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Apr 12, 2023
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IT2001PAEngineering Essentials (2/2)
Chapter 3 - Basic Logic Gates
2
Chapter 3 - Basic Logic Gates
IT2001PA Engineering Essentials (2/2)
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.
Chapter 3 - Basic Logic Gates
IT2001PA Engineering Essentials (2/2)
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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Chapter 3 - Basic Logic Gates
IT2001PA Engineering Essentials (2/2)
Logic Gates
In digital logic system, events are describedas 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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Chapter 3 - Basic Logic Gates
IT2001PA Engineering Essentials (2/2)
Logic Gates
Positive Logic
In a positive logic system, a high voltage is used to represent logicaltrue(1), and a low voltage for logical false (0).In positive logic circuits it is normal to use +5V for true and0V for false.
In a negative logic system, a low voltage is used to representlogical true (1) and a high voltage for a logical false (0).
Negative Logic
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Chapter 3 - Basic Logic Gates
IT2001PA Engineering Essentials (2/2)
Gate
- - it has 2 or more binary inputs and 1 outputit has 2 or more binary inputs and 1 output
GateGateBinaryInputs
Binary Output
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Chapter 3 - Basic Logic Gates
IT2001PA Engineering Essentials (2/2)
7 Basic Logic Gates
AND gate OR gate INVERTER ( NOT ) gate NAND gate NOR gate XOR gate XNOR gate
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Chapter 3 - Basic Logic Gates
IT2001PA Engineering Essentials (2/2)
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
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
A logic gate with 2 inputs 22= 4 possible combinations from its inputs
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Chapter 3 - Basic Logic Gates
IT2001PA Engineering Essentials (2/2)
The AND Operation
A
Lamp: Off=0Off=0 Switch: Open=0Open=0 ON=1 Closed=1ON=1 Closed=1
B
L = A . B
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Chapter 3 - Basic Logic Gates
IT2001PA Engineering Essentials (2/2)
Truth Table of AND Gate
A B LA B L
0 0 0
0 1 0
1 0 0
1 1 1
Lamp : Off = 0 On = 1
Switch : Open =0 Closed=1
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Chapter 3 - Basic Logic Gates
IT2001PA Engineering Essentials (2/2)
The AND Gate
Equation : Y = A.B.C
SymbolSymbol
A
B Y = A . B . CC
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Chapter 3 - Basic Logic Gates
IT2001PA Engineering Essentials (2/2)
Summary of AND Gate
The AND gate produces a HIGH output only when all of the inputs are HIGH
1
11
When any of the inputs is LOW, the output is LOW
0
10
1
00
0
00
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Chapter 3 - Basic Logic Gates
IT2001PA Engineering Essentials (2/2)
Truth Table of AND Gate
A B CA B C LL
00 0 00 10 0
00 01
00 1 1
1 0 0 01 0 1 0
1 1 0 0
1 1 1 1 Output = 1 only if all inputs are 11 1 1 1
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Chapter 3 - Basic Logic Gates
IT2001PA Engineering Essentials (2/2)
Example
Determine the output waveform for the AND gate shown.
