1. CHAPTER 1 : INTRODUCTION
EKT 121 / 4 ELEKTRONIK DIGIT 1
CHAPTER 1 : INTRODUCTION

2. 4.0 BOOLEAN ALGEBRA
Boolean Operations & expression
Laws & rules of Boolean algebra
DeMorgan’s Theorems
Boolean analysis of logic circuits
Simplification using Boolean Algebra
Standard forms of Boolean Expressions
Boolean Expressions & truth tables
The Karnaugh Map

3. Karnaugh Map SOP minimization
Karnaugh Map POS minimization
5 Variable K-Map
Programmable Logic

4. Boolean Operations & expression
Variable – a symbol used to represent logical quantities (1 or 0)
ex : A, B,..used as variable
Complement – inverse of variable and is indicated by bar over variable
ex : Ā

5. Operation : Boolean Addition – equivalent to the OR operation
X = A + B
Boolean Multiplication – equivalent to the AND operation
X = A∙B A X B A X B

6. Laws & rules of Boolean algebra

7. Commutative law of addition
A+B = B+A
the order of ORing does not matter.

8. Commutative law of Multiplication
AB = BA
the order of ANDing does not matter.

9. Associative law of addition
A + (B + C) = (A + B) + C
The grouping of ORed variables does not matter

10. Associative law of multiplication
A(BC) = (AB)C
The grouping of ANDed variables does not matter

11. (A+B)(C+D) = AC + AD + BC + BD
Distributive Law
A(B + C) = AB + AC
(A+B)(C+D) = AC + AD + BC + BD

12. Boolean Rules 1) A + 0 = A
In math if you add 0 you have changed nothing
In Boolean Algebra ORing with 0 changes nothing

13. Boolean Rules 2) A + 1 = 1
ORing with 1 must give a 1 since if any input
is 1 an OR gate will give a 1

14. Boolean Rules 3) A • 0 = 0
In math if 0 is multiplied with anything you
get 0. If you AND anything with 0 you get 0

15. Boolean Rules 4) A • 1 = A
ANDing anything with 1 will yield the anything

16. Boolean Rules 5) A + A = A
ORing with itself will give the same result

17. Boolean Rules 6) A + A = 1
Either A or A must be 1 so A + A =1

18. Boolean Rules 7) A • A = A
ANDing with itself will give the same result

19. Boolean Rules 8) A • A = 0
In digital Logic 1 =0 and 0 =1, so AA=0 since one of the inputs must be 0.

20. Boolean Rules 9) A = A
If you not something twice you are back to the beginning

21. Boolean Rules 10) A + AB = A Proof: A + AB = A(1 +B) DISTRIBUTIVE LAW
= A∙ RULE 2: (1+B)=1
= A RULE 4: A∙1 = A

22. Boolean Rules 11) A + AB = A + B
If A is 1 the output is 1 , If A is 0 the output is B
Proof:
A + AB = (A + AB) + AB RULE 10
= (AA +AB) + AB RULE 7
= AA + AB + AA +AB RULE 8
= (A + A)(A + B) FACTORING
= 1∙(A + B) RULE 6
= A + B RULE 4

23. Boolean Rules 12) (A + B)(A + C) = A + BC
PROOF
(A + B)(A +C) = AA + AC +AB +BC DISTRIBUTIVE LAW
= A + AC + AB + BC RULE 7
= A(1 + C) +AB + BC FACTORING
= A.1 + AB + BC RULE 2
= A(1 + B) + BC FACTORING
= A.1 + BC RULE 2
= A + BC RULE 4

24. END OF BOOLEAN
RULES & LAWS