Digital Teaching Aid (DED Philippinen, 86 p.) 
Introduction Boolean Algebra  Lesson 2 

Titel: Introduction Boolean Algebra
Objectives:
 Able to express the basic operations in Boolean algebra
 Know how to describe a logic circuit in a Boolean equation
 Understand the basic Boolean theorems.
Time 
Method 
Topic 
Way 
Remark  

Q/A 
* Review Lesson 1 
B   

S 
* Introduction  George Boole 
B   

S 
* Boolean algebra 
B,Ex  

 
S,E  
 NOT operation 
 
 
 
 OR operation 
 
 
 
 AND operation 
 
 
S,E  
 Boolean equations of logic circuits 
B,Ex  
   
 NOR gates Truth table 
B  
 
S,D  
 De Morgan's 1. theorem 
B  
 
 
 NAND gates Truth table 
B  
 
E  
 De Morgan's 2. theorem 
B,HO  

E 
* Review Exercise 
WS 
Worksheet No. 2  

S: Speech  
B: Boardscript  
George Boole (1854) invented a new kind of algebra that could be used to analyse and design digital and computer circuits.
NOT operation
Fig. 21: Inverter symbol and
Boolean notation
Ex: If A is 0 (low) ® X = NOT 0 = 1
In Boolean algebra the overbar stands for NOT operation.
_{}
OR operation
Fig. 22: OR symbol and Boolean
notation
Ex: If A = 0, B = 1 ® X = A or B = 0 or 1 = l
In Boolean algebra the + sign stans for the OR operation:
X = A + B
Ex: If A = 1, B = 0 ® X = A + B = 1 + 0 = 1
AND operation
Fig. 23: AND symbol and Boolean
notation
In Boolean algebra the multiplication sign stands for the AND operation:
X = A · B
or simply:
X = A B
Ex: If A = 1, B = 0 ® X = A B = 1 · 0 = 0
You can use Boolean algebra as a shorthand notation for digital circuits.
Ex:
Fig. 24: Digital circuit
Output of the first gate:
X3 = A + B
Output of the second gate:
X6 = X3 + C = A + B + C
The final output is:
X8 = X6 + D = A + B + C + D = X
HO: Find the Boolean equation for the following circuit.
Fig. 25: Logic circuit
Solution:
X = (A + B) (C + D)
NOR gate
Based on the three fundamental logic operations it is possible to design additionel logic devices.
Fig. 26: NOR gate, symbol and
truth table
Formula: _{}
NAND gate
Fig. 27: NAND grate, symbol and
truth table
Formula: _{}
Augustus De Morgan was the first who found the link between logic and mathematics.
Fig. 28: Logic circuits with the
same output
Although the circuits are different but the output, as we can see in the truth table, is equal. Therefore we can write:
_{}De Morgan's First Theorem
Also if we compare the two circuits on the next page we can easily see that the output is the same, although the circuits are different.
(see Fig. 29)
Fig. 29: Logic circuits with the
same output
So we can write:
_{}De Morgan's Second Theorem
HO: How can you connect a NAND gate to get an inverter
Solution:
Figure
HO: How can you connect NAND gates to get an OR gate?
Solution:
Figure
No. 1 What is the
Boolean equation? What is the truth table?
No. 2 What is the
Boolean equation? What is the truth table?
No. 3 What is the
Boolean equation? What is the truth table?
No. 4 Construct the
truth table.
No. 5 Draw the logic circuit whose Boolean equation is
_{}
Use the 7404 and the 7432 with pin numbers
No. 6 Draw the logic circuit whose Boolean equation is
_{}
Use the 7404, 7432 and the 7411 with pin numbers.