EKT 121 / 4 ELEKTRONIK DIGIT 1

PGT 104ELEKTRONIK DIGIT CHAPTER 1 INTRODUCTION TO DIGITAL LOGIC1LOGIC GATES NOT Gate (Inverter) AND Gate OR Gate NAND Gate NOR Gate X-OR and X-NOR Gates Fixed-function logic: IC Gates

2Introduction(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

3 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 systemThere 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

Introduction(2)4NOT Gate (Inverter)

a) Gate Symbol & Boolean Equationb) Truth Table c) Timing Diagram

5OR Gate

a) Gate Symbol & Boolean Equationb) Truth Table c) Timing Diagram

6AND Gate

a) Gate Symbol & Boolean Equationb) Truth Table c) Timing Diagram

7NAND Gate

a) Gate Symbol, Boolean Equation & Truth Table b) Timing Diagram 8NOR Gate

a) Gate Symbol, Boolean Equation & Truth Table b) Timing Diagram 9Exclusive-OR (XOR)Gate

a) Gate Symbol, Boolean Equation & Truth Table b) Timing Diagram 10Exclusive-NOR (XNOR)Gate

XNOR

a) Gate Symbol, Boolean Equation 1001DIP and SOIC packages

Universality of Gates(1)

NAND Gate

NOR GateUniversality of Gates(2)

Examples : Logic Gates ICNOT gateAND gateNote : x is referring to family/technology (eg : AS/ALS/HCT/AC etc.) 15Performance 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 LoadingBOOLEAN ALGEBRA Boolean Operations & expression Laws & rules of Boolean algebra DeMorgans 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

17Boolean Operations & expression Expression:Variable: a symbol used to represent logical quantities (1 or 0)Eg.: A, B,..used as variableComplement: inverse of variable and indicated by bar over variableEg.: Operation:Boolean Addition equivalent to the OR operationEg.: X = A + B

Boolean Multiplication equivalent to the AND operation Eg.: X = AB

XXABAB18Laws & Rules of Boolean algebra19Commutative Law of AdditionCommutative law of addition, A+B = B+Athe order of ORing does not matter.

20Commutative Law of MultiplicationCommutative law of Multiplication AB = BAthe order of ANDing does not matter.

21Associative Law of AdditionAssociative law of additionA + (B + C) = (A + B) + CThe grouping of ORed variables does not matter

22Associative Law of MultiplicationAssociative law of multiplicationA(BC) = (AB)CThe grouping of ANDed variables does not matter

23Distributive LawA(B + C) = AB + AC

(A+B)(C+D) = AC + AD + BC + BD24Boolean Rules (1)

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

25Boolean 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

26Boolean 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

27Boolean Rules (4)

4) A 1 = A ANDing anything with 1 will yield the anything

28Boolean Rules (5)

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

29Boolean Rules(6)

6) A + A = 1 Either A or A must be 1 so A + A =1

30Boolean Rules(7)

7) A A = A ANDing with itself will give the same result

31Boolean 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.

32Boolean Rules(9) 9) A = A If you NOT something twice you are back to the beginning

33Boolean Rules(10)

10) A + AB = AProof: A + AB = A(1 + B) DISTRIBUTIVE LAW = A1 RULE 2: (1+B)=1 = A RULE 4: A1 = A34Boolean Rules(11)

11) A + AB = A + B If A is 1 the output is 1 , If A is 0 the output is BProof :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 435Boolean Rules(12)

12) (A + B)(A + C) = A + BCProof :(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 436END OF BOOLEAN THEOREM