Boolean Logic
Presentation
•
Computers
•
11th Grade
•
Practice Problem
•
Easy
Robert B.A
Used 9+ times
FREE Resource
25 Slides • 20 Questions
1
Boolean Logic
2
Outline
Standard logic gate symbols
Use logic gates to create logic circuits
Complete a truth table
Write logic expression
3
Introduction
Electronic circuits in computers, solid state drives and controlling devices are made up of thousands of logic gates
Logic gates take binary inputs and produce a binary output.
Several logic gates combined together form a logic circuit and these circuits are designed to carry out a specific function.
4
Logic gate expressions
Truth table: Shows all the combinations that can be used as input and output.
Logic expression: Used to represent the logic of the logic gate.
5
NOT Logic gate
It is the simplest logic gate with one input and one output.
It is used to reverse the input to get the output.
NOT Logic gate
Truth table
A | NOT A |
|---|---|
0 | 1 |
1 | 0 |
6
Fill in the Blanks
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Fill in the Blanks
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Fill in the Blanks
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Questions
You can withdraw money from an ATM only if you enter the correct PIN AND have sufficient funds in your account.
In a room, the light is designed to turn off when you press the switch, AND it turns on when the switch is released.
A security light is set to turn on at night when it gets dark AND off during the day when it is light.
A security light is set to turn on at night when it gets dark and off during the day when it is light.
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AND GATE
Has two input and one output. Output is 1 when both inputs are 1 Otherwise the output is zero.
AND Gate diagram
AND gate truth table
Z = A AND B (Logic notation)
Z = A.B (Boolean Notation)
A | B | Z |
|---|---|---|
0 | 0 | 0 |
0 | 1 | 0 |
1 | 0 | 0 |
1 | 1 | 1 |
11
Fill in the Blanks
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Multiple Choice
What is the output of an AND gate if both inputs are FALSE?
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Multiple Choice
Given that Input 1 is TRUE and Input 2 is FALSE, what will be the output of the AND gate?
14
Multiple Choice
If an AND gate has three inputs (A, B, C) and all inputs are TRUE, what will the output be?
15
Multiple Choice
An AND gate will produce a TRUE output only when:
16
OR GATE
Has two inputs and one output. The output is one when one of the inputs is one or both inputs are one.
OR Gate diagram
OR Gate truth table
Z = A OR B (Logic notation)
Z = A + B (Boolean notation)
A | B | Z |
|---|---|---|
0 | 0 | 0 |
0 | 1 | 1 |
1 | 0 | 1 |
1 | 1 | 1 |
17
Multiple Choice
Which of the following inputs will result in a TRUE output from an OR gate?
18
Multiple Choice
What is the output of an OR gate if both inputs are FALSE?
19
Multiple Choice
Given that Input 1 is TRUE and Input 2 is FALSE, what will be the output of the OR gate?
20
Multiple Choice
If an OR gate has three inputs (A, B, C) and at least one input is TRUE, what will the output be?
21
NAND Gate (NOT AND)
Has two inputs and one output. Output is 0 when both inputs are 1. Otherwise the output is 0.
NAND gate diagram
NAND gate truth table
Z = NOT (A AND B).
Z = A.B
A | B | Z |
|---|---|---|
0 | 0 | 1 |
0 | 1 | 1 |
1 | 0 | 1 |
1 | 1 | 0 |
22
NOR Logic Gate (NOT OR)
Has two inputs and one output.
The only time the output is 1 is when both inputs are 0.
NOR gate diagram
Truth table
Q = NOT(A OR B)
Q = A+B
A | B | Q |
|---|---|---|
0 | 0 | 1 |
0 | 1 | 0 |
1 | 0 | 0 |
1 | 1 | 0 |
23
XOR gate
It is also known as EOR gate. It is known as exclusive OR gate. It has two input and one output.
The output is one when inputs are different and zero when inputs are the same.
Diagram
A | B | Y |
|---|---|---|
0 | 0 | 0 |
0 | 1 | 1 |
1 | 0 | 1 |
1 | 1 | 0 |
24
Match
Match the following
AND GATE
OR GATE
NOR GATE
XOR GATE
NOT GATE
AND GATE
OR GATE
NOR GATE
XOR GATE
NOT GATE
25
Fill in the Blanks
26
Fill in the Blanks
27
Multiple Choice
Which of the following is the output of an AND gate when both inputs are 1?
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Multiple Choice
Which logic gate produces an output of 1 when at least one of its inputs is 1?
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Multiple Choice
Which gate inverts the input it receives?
30
Multiple Choice
Which of the following is true for a NOR gate?
31
Multiple Choice
If one input of an XOR gate is 0 and the other is 1, what is the output?
