This document provides information about logic gates and Boolean expressions: - It defines common logic gates (AND, OR, NOT) and their truth tables. It also introduces more complex gates like NAND and NOR. - It explains how to write Boolean expressions, evaluate them using truth tables, and draw the corresponding logic circuits. - Examples are provided for writing Boolean expressions for given logic circuits, drawing circuits for given expressions, and evaluating expressions using truth tables. - The purpose is for students to understand basic logic gates, Boolean expressions, and how to represent logic relationships in circuits.

1. Computer System
2.4 Logic Gate & Simple Logic Circuit
2.4.1
2.4.2
2.4.3
Boolean Expression
Logic Gate
Logic Circuit
Chapter
PDT - 2017/2018

2. At the end of this topic, students
should be able to:
a)
b)
c)
Identify logical operators
Form valid Boolean expressions
Evaluate Boolean expression using
truth
table
Computer System
2.4 Logic Gate & Simple Logic Circuit
2.4.1 Boolean Expression
Chapter
PDT - 2017/2018

3. Logical Operators
•
•
•
AND (.)
OR (+)
NOT (¯)
*Other operator symbol
for NOT operator
~A, A’, !A
Logical Operator and symbol

4. Logic Operation
• OR (Sum)
0 + 0 = 0
0 + 1 = 1
1 + 0 = 1
1 + 1 = 1
• AND (Product)
0 . 0 = 0
0 . 1 = 0
1 . 0 = 0
1 . 1 = 1
• NOT (Inverse)
0 = 1
1 = 0

5. At the end of this topic, students
should be able to:
a) Identify symbol for logic gate
Computer System
2.4.2 Logic Gate
Chapter
PDT - 2017/2018

6. Logic Gates
•
An electronic circuit operates on one or
more input signals to produce an output
signal.
Gates are digital (two-state, On and Off)
circuits and can be analyzed with Boolean
algebra•

7. The three basic logic gates are :
AND gate OR gate NOT gate
Logic Gates

8. More gates
– Universal gates :
NAND-gate
NOR-gate
Logic Gates

9. Truth
Table
● A truth table is a good way to show the function of a
logic gate.
● It shows the output states for every possible
combination of input states
● The symbols of 1 (True) or 0 (False) are used
● For a logic gate with n inputs, there are 2n entries in
the truth table
● Eg : A logic gate with 3 inputs will have 8 entries
(2n=8)

10. STEP BY STEP CREATING A BASIC TRUTH TABLE
1. Identify how many input (n) form the given Boolean expression
and logic circuit.
2. Determine number of entry (2n)
3. Creating a table
e.g; Y= A + B 2 input (A, B)
input (n)
2n ; 22 = 4 entries
INPUT
A
INPUT
B
OUTPUT
Y
4 entries

11. A
B
Y = A . B
INPUT
A
INPUT
B
OUTPUT
Y = A. B
0 0 0
0 1 0
1 0 0
1 1 1
Boolean expression : Y = A . B
@ Y = AB
TRUTH TABLE
AND GATE (logic gate, Boolean
expression and Truth Table

12. Electrical Switches – Illustrate switches for AND Gate
SWITCH A SWITCH B LAMP
Open (O) Open (O) OFF (O)
Closed (1) Open (O) OFF (O)
Open (O) Closed (1) OFF (O)
Closed (1) Closed (1) ON (1)
he The AND gate
is an electronic
circuit that gives
a ON(1) output
only if ALL its
inputs are ON(1).

