1. IT2001PA
Engineering Essentials (2/2)
Chapter 3 - Basic Logic Gates
Lecturer Name
lecturer_email@ite.edu.sg
Nov 20, 2012
Contact Number

2. Chapter 3 - Basic Logic Gates
Lesson Objectives
Upon completion of this topic, you should be able to:
 Relate the operation of basic logic gates such as AND,
OR, NOT, NAND, NOR, EX-OR and EX-NOR, and
construct its truth table.
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3. Chapter 3 - Basic Logic Gates
Specific Objectives
Students should be able to :
 Explain the use of logic gate.
 Describe the function of the basic logic gates (i.e. NOT, AND,
NAND, OR, NOR, EX-OR and EX-NOR) with the help of symbol,
truth table and its equivalent switching circuit.
 Describe how NOT, AND, OR, NOR can be constructed from
NAND gates.
 Describe how NOT, AND, OR, NOR can be constructed from
NOR gates.
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4. Chapter 3 - Basic Logic Gates
Logic Gates
In digital logic system, events are described
as either ‘0’ or ‘1’
Logic 1 Logic 0
Switch ON Switch OFF
Bulb lights up Bulb unlighted
High Low
True False
5 volts 0 volts
2.4V to 5V 0V to 0.4V
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5. Chapter 3 - Basic Logic Gates
Logic Gates
Positive Logic
In a positive logic system, a high voltage is used to represent logical
true(1), and a low voltage for logical false (0).
In positive logic circuits it is normal to use +5V for true and
0V for false.
Negative Logic
In a negative logic system, a low voltage is used to represent
logical true (1) and a high voltage for a logical false (0).
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6. Chapter 3 - Basic Logic Gates
Gate
- it has 2 or more binary inputs and 1 output
Binary Binary
Inputs
Gate Output
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7. Chapter 3 - Basic Logic Gates
7 Basic Logic Gates
 AND gate
 OR gate
 INVERTER ( NOT ) gate
 NAND gate
 NOR gate
 XOR gate
 XNOR gate
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8. Chapter 3 - Basic Logic Gates
Truth Table
 Table which relates the output of a logic function to all
the possible combinations of the inputs.
 The number of possible combinations of the inputs is
equal to 2N, where N is the number of inputs
A logic gate with 2 inputs 22= 4 possible combinations from its inputs
Inputs Output
0 0 Depends on the logic function
0 1 Depends on the logic function
1 0 Depends on the logic function
1 1 Depends on the logic function
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9. Chapter 3 - Basic Logic Gates
The AND Operation
A B
L=A.B
Lamp: Off=0 Switch: Open=0
ON=1 Closed=1
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10. Chapter 3 - Basic Logic Gates
Truth Table of AND Gate
A B L
Lamp : Off = 0
0 0 0 On = 1
0 1 0
1 0 0 Switch : Open =0
Closed=1
1 1 1
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11. Chapter 3 - Basic Logic Gates
The AND Gate
Symbol
A
B Y=A.B.C
C
Equation : Y = A.B.C
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12. Chapter 3 - Basic Logic Gates
Summary of AND Gate
The AND gate produces a HIGH output only when all
of the inputs are HIGH
1
1
1
When any of the inputs is LOW, the output is LOW
0 1 0
0 0 0
1 0 0
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13. Chapter 3 - Basic Logic Gates
Truth Table of AND Gate
A B C L
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 Output = 1 only
1 1 1 1 if all inputs are 1
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14. Chapter 3 - Basic Logic Gates
Example
Determine the output waveform for the AND gate shown.
