The document discusses basic logic gates. It defines logic gates and their truth tables, and describes the operations and symbols of common logic gates including AND, OR, NOT, NAND and NOR gates. The objectives are to understand the functions of these basic logic gates through their truth tables and equivalent switching circuits. Examples are also provided to illustrate how to determine the output waveforms of AND and OR gates.

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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