A
B
A
B
Y
0
0
0Y
1
0
0
0
0
0
1
0
0
1
1
1
0
0
0
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Chapter 3 - Basic Logic Gates
IT2001PA Engineering Essentials (2/2)
The OR Operation
Lamp: OFF=OFF= 0 0 ON=1ON=1
B
A
Switch: Open=0 Open=0 Closed=1Closed=1
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Chapter 3 - Basic Logic Gates
IT2001PA Engineering Essentials (2/2)
Truth Table of OR Gate
A B LA B L
0 0 0
0 1 1
1 0 1
1 1 1
Lamp : OFF =0 ON=1
Switch : Open=0 Closed=1
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Chapter 3 - Basic Logic Gates
IT2001PA Engineering Essentials (2/2)
The OR Gate
Equation : Y = A + B + C
SymbolSymbol
A
BC
Y
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Chapter 3 - Basic Logic Gates
IT2001PA Engineering Essentials (2/2)
Summary of OR Gate
The OR gate produces a HIGH on the output when any of the inputs is HIGH
1
01
The output is LOW only when all the inputs are LOW
0
00
0
11
1
11
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Chapter 3 - Basic Logic Gates
IT2001PA Engineering Essentials (2/2)
Truth Table of OR Gate
A B CA B C LL
0 0 0 00 10 1
10 01
10 1 1
1 0 0 11 0 1 1
1 1 0 1
1 1 1 1Output = 1 only if any of inputs is 1
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Chapter 3 - Basic Logic Gates
IT2001PA Engineering Essentials (2/2)
Example
Draw the output waveform for the OR gate
A
BYA
B
Y
0
0
0
1
1
1
0
1
1
1
0
1 0
0
0
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Chapter 3 - Basic Logic Gates
IT2001PA Engineering Essentials (2/2)
The NOT Operation (Inverter)SymbolSymbol
Equation
A A
A A
Y = A Y = A
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Chapter 3 - Basic Logic Gates
IT2001PA Engineering Essentials (2/2)
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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Chapter 3 - Basic Logic Gates
IT2001PA Engineering Essentials (2/2)
NAND Gate
X = A B
A
B
EquationEquation
X = A BX = A B
X = A B
A
B
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Chapter 3 - Basic Logic Gates
IT2001PA Engineering Essentials (2/2)
Truth Table of NAND Gate
Inputs
A B
0 0
0 1
1 0
1 1
AND
AB
0
0
0
1
NAND
AB
1
1
1
0
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Chapter 3 - Basic Logic Gates
IT2001PA Engineering Essentials (2/2)
Summary of NAND Gate
The NAND gate produces a LOW output only when all the inputs are HIGH
When any of the inputs is LOW , the output will be HIGH
01
1
1
01
0
11
0
01
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Chapter 3 - Basic Logic Gates
IT2001PA Engineering Essentials (2/2)
Example
Draw the output waveform for the NAND gate shown
A
BY
A
B
Y
0
1
1
1
1
0
0
1
1
0
0
1
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Chapter 3 - Basic Logic Gates
IT2001PA Engineering Essentials (2/2)
NOR Gate
X = A + BA
B
EquationEquation
A
BX = A + B
X = A + BX = A + B
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Chapter 3 - Basic Logic Gates
IT2001PA Engineering Essentials (2/2)
Truth Table of NOR Gate
Inputs
A B
0 0
0 1
1 0
1 1
OR
A+B
0
1
1
1
NOR
A+B
1
0
0
0
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Chapter 3 - Basic Logic Gates
IT2001PA Engineering Essentials (2/2)
Summary of NOR Gate
The NOR gate produces a HIGH output only when all the inputs are LOW
When any of the inputs is HIGH , the output will be LOW
0
01
1
00
0
10
1
10
30
Chapter 3 - Basic Logic Gates
IT2001PA Engineering Essentials (2/2)
Example
Draw the output waveform for the NOR gate shown
A
B
A
BY
Y
0
1
0
1
1
0
0
0
1
1
1
0
0
0
1
1
0
0
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Chapter 3 - Basic Logic Gates
IT2001PA Engineering Essentials (2/2)
EX-NOR Gate
EX-OR Gate
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Chapter 3 - Basic Logic Gates
IT2001PA Engineering Essentials (2/2)
EX-OR Gate
A
BBAX
A B Y
0 0 0
0 1 1
1 0 1
1 1 0
Its output is High only when the inputs are at different levels.BAX
BABAX
Logic Equation
Truth Table
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Chapter 3 - Basic Logic Gates
IT2001PA Engineering Essentials (2/2)
EX-NOR Gate
A B Y
0 0 1
0 1 0
1 0 0
1 1 1
Its output is High only when the inputs are at the same levels.BAX
ABBAX
Logic Equation
Truth Table
A
BBAX
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Chapter 3 - Basic Logic Gates
IT2001PA Engineering Essentials (2/2)
Exercise on Timing Diagram
Draw the output waveform X of the EX-OR gate with inputsA and B given below:
A
B
A
B
X
X
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Chapter 3 - Basic Logic Gates
IT2001PA Engineering Essentials (2/2)
Exercise on Timing Diagram
Draw the output waveform X of the EX-NOR gate with inputs A and B given below:A
B
X
A
B
X
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Chapter 3 - Basic Logic Gates
IT2001PA Engineering Essentials (2/2)
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