 # CHAPTER 1 INTRODUCTION TO DIGITAL LOGIC

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

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

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 “¯”

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

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

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

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

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

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

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

Exclusive-NOR (XNOR)Gate a) Gate Symbol, Boolean Equation
1 a) Gate Symbol, Boolean Equation

DIP and SOIC packages

Universality of Gates(1)
NAND Gate

Universality of Gates(2)
NOR Gate

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

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

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

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

Laws & Rules of Boolean algebra

A+B = B+A the order of ORing does not matter.

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

A + (B + C) = (A + B) + C The grouping of ORed variables does not matter

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

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

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

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

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

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

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

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

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

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.

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

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

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

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

END OF BOOLEAN THEOREM