32
Logic Circuit
Combination of several logic gates that are linked together.
33
Example 01
Give the logic expression and truth table for the following logic circuit
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Answer
Y = (A OR B ) AND NOT C
A | B | C | NOT C | A OR B | (A OR B) AND NOT C |
|---|---|---|---|---|---|
0 | 0 | 0 | 1 | 0 | 0 |
0 | 0 | 1 | 0 | 0 | 0 |
0 | 1 | 0 | 1 | 1 | 1 |
0 | 1 | 1 | 0 | 1 | 0 |
1 | 0 | 0 | 1 | 1 | 1 |
1 | 0 | 1 | 0 | 1 | 0 |
1 | 1 | 0 | 1 | 1 | 1 |
1 | 1 | 1 | 0 | 1 | 0 |
35
Example 02
Give the logic expression and truth table for the following logic circuit
36
Answer
Q =A OR (NOT B AND C)
A | B | C | NOT B | NOT B AND C | A OR (NOT B AND C) |
|---|---|---|---|---|---|
0 | 0 | 0 | 1 | 0 | 0 |
0 | 0 | 1 | 1 | 1 | 1 |
0 | 1 | 0 | 0 | 0 | 0 |
0 | 1 | 1 | 0 | 0 | 0 |
1 | 0 | 0 | 1 | 0 | 1 |
1 | 0 | 1 | 1 | 1 | 1 |
1 | 1 | 0 | 0 | 0 | 1 |
1 | 1 | 1 | 0 | 0 | 1 |
37
Example 03
Give the logic expression and truth table for the following logic circuit
38
Answer
Z = (NOT(P AND Q)) XOR NOT Q) AND R
A = P AND Q
B = NOT (P AND Q)
C = NOT Q
D = A XOR C
E = D AND R
P | Q | R | A | B | C | D | E |
|---|---|---|---|---|---|---|---|
0 | 0 | 0 | 0 | 1 | 1 | 0 | 0 |
0 | 0 | 1 | 0 | 1 | 1 | 0 | 0 |
0 | 1 | 0 | 0 | 1 | 0 | 1 | 0 |
0 | 1 | 1 | 0 | 1 | 0 | 1 | 1 |
1 | 0 | 0 | 0 | 1 | 1 | 0 | 0 |
1 | 0 | 1 | 0 | 1 | 1 | 0 | 0 |
1 | 1 | 0 | 1 | 0 | 0 | 0 | 0 |
1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 |
39
Homework
Give the logic expression and truth table for the following logic circuit
40
Give the logic expression and truth table for the following logic circuits
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Question
Complete the truth table for this logic circuit.
A | B | C | Working Place | Z |
|---|---|---|---|---|
0 | 0 | 0 | | |
0 | 0 | 1 | | |
0 | 1 | 0 | | |
0 | 1 | 1 | | |
1 | 0 | 0 | | |
1 | 0 | 1 | | |
1 | 1 | 0 | | |
1 | 1 | 1 | | |
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Answer
A | B | C | Working Place | Z |
|---|---|---|---|---|
0 | 0 | 0 | | 0 |
0 | 0 | 1 | | 1 |
0 | 1 | 0 | | 0 |
0 | 1 | 1 | | 0 |
1 | 0 | 0 | | 1 |
1 | 0 | 1 | | 0 |
1 | 1 | 0 | | 0 |
1 | 1 | 1 | | 0 |
43
Question
Consider the logic expression:
Z = (A NAND B) OR NOT (B XOR C)
Complete the truth table
from the given logic expression.
A | B | C | Working Place | Z |
|---|---|---|---|---|
0 | 0 | 0 | | 0 |
0 | 0 | 1 | | 1 |
0 | 1 | 0 | | 0 |
0 | 1 | 1 | | 0 |
1 | 0 | 0 | | 1 |
1 | 0 | 1 | | 0 |
1 | 1 | 0 | | 0 |
1 | 1 | 1 | | 0 |
44
Answer
A | B | C | Working Place | Z |
|---|---|---|---|---|
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 | | 0 |
1 | 1 | 1 | | 1 |
45
Question
Consider this logic circuit.
Write a logic expression for this logic circuit.Complete the truth table from the given
logic circuit.
A | B | C | Working Place | Z |
|---|---|---|---|---|
0 | 0 | 0 | | 0 |
0 | 0 | 1 | | 1 |
0 | 1 | 0 | | 0 |
0 | 1 | 1 | | 0 |
1 | 0 | 0 | | 1 |
1 | 0 | 1 | | 0 |
1 | 1 | 0 | | 0 |
1 | 1 | 1 | | 0 |
Boolean Logic
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