13. A
B
Y = A + B
INPUT
A
INPUT
B
OUTPUT
Y = A+ B
0 0 0
0 1 1
1 0 1
1 1 1
Boolean expression : Y = A + B
TRUTH TABLE
OR GATE (logic gate, Boolean expression
and Truth Table

14. Electrical Switches – Illustrate switches for OR Gate
SWITCH A SWITCH B LAMP
Open (O) Open (O) OFF (O)
Closed (1) Open (O) ON (1)
Open (O) Closed (1) ON (1)
Closed (1) Closed (1) ON (1)
hOR gate is an
electronic circuit
that gives a ON(1)
output if one or
more of its inputs
are ON(1)

15. NOT GATE (logic gate, Boolean
expression and Truth Table
A Y = A
INPUT
A
OUTPUT
Y = A
0 1
1 0
Boolean expression : Y = A
TRUTH TABLE
*Other operator symbol
~A, A’, !A
- The NOT gate has one binary input and one binary output.
- The NOT gate's output is the inverse of its input.

16. A
B
Y = (A . B)
INPUT
A
INPUT
B
OUTPUT
Y = (A.B)
0 0 1
0 1 1
1 0 1
1 1 0
Boolean expression : Y = (A . B)
TRUTH TABLE
NAND GATE (logic gate, Boolean expression
and Truth Table
A
B

17. A
B
Y = (A . B)
INPUT
A
INPUT
B
OUTPUT
Y = (A+B)
0 0 1
0 1 0
1 0 0
1 1 0
Boolean expression : Y = (A + B)
TRUTH TABLE
NOR GATE (logic gate, Boolean expression
and Truth Table

18. Computer System
Form valid Boolean
expressions
Chapter
PDT - 2017/2018

19. EXAMPLE 1:
Write a boolean expression

20. EXAMPLE 1:
Write a boolean expression
Hence, Y = (A+B). C

21. EXAMPLE 1:
Write a boolean expression
Hence, Y = (A+B). C

22. Boolean Expression :
Q = (A.B)+(A+B)
Q = (A.B)+ (A+B)
EXAMPLE 2:

23. Write a boolean expression and draw the truth table to represent this
logic circuit diagram.
Y = (A.B) . C
A B C Y
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

24. Write a boolean expression and draw the truth table to represent this
logic circuit diagram.
Y = (A.B) + C
A B C Y
0 0 0 0
0 0 1 1
0 1 0 0
0 1 1 1
1 0 0 0
1 0 1 1
1 1 0 1
1 1 1 1

25. At the end of this topic, students
should be able to:
a) Draw simple logic circuit for a given
Boolean expression
Computer System
2.4.3 Logic Circuit
Chapter
PDT - 2017/2018

26. • First, perform all inversions of single terms
• Perform all operations with parentheses ( )
• Perform an AND operation before and OR
operation unless parentheses indicate otherwise
• If an expression has a bar over it, perform the
operations inside the expression first and then
invert the result
Step by step drawing a logic circuit
Precedence

27. Simple Logic Circuit
F = (A + B).C
1. Draw the operations with parentheses ( ) ; (A+B)
2. Joint the output of (A+B) with .C (AND gate)
A
B
C
F

28. Simple Logic Circuit
F = (A . B)+C
1. Draw the operations with parentheses ( ) ; (A.B)
2. Joint the output of (A.B) with .C (OR gate)
A
B
C
F

29. Simple Logic Circuit
F = A + (B.C)
1. First, draw inversions of single terms ; A
2. Draw the operations with parentheses ( ) ; (B.C)
3. Joint the output of A with output of B.C using OR gate
A
B
C
F

30. Simple Logic Circuit
Draw the logic circuit for the Boolean expression
Y = A + B.C + D

31. Simple Logic Circuit
Draw the logic circuit for the Boolean expression
Y = ((A.B)+C)

32. Draw the logic circuit for the question below
1. F = (B+A).C+(A’+D)
2. Y = (B.C+A).(A’+C)
3. Adi will be the football coach if Emran is the goalkeeper or Irfan is not a
striker. However, Emran will only be a goalkeeper only if ZIkri and Afif are the
defender
4. Amy will reach the International Airport as schedules if she checks in before
9am and her luggage is not more than 20kg
5. PSPM is around the corner. Amni and Anna decided to study at the library.
Elsa and Olaf are interested to join them. Amni will goes to the library if Elsa
or Olaf not goes but Anna goes
Exercise