EKT 124 3 ELEKTRONIK DIGIT 1 CHAPTER 1

EKT 124 / 3 ELEKTRONIK DIGIT 1 CHAPTER 1 INTRODUCTION TO DIGITAL LOGIC

BOOLEAN ALGEBRA q q q q Boolean Operations & expression Laws & rules of Boolean algebra Basic logic gates De. Morgan’s Theorems Boolean analysis of logic circuits Simplification using Boolean Algebra Standard forms of Boolean Expressions & truth tables

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

Laws & Rules of Boolean algebra

Commutative Law of Addition Commutative law of addition, A+B = B+A the order of ORing does not matter.

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

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

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

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

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

Boolean Rules (2) 2) A + 1 = 1 q 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 q 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 q ANDing anything with 1 will yield the anything

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

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

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

Boolean Rules(8) 8) A • A = 0 q 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 q If you NOT something twice you are back to the beginning

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

Boolean Rules(11) A + AB = A + B q 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) (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

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

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

Introduction(2) q Think about these logic gates as bricks in a structure. q Individuals bricks can be arranged to form various type of buildings, and bricks can be used to build fireplaces, steps, walls, walkways and floor. q Likewise, individual logic gates are arranged and interconnected to form various function in a digital system q. 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 b) Truth Table c) Timing Diagram

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

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

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 XNOR 1 0 0 1 a) Gate Symbol, Boolean Equation

DIP and SOIC packages

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

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

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