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ISC sample paper
Answer all questions in Part I (compulsory) and seven 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 questions are given in brackets [ ].
PART I
Answer all questions
Question1. [ 1 x 5 = 5]
- a) State the two distributive laws of Boolean Algebra. Prove any one of them with the help of truth tabl
- b) Using truth table, verify whether the following is true or false:
(p →q) = (q’→p’)
- c) Find the complement of the following: [(xy)’.x][(xy)’.y]
- d) Simplify the following Boolean expression using laws of Boolean Algebra. At each step, clearly state the law used for simplification. z(z+x).x(y+y’)
- e) Given F(x,y,z)= xz+xy +yz Write the function in canonical sum of product form.
Question 2. [ 2 x 5 = 10]
- a) What do LIFO and FIFO stand for?
- b) For an array of real numbers x[-6…8, -12…. 20], find the address of x[5][4] , if x[1][1] is stored in location 100 in the column major order. Assume that each element requires 4 bytes.
- c) State the difference between an abstract class and an interface.
- d) Convert the following infix expression to its postfix form. b*[(a/d) – (c * (e-f))]
- e) Define a binary tree.
Question 3. [5]
The following is a function of some class. What will be the output of the function test( ) when the value of count is equal to 4?Show the dry run / working.
class Sample
{
public void test( int count)
{
if(count == 0)
System.out.println(” “);
else
{
System.out.println(“Bye ” +count);
test(–count);
System.out.println(” “+ count);
}
}
}
Part II
Answer six questions in this part, choosing two questions from Section A, two from Section B and two from Section C.
Section A
Answer any two questions
Question 4.
a) Given F(P,Q,R,S)= ∏(0,1,2,3,5,7,8,9,10,11)
- i) Reduce the above expression by using 4 variable Karnaugh map, showing the various groups( i.e. octal, quads and pairs). [4]
ii) Draw the logic gate diagram for the reduced expression. Assume that the variables and their complements are available as inputs. [1] - b) Given P(A,B,C,D)= ABC’D’ + A’BC’D’+ A’BC’D+ ABC’D+A’BCD+ABCD
- i) Reduce the above expression by using 4 variable Karnaugh map, showing the various groups (i.e. octal, quads and pairs). [4]
ii) Draw the logic gate diagram for the reduced expression. Assume that the variables and their complements are available as inputs. [1]
Question 5
- Draw the truth table and logic circuit diagram for a 3X 8 decoder. [5]
- What do you understand by a multiplexer? State any one application of a multiplexer circuit. [2]
- Draw the logic gate diagram to implement the AND gate by using NOR gate and NAND gate. [3]
Question 6
The main safe in the nationalize bank can be opened by means of a unique password consisting of three parts. Different parts of the password are held by the chairman, Regional Manager, Bank Manager and Head Cashier of the bank, respectively.
In order to open the safe any one of the following conditions must be satisfied:
The password of the chairman, together with passwords of any two other officials, must be entered.
OR
The password of all three bank officials, excluding the chairman, must be entered.
The inputs are: INPUTS
A Denotes the chairman’s password
B Denotes the Regional Manager’s password
C Denotes the Bank Manager’s password
D Denotes the Head Cashier’s password
Output
X Denotes the safe can be opened [ 1 indicates YES ad 0 indicates NO in all cases]
- Draw the truth table for the inputs and outputs given above and write the SOP expression for X(A,B,C,D).
- Reduce X(A,B,C,D) using Karnaugh’s map, if possible.
Draw the logic gate diagram for the reduced SOP expression for X(A,B,C,D) using AND and OR gates. You may use gates with two or more inputs. Assume that the variable and their complements are available as inputs. [10]
Section B
Answer two questions
Each program should be written in such a way that it clearly depicts the logic of the problem. use mnemonic names and comments in the program. (Flowcharts and algorithms are not required)
The programs must be written in Java.
Question 7.
