Digital Teaching Aid (DED Philippinen, 86 p.) 
Circuit Analysis and Design  Lesson 3 
Lesson Plan 

Titel: Circuit Analysis and Design
Objectives:
 Know how to apply the basic Boolean laws
 Able to create digital circuits with the help of the sum of products method
Time 
Method 
Topic 
Way 
Remark  


* Review Lesson 2 
  
 
* Introduction 
  
 
* Boolean laws and theorems 
HO 
Handout No. 2 (Boolean Algebra Theorems)  
 

 Basic laws 
 
 

 Boolean relation about OR operations  

  
 Boolean relations about AND operations  

 
* Sum of products method    
 

 Fundamental products   
 

 Sum of products equations   
 
* Review Exercise 
WS 
Worksheet No. 3  

S: Speech  
B: Boardscript  
Circuit Analysis and Design
Basic laws
(see also Handout No. 2)
Commutative law:
A + B = B + AA B = B A
Fig. 31: Commutative law
Associative law:
A + (B + C) = (A + B) + CA (B + C) = (A B) C
Fig. 32: Associative law
Distributive law:
A (B + C) = AB + AC
Fig. 33: Distributive law
Boolean relations about OR operations
A + 0 = A
Proof:
when A is 0
0 + 0 = 0
when A is 1
1 + 0 = 1
A + A = A
Proof:
when A is 0
0 + 0 = 0
when A is 1
1 + 1 = 1
A + 1 = 1
Proof:
when A is 0
0 + 1 = 1
when A is 1
1 + 1 = 1
A + A = 1
If one input is high, the output is high no matter what the other input is.
Boolean relations about AND operations
A · 1 = A
A · A = A
A · 0 = 0
HO: Check the equations above in the same way as we did it before.
A · A = 0
If one input is low, the output is low no matter what the other input is.
Double inversion
_{}
De Morgan's theorems
_{} see also Lesson 1
_{}
Duality theorem
1. Change each OR sign to an AND sign
2. Change ech AND sign to an OR sign
3. Complement any 0 or 1 appearing in the expression
Ex:  
A + 0 = A 

® 
A 1 = A 
Ex:  
A (B + C) = AB + AC 

® 
A + B C = (A + B) (A + C) 
TIP: Proof it with a truth table
Ex: Simplify the following Boolean equation
_{}
Solution: (see also Handout No. 2)
_{} 
Handout 2 
No. 3a 
X = A (1)  
No. 8a 
X = A  
No. 7b 
HO: Simplify the following Boolean equation
_{}
_{}
_{}
_{}
X = B + B
X = B
Fig. 34: Example truth table with fundamental products
A 
B 
X 
Fundamental Products 
0 
0 
0 
_{} 
0 
0 
1 
_{} 
0 
1 
0 
_{} 
0 
1 
1 
_{} 
1 
0 
0 
_{} 
1 
0 
1 
_{} 
1 
1 
0 
_{} 
1 
1 
1 
_{} 
Sum of products equation
Given is the following truth table:
Fig. 35: Example truth table
A 
B 
C 
X  

0 
0 
0 
0   
0 
0 
1 
0   
0 
1 
0 
0   
0 
1 
1 
1 
® 
_{} 
1 
0 
0 
0   
1 
0 
1 
1 
® 
_{} 
1 
1 
0 
1 
® 
_{} 
1 
1 
1 
1 
® 
_{} 
We have to locate each output 1 in the truth table and write down the fundamental product.
The next step is to OR the fundamental products:
_{}
Now we can derive the corresponding logic circuit:
Fig. 36: Logic circuit
HO: What is the sum of product circuit for the given truth table?
Fig. 37: Truth table
A 
B 
C 
X 
0 
0 
0 
1 
0 
0 
1 
0 
0 
1 
0 
1 
0 
1 
1 
0 
1 
0 
0 
1 
1 
0 
1 
0 
1 
1 
0 
1 
1 
1 
1 
0 