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COMPUTER SCIENCE PAPER 1 (Theory) (Maximum marks: 70) (Time allowed: Three hours) (Candidates are allowed additional 15 minutes for only reading the question paper. They must NOT start writing during this time.) --------------------------------------------------------------------------------------------------------------------------------------------Answer all questions in Part I(compulsory)and six questions from Part II, choosing two questions from Section A, two from Section B and two from Section C. All working, including rough work, should be done on the same sheet as the rest of the answer. The intended marks for questions or parts of question are given in brackets [ ]. ---------------------------------------------------------------------------------------------------------------------------------------------Part I (20 Marks) Attempt all questions While answering questions in this Part , indicate briefly your working and reasoning, wherever required. Question 1 a) b) c) d) e) f) Question 2 a) b) c) d) e) f) T21263 State the commutative laws and prove any one of the law using truth table. Convert the following expression into its canonical POS form: F(X,Y,Z) = (X+Y ).(Y +Z) Convert the Boolean expression F(X,Y,Z) = X Y Z + X YZ +XYZ into cardinal form. Verify the following proposition with the help of the truth table: (P Q) (P ~Q) = P If F(A,B,C) = A (BC +B C) then find F If (~P => Q) then write its: i) Converse ii) Inverse Convert the following infix notation to postfix notation: A*(B/C)/E+F Define Interface. How is it different from class? A matrix A[m][m] is stored in the memory with each elements requiring 4 bytes of storage. If the base address at A[1][1] is 1500 and address of A[4][5] is 1608, determine the order of matrix when it is stored in Column Major wise. What is the purpose of front and rear in the queue data structure? Write one difference each between constructor and method? Explain one advantage and one disadvantage of recursion over iteration. THIS PAPER COMPRISES OF 6 PRINTED PAGES AND 0 BLANK PAGE TURN OVER [1] [1/2] [1/2] [1] [1] [1] [2] [2] [2] [2] [1] [1] Question 3 The following function check ( ) is a part of some class. What will the function check ( ) return when the values of both m and n are equal to 5? Show the dry run / working. int check(int m, int n) { if(n==1) return m- -; else return ++m + check(m,- -n); } [5] Part II (50 Marks) Answer six questions in this part, choosing two questions from Section A, two questions from Section B and two questions from Section C. Section A (20 Marks) Attempt any two questions. Question 4. a) Given the Boolean function F(A,B,C,D) = (1,3,5,7,8,9,10,11,14,15). i) Reduce the above expression by using 4 variable Karnaugh map, showing the various groups (i.e. octals, quads and pairs) ii) b) Given the Boolean function F(A,B,C,D) = (4,6,7,10,11,12,14,15). i) Reduce the above expression by using 4 variable Karnaugh map, showing the various groups (i.e. octals, quads and pairs) ii) Question 5 a) b) c) T21263 Draw the logic gate diagram for the reduced expression. Assume that the variables and their complements are available as input. Draw the logic gate diagram for the reduced expression. Assume that the variables and their complements are available as input. [4] [1] [4] [1] What is decoder? Draw the logic diagram for a binary to octal (3 to 8) decoder. [3] How half adder is different from a full adder? Draw the truth table and derive the SUM & CARRY expression for a full adder. Also, draw the logic diagram for a full adder. [4] State whether the following expression is a Tautology, Contradiction or a Contingency with help of a truth table: ( X => Z) ~[(X => Y) (Y =>Z)] [3] 2 TURN OVER Question 6 a) Draw a truth table with 3 input combination (A,B,C) which outputs 1 if either A and B or A and C is 1 or B and C together is 1. Derive the SOP expression and draw the truth table of the expression. [4] b) Find the complement of the following F(x,y) = ((x.y) +x).(x.y + y ). [3] c) Simplify using Boolean laws : F(x,y,z) = z . (z+x) . x . (x+y ) [3] Section B(20 Marks) Attempt any two questions Each program must be written in such a way that it clearly depicts the logic of the problem. This can be achieved by using mnemonics names and comments in the program. (Flowcharts and Algorithm are not required) The programs must be written in Java. Question 7 A disarium number is a number in which the sum of the digits to the power of their respective position is equal to the number itself. Example : 135 = 11 + 32 + 53 Hence , 135 is a disarium number Design a class Disarium to check if a given number or not . Some of the members of the class are given below: Class name: Disarium Data members / instance variables: int num stores the numbers int size stores the size of the numbers Methods / Members functions Disarium( int nn) parameterized constructor to initialize the data members num = nn and size =0 void count_Digit( ) counts the total number of digits and assign its size int sum_of_Digits(int n, int p ) returns the sum of the digits of the numbers (n) to power of their respective position (p) using recursive technique. void check( ) check whether the number is a disarium number and displays the results with an appropriate message. Specify the class Disarium giving details of the constructor Disarium ( ) , void count_Digit( ), int sum_of_Digits(int, int) and void check( ). Define the main( ) function to create an object and call the functions accordingly to enable the task. [10] Question 8 A class Adder has been defined to add any two accepted time. Example : Time A- 6 hours 35 minutes Time B 7 hours 45 minutes Their sum is 14 hours 20 minutes (continue ) T21263 3 TURN OVER The details of the members of the class are given below: Class Name Adder Data members/instance variable Adder( ) constructor to assign zero to the array elements void read_time( ) to enter the elements in the array void addtime (Adder X, Adder Y) add the time of two parameterized objects X & Y and store the sum in the current calling object void disptime( ) display the array elements with appropriate message (ie: hours = and minutes = ) Specify the class Adder giving details of the constructor ( ) , void read_time( ), void addtime( Adder, Adder) and void disptime( ). Define the main ( ) function to create objects and call the functions accordingly to enable task. [10] Question 9 Define a class ProcessStr to accept a string from the user and replace duplicate characters in sequence by its single occurrence. The program should also remove extra spaces between the words of the string of present.) The details of the class is given below: Class name ProcessStr Data member/ Instance variables String str to store the string in the original form int len to store the length of the string Member function ProcessStr default constructor void readString( ) to accept the string from the user void removeDupli( ) It will replace duplicate characters in a sequence by its single occurrence. Example: Heee iiisss ggoiinggg foorrr moovvie then output will be He is going for movie. void removespace( ) it will remove extra spaces between the words in a string. Hence modified string will be Heisgoingformovie. void display( ) print the modified and original string [10] Section- C( 10 Marks) Attempt any two questions Each program must be written in such a way that it clearly depicts the logic of the problem stepwise. This can also be achieved by using comments in the program and mnemonics or pseudocode for the algorithm. The programs must be written in Java and the algorithm must be written in general /standard form, wherever required/specified. (Flowcharts not required) T21263 4 TURN OVER Question 10 Queue is an entity which can hold a maximum of 100 integers. The queue enables the user to add integers from the rear end and remove integers from the front end. Define a class Queue with the following details: Class name Queue Data members/ instance variables Que [ ] array to hold the integers elements size stores the size of the array front the pointer variable indicating front index rear the pointer variable indicating rear index Member functions Queue(int mm) constructor to initialize the data size=mm, front=0 rear = 0. void addele(int v) the rear if possible else display message overflow. int delete( ) returns elements from front if present else display UNDERFLOW and return -9999. void display( ) display the array elements. Specify the class Queue giving details of only methods void addele(int) and int delete( ). Assume that the other functions have been defined. The main function and algorithm need not to be written. [5] Question 11 An interface Shape is defined with a method area ( ) which returns the area of the implementing shape. Create the classes Circle & Rectangle which implement the interface Shape. These classes have attributes which reflect their dimensions(radius of a circle, height and width for a rectangle) which are set by their constructors. The detail of the members of the interface and both the classes are given below: Interface name: Shape Methods: double area( ): returns of the implementing shape Class name: Circle Data members / instance variables: radius: to store the radius of the circle in decimal Member methods/functions: Circle(int r): parameterized constructor double area( ): to calculate the area of the circle Class name: Rectangle Data members/instance variables length: to store the value of length breadth: to store the value of breadth Member methods/functions: Rectangle( int l, int b): parameterized constructor double area( ): to calculate the area of the rectangle Assume that the interface Shape has been defined. Using the concept of inheritance, specify the classes Circle and Rectangle giving the details of the constructor and double area ( ) respectively. The interface, algorithm and main function need NOT to be written. T21263 5 TURN OVER [5] Question 12 i) ii) iii) iv) v) T21263 Name the leaf nodes of the right sub tree. Write post order traversal of right sub tree. Write pre order traversal of left sub tree. State the level number of nodes R and M when root level is 0. Name the internal nodes of the tree. 6 [1] [1] [1] [1] [1] TURN OVER
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