A perfect square is an integer which is the square of another integer. For example, 4,9,16… are perfect squares. Design a class Perfect with the following description:
Class Name : Perfect
Data members
n : stores an integer number
Member functions
Perfect() : default constructor
Perfect(int) : parameterized constructor to assign value to n
void perfect_sq() : to display the first 5 perfect squares larger than
‘n’ (if n=15, the next 3 perfect squares are 16,25,36).
void sum_of() : to display all combinations of consecutive integers whose sum is = n. (The number n=15 can be expressed as :
1 2 3 4 5
4 5 6
7 8
Specify the class Perfect giving details of the constructors, void perfect_sq() and void sum_of(). Also define the main function to create an object and call methods accordingly to enable the task. [ 10 ]
Question 8.
In a class VowelWord to accept sentence and calculate the frequency of words that begin with a vowel. The words in the input string are separated by a single blank space and terminated by a full stop. The description of the class is given below:
Class name VowelWord
Data members
str to store the sentence
freq store the frequency of the words beginning with a vowel
Member functions
VowelWord() constructor to initialize data members to legal initial value.
void readstr() to accept a sentence
void freqvowel() counts the frequency of the words that begin with a vowel
void display() to display the original string and the frequency of the words that begin with a vowel.
Specify the class VowelWord giving details of the constructors and all the functions. Also write the main function. [10]
Question 9.
A Transpose of any array is obtained by interchanging the elements of the rows and columns.
A class Transarray contains a two dimensional integer array of order [ m x n]. The maximum value possible for both ‘m’ and ‘n’ is 20. Design a class Transarray to find the transpose of a given matrix. The details of the members of the class are given below :
Class name : Transarray
Data members
arr[][] : stores the matrix elements
m : integer to store the number of rows
n : integer to store the number of columns
Member functions :
Transarray() : default constructor
Transarray(int mm, int nn) : to initialize the size of the matrix, m=mm, n=nn
void fillaray() : to enter the elements of the matrix
void transpose(Transarray A) : to find the transpose of a given matrix
void disparray() : displays the array in a matrix form
Specify the class Transarray giving the details of the constructor and other member functions. You need not to write the main function. [10]
ISC sample paper
Section C
Answer any 2 questions.
Each program/algorithm should be written in such a way that it clearly depicts the logic of the problem step wise. This can also be achieved by using pseudo codes.
(Flowcharts are not required)
The programs must be written in Java.
The algorithm must be written in general standard form wherever required.
Question 10.
A class Author contains details of the author and another class BookList contains details of the books written by him. The details of the 2 classes are given below:
Class name : Author
Data members
authorno : stores the author’s number
name : stores the author’s name Member functions
Author() : default constructor
Author(…..) : parameterized constructor to assign values to author number and name.
void show() : to display the author’s details.
Class name : Booklist
Data members
bookno : long type variable to store the book number.
bookname : stores the book name
price : float variable to store price
edition : integer type variable to store the edition number
Member functions
Booklist(…..) : parameterized constructor to assign values to data members of both the classes.
void show() : to display all the details.
Specify the class Author giving details of the constructors and member function void show(). Using the concept of inheritance, specify the class Booklist giving details of the constructor and the member function void show(). Also define the main function to create an object and call methods accordingly to enable the task. [ 5 ]
Question 11.
In a computer game, a vertical column and a pile of rings are displayed. The objective of the game is to pile up rings on the column till it is full. It can hold 10 rings at the most. Once the column is full, the rings have to be removed from the top till the column is empty and the game is over. Define the class RingGame with the following details:
Class Name : RingGame
Data members
ring[] : array to hold rings (integer)
max : integer to hold maximum capacity of ring array
upper : integer to point to the uppermost element
Member functions
RingGame(int m) : constructor to initialize, max = m & upper to -1.
void jump-in(int) : adds a ring to the top of the column, if possible, otherwise, displays a message “Column full. Start removing rings”.
void jump-out() : removes the ring from the top, if column is not empty, otherwise outputs a message, “Congratulations the game is over “.
Specify the class RingGame giving details of the constructor and functions void jump-in(int) and void jump-out(). Also define the main function to create an object and call methods accordingly to enable the task. [5]
Question 12.
- a) A linked list is formed from the objects of the class. [2]
class Node
{
int info;
Node link;
}
Write an algorithm OR a method for deleting a node after ‘n’ nodes from a linked list. The method declaration is given:
void deletenode(Node start, int n).
(c) Answer the following from the diagram of a binary tree [3]
- Write the postorder tree traversal.
- Name the root of the right subtree
- Level of the tree.
ISC sample paper
