1. CHAPTER 1 INTRODUCTION TO DIGITAL LOGIC
PGT 104 ELEKTRONIK DIGIT
CHAPTER 1
INTRODUCTION TO DIGITAL LOGIC

2. LOGIC GATES NOT Gate (Inverter) AND Gate OR Gate NAND Gate NOR Gate
X-OR and X-NOR Gates
Fixed-function logic: IC Gates

3. Introduction(1)
All Logic circuit and functions are made from basic logic gates
Three basic logic gates:
AND gate – expressed by “ . ”
OR gate – expressed by “+” sign (NOTE: it is not an ordinary addition)
NOT gate – expressed by “ ’ “ or “¯”

4. Introduction(2)
Think about these logic gates as bricks in a structure.
Individuals bricks can be arranged to form various type of buildings, and bricks can be used to build fireplaces, steps, walls, walkways and floor.
Likewise, individual logic gates are arranged and interconnected to form various function in a digital system
There are several type of logic gates, just as there may be several shapes/sizes of bricks in a structure.
By: Thomas L. Floyd & David M. Buchla

5. NOT Gate (Inverter) a) Gate Symbol & Boolean Equation b) Truth Table
c) Timing Diagram

6. OR Gate a) Gate Symbol & Boolean Equation c) Timing Diagram
b) Truth Table
c) Timing Diagram

7. AND Gate a) Gate Symbol & Boolean Equation b) Truth Table
c) Timing Diagram

8. a) Gate Symbol, Boolean Equation
NAND Gate
a) Gate Symbol, Boolean Equation
& Truth Table
b) Timing Diagram

9. a) Gate Symbol, Boolean Equation
NOR Gate
a) Gate Symbol, Boolean Equation
& Truth Table
b) Timing Diagram

10. Exclusive-OR (XOR)Gate a) Gate Symbol, Boolean Equation & Truth Table
b) Timing Diagram

11. Exclusive-NOR (XNOR)Gate a) Gate Symbol, Boolean Equation1
a) Gate Symbol, Boolean Equation

12. DIP and SOIC packages

13. Universality of Gates(1)
NAND Gate

14. Universality of Gates(2)
NOR Gate

15. Examples : Logic Gates IC
AND gate
NOT gate
Note : x is referring to family/technology (eg : AS/ALS/HCT/AC etc.)

16. Performance Characteristics and Parameters
Propagation delay Time
High-speed logic has a short pdt.
DC Supply Voltage (VCC)
Power Dissipation
Lower power diss. means less current from dc supply
Input and Output (I/O) Logic Levels
Speed-Power product
Fan-Out and Loading

17. 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 (K-Map) – SOP, POS, 5 Variables
Programmable Logic

18. Boolean Operations & expression
Variable: a symbol used to represent logical quantities (1 or 0)
Eg.: A, B,..used as variable
Complement: inverse of variable and indicated by bar over variable
Eg.: Ā
Operation:
Boolean Addition – equivalent to the OR operation
Eg.: X = A + B
Boolean Multiplication – equivalent to the AND operation
Eg.: X = A∙B A X B A X B

19. Laws & Rules of Boolean algebra

20. Commutative Law of Addition
A+B = B+A
the order of ORing does not matter.

21. Commutative Law of Multiplication
AB = BA
the order of ANDing does not matter.

22. Associative Law of Addition
A + (B + C) = (A + B) + C
The grouping of ORed variables does not matter

23. Associative Law of Multiplication
A(BC) = (AB)C
The grouping of ANDed variables does not matter

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

25. Boolean Rules (1) 1) A + 0 = A
Mathematically if you add O you have changed nothing
In Boolean Algebra ORing with 0 changes nothing

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

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

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

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

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

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

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

33. Boolean Rules(9) 9) A = A
If you NOT something twice you are back to the beginning

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

35. Boolean Rules(11) 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

36. Boolean Rules(12) 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

37. END OF BOOLEAN THEOREM