A 0 1 0 0 1 0 A
Y
B 0 0 0 1 0 B
1
Y 0 0 0 0 0
1
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15. Chapter 3 - Basic Logic Gates
The OR Operation
A
B
Lamp: OFF= 0 Switch: Open=0
ON=1 Closed=1
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16. Chapter 3 - Basic Logic Gates
Truth Table of OR Gate
A B L
Lamp : OFF =0
0 0 0 ON=1
0 1 1
1 0 1 Switch : Open=0
Closed=1
1 1 1
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17. Chapter 3 - Basic Logic Gates
The OR Gate
Symbol
A
B Y
C
Equation : Y = A + B + C
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18. Chapter 3 - Basic Logic Gates
Summary of OR Gate
The output is LOW only when all the inputs are LOW
0
0
0
The OR gate produces a HIGH on the output when any of
the inputs is HIGH
1 0 1
1 1 1
0 1 1
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19. Chapter 3 - Basic Logic Gates
Truth Table of OR Gate
A B C L
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
Output = 1 only if
1 1 1 1 any of inputs is 1
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20. Chapter 3 - Basic Logic Gates
Example
Draw the output waveform for the OR gate
A
A0 1 0 1 0 Y
B
B 0 1 1 0 0
Y 0
1 1 1 0
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21. Chapter 3 - Basic Logic Gates
The NOT Operation (Inverter)
Symbol
A A
A A
Equation
Y = A
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22. Chapter 3 - Basic Logic Gates
Truth Table of Inverter
Inputs Output
0 1
1 0
Its logic output is always the inverse of the logic inputs
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23. Chapter 3 - Basic Logic Gates
NAND Gate
A A
X=AB X=AB
B B
Equation
X= AB
X= AB
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24. Chapter 3 - Basic Logic Gates
Truth Table of NAND Gate
Inputs AND NAND
A B AB AB
0 0 0 1
0 1 0 1
1 0 0 1
1 1 1 0
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25. Chapter 3 - Basic Logic Gates
Summary of NAND Gate
The NAND gate produces a LOW output only when all
the inputs are HIGH
1
0
1
When any of the inputs is LOW , the output will be HIGH
0 1 0
1 1 1
1 0 0
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26. Chapter 3 - Basic Logic Gates
Example
Draw the output waveform for the NAND gate shown
0 0
A 0 1 1 A
Y
B
0 0
1 1 1
B
Y 1 1
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27. Chapter 3 - Basic Logic Gates
NOR Gate
A A
X=A+B
X=A+B B
B
Equation
X= A+B
X= A+B
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28. Chapter 3 - Basic Logic Gates
Truth Table of NOR Gate
Inputs OR NOR
A B A+B A+B
0 0 0 1
0 1 1 0
1 0 1 0
1 1 1 0
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29. Chapter 3 - Basic Logic Gates
Summary of NOR Gate
The NOR gate produces a HIGH output only when all
the inputs are LOW
0
1
0
When any of the inputs is HIGH , the output will be LOW
0 1 1
0 0 0
1 0 1
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30. Chapter 3 - Basic Logic Gates
Example
Draw the output waveform for the NOR gate shown
A 0 1 0 1 0 1 A
Y
B
1 1 0 1 0 0
B
Y 0 0 1 0 0
1
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31. Chapter 3 - Basic Logic Gates
EX-OR
Gate
EX-NOR
Gate
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32. Chapter 3 - Basic Logic Gates
EX-OR Gate
Truth Table
A B Y
A
0 0 0
X = A ⊕B
B 0 1 1
1 0 1
1 1 0
Logic Equation
X = AB + A B Its output is High only when the
X = A⊕B inputs are at different levels.
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33. Chapter 3 - Basic Logic Gates
EX-NOR Gate
Truth Table
A A B Y
X = A⊕B 0 0 1
B
0 1 0
1 0 0
1 1 1
Logic Equation
X = A B + AB Its output is High only when the inputs are
X = A⊕B at the same levels.
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34. Chapter 3 - Basic Logic Gates
Exercise on Timing Diagram
Draw the output waveform X of the EX-OR gate with inputs
A and B given below:
A
X
B
A
B
X
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35. Chapter 3 - Basic Logic Gates
Exercise on Timing Diagram
Draw the output waveform X of the EX-NOR gate with inputs A
and B given below:
A
X
B A
B
X
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36. Chapter 3 - Basic Logic Gates
Next Lesson
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