. The NAND gate
2 input NAND gate:
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Inputs Output
B A Q
0 0 1
0 1 1
1 0 1
1 1 0
The truth table for the 2
input NAND gate
Symbol for a 2 input
NAND gate
Q = A . B
Boolean expression for a 2
input NAND gate
3 input NAND gate:
Inputs Output
C B A Q
0 0 0 1
0 0 1 1
0 1 0 1
0 1 1 1
1 0 0 1
1 0 1 1
1 1 0 1
1 1 1 0
Symbol for a 3 input
NAND gate
The truth table for the 3
input NAND gate
Q = A . B . C
Boolean expression for a 3
input NAND gate
A
B
Q Q
A
B
C
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11. The NOR gate
2 input NOR gate:
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Inputs Output
B A Q
0 0 1
0 1 0
1 0 0
1 1 0
The truth table for the 2
input NOR gate
Symbol for a 2 input
NOR gate
Q = A + B
Boolean expression for a 2
input NOR gate
3 input NOR gate:
Inputs Output
C B A Q
0 0 0 1
0 0 1 0
0 1 0 0
0 1 1 0
1 0 0 0
1 0 1 0
1 1 0 0
1 1 1 0
Symbol for a 3 input
NOR gate
The truth table for the 3
input NOR gate
Q = A + B + C
Boolean expression for a 3
input NOR gate
A
B
Q
Q
A
B
C
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12. The XOR gate
2 input XOR gate:
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Inputs Output
B A Q
0 0 0
0 1 1
1 0 1
1 1 0
The truth table for the 2
input XOR gate
Symbol for a 2 input
XOR gate
Boolean expression for a 2
input XOR gate
A
B
Q
B
A
B
A
Q
or
B
A
Q
.
. 



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13. The XNOR gate
2 input XNOR gate:
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Inputs Output
B A Q
0 0 1
0 1 0
1 0 0
1 1 1
The truth table for the 2
input XNOR gate
Symbol for a 2 input
XNOR gate
Boolean expression for a 2
input XNOR gate
A
B
Q
B
A
B
A
Q
or
B
A
Q
.
. 



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14. Universal Logic Gates
 NAND and NOR gates are referred to as universal gates as
the three basic gates can be constructed using either one of
the two.
 This therefore implies that all logic circuits can be
constructed using either of the gates.
 NAND and NOR gates are economical and easier to
implement.
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15. Implementation of other gates using
Universal Logic Gates
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Basic Gates Using NOR Gate Basic Gates Using NAND Gate
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16. Exercise - 1.1
1. Look at the following logic symbols labeled A – G.
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i. Which is the correct symbol for an AND gate. ……………
ii. Which is the correct symbol for a NOT gate. ……………
iii.Which is the correct symbol for a NOR gate. ……………
iv.Which is the correct symbol for an EXOR gate. ……………
v. Which is the correct symbol for a NAND gate. ……………
vi.Which is the correct symbol for an XNOR gate. ……………
vii.Which is the correct symbol for an OR gate. ……………
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17. Exercise - 1.1 (Cont…)
2. Complete the following truth tables.
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i. AND gate.
Inputs Output
B A Q
0 0
0 1
1 0
1 1
ii. NOR gate.
Inputs Output
B A Q
0 0
0 1
1 0
1 1
iii. XNOR gate.
Inputs Output
B A Q
0 0
0 1
1 0
1 1
iv. NAND gate.
Inputs Output
B A Q
0 0
0 1
1 0
1 1
v. OR gate.
Inputs Output
B A Q
0 0
0 1
1 0
1 1
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18. Exercise - 1.1 (Cont…)
3. The Boolean equations labeled 1 – 9, below are to be used to answer the
following questions.
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B
A
Q .

B
A
Q 

B
A
Q 

B
A
B
A
Q .
. 

B
A
Q 

B
A
B
A
Q .
. 

A
Q 
B
A
Q .

B
A
Q 

1.
2.
3.
4.
5.
6.
7.
8.
9.
i. Which expression is correct for an AND gate.……………
ii. Which expression is correct for a NOT gate.……………
iii. Which expression is correct for a NOR gate.……………
iv. Which two expressions are correct for an EXOR gate.……… & ………
v. Which expression is correct for a NAND gate.……………
vi. Which two expressions are correct for an XNOR gate.……… & ………
vii. Which expression is correct for an OR gate.……………
CSC-103

19. Equation to Circuit
To convert a Boolean expression to a gate circuit, evaluate
the expression using standard order of operations:
1. To solve the equation start from the left to right
2. Parentheses
3. Inverse (Not Gate)
4. Multiplication (AND Gate)
5. Addition (OR Gate)
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20. Circuit to Equation
To convert a gate circuit to a Boolean expression, label each
gate output with a Boolean sub-expression corresponding
to the gates' input signals, until a final expression is
reached at the last gate.
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The Expression for above circuit is XʹY+XYʹ.
CSC-103

21. Class Practice
1. Draw the circuit diagram for the equation
i. AB + (AC)ʹ.
ii. (A+B) . (B+C)
iii. (A+B+C) . B . C
2. Write down the corresponding Boolean expression for
following circuit.
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22. Exercise – 1.2
1. Draw the corresponding circuit and truth table for
following Boolean expression
XYZ(YZ’+ZY’)
2. Draw a logic circuit and truth table for (A + B)C.
3. Find the Boolean expression and truth table for
following circuit.
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23. Thank You
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