Maximum Marks: 70 Time allowed:
Three hours
(Candidates are allowed additional
15 minutes for only reading the
paper. They must NOT
start writing during
this time.)
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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 questions are given in brackets [].
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PART I – 20 MARKS
Answer all questions.
While answering questions in this Part, indicate briefly your working and reasoning, wherever required.
(i)
According to De Morgan’s law (a + b + c’)’ will be equal to: 1
(a) a’ + b’ + c’ (b) a’ + b’ + c
(c) a’ . b’ . c’ (d) a’ . b’ . c
(ii)
The dual of (X’ + 1) . (Y’ + 0) = Y’ is: 1
(a) X . 0 + Y . 1 = Y (b) X’ . 1 + Y’ . 0 = Y’
(c) X’ . 0 + Y’ . 1 = Y’ (d) (X’ + 0) + (Y’ + 1) = Y’
(iii)
The reduced expression of the Boolean
function F(P, Q) = P’ + PQ is: 1
(a) P’ + Q (b) P
(c) P’ (d) P + Q
(iv)
If (~p => ~q) then its contra positive will be: 1
(a) p => q (b) q => p
(c) ~q => p (d) ~p => q
(v)
The keyword that allows multi-level inheritance in Java programming is: 1
(a) implements (b) super
(c) extends (d) this
(vi)
Write the minterm
of F(A, B, C, D) when A = 1, B = 0, C = 0 and D = 1. 1
(vii)
Verify if (A + A’)’ is a Tautology, Contradiction, or a Contingency. 1
(viii)
State any one purpose of using the keyboard
this in Java programming. 1
(ix)
Mention any two properties of the data members of an Interface. 1
(x)
What is the importance of the reference part
in a Linked List? 1
(i)
Convert the following
infix notation to prefix notation. 2
(A – B)/C*(D + E)
(ii)
A matrix M[–6...10m 4. 15] is stored in the memory with each element requiring
4 bytes of storage. If the base
address is 1025, find the address
of M[4][8] when the matrix is stored in Column Major Wise. 2
(iii)
With reference to the code given below, answer the
questions that follow along with dry run/working. boolean num(int x)
{int a=1;
for(int c=x; c>0’c/=10) a*=10;
return(x*x%a)=x;}
(a)
What will the function num() return when the value of x = 25? 2
(b)
What is the method num() performing? 1
(iv)
The following function
task() is a part of some class.
Assume ‘m’ and ‘n’ are positive integers, greater than 0. Answer
the questions given below along with dry run/working.
int task(int
m, int n)
{if(m==n) return m;
else if(m>n)
return task(m–n,n); else
return task(m,n–m);
}
(a)
What will the function task()
return when the value of m = 30 and n = 45? 2
(b)
What function does task() perform,
apart from recursion? 1
PART II – 50 MARKS
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Answer any two questions.
(i)
Given the Boolean
function F(A, B, C, D) = S(2, 3, 6, 7, 8, 10, 12, 14, 15).
(a)
Reduce the above expression by using 4-variable Karnaugh map, showing
the various groups (i.e., octal, quads
and pairs). 4
(b)
Draw the logic gate diagram for the reduced
expression. Assume that the variables and their complements are available as inputs. 1
(ii)
Given the Boolean
function F(A, B, C, D) = p(0, 1, 2, 4, 5, 8, 10, 11, 14, 15).
(a)
Reduce the above expression by using 4-variable Karnaugh map, showing
the various groups (i.e., octal, quads
and pairs). 4
(b)
Draw the logic gate diagram for the reduced
expression. Assume that the variables and their complements are available as inputs. 1
Question 4
(i)
A shopping mall allows customers
to shop using cash or credit card or any nationalised bank. It awards’
bonus points to their
customers on the basis of criteria given below: 5
l The customer
is an employee of the shopping mall and makes the payment
using a credit card.
OR
l The customer
shops items which carry bonus points and makes the payment using a credit card with a shopping amount of less than `10,000
OR
l The customer is not an employee of the shopping
mall and makes
the payment not through a credit card but in cash for the shopping amount
above `10,000
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INPUTS |
|
|
C |
Payment through
a credit card |
|
A |
Shopping amount
is above `10,000 |
|
E |
The customer is an employee of the shopping mall |
|
I |
Item carries a bonus point |
(In all the above cases, I indicates yes and 0 indicated nd.)
Output: X[1 indicates bonus point awarded, 0 indicates bonus point not awarded for all cases]
Draw the truth table for the inputs and outputs given above and write the POS expression for X(C, A, E, I).
(ii)
Differentiate between half adder
and full adder. Write the Boolean
expression and draw the logic circuit diagram
for the SUM and CARRY of a
full adder. 3
(iii)
Verify the following
expression by using the truth table: 2
(A Å B)’ = (A Å B)
Question 5
(i)
What is an encoder?
How is it different from a decoder? Draw the logic circuit for a 4 : 1
multiplexer and explain its working. 5
(ii)
Form the logic diagram given below, write the Boolean
expression for (1) and (2). Also, derive the Boolean
expression (F) and simplify it. 3
(iii)
Convert the following
cardinal expression to its canonical
form: 2
F(P, Q, R) = p(0, 1, 3, 4)
Answer any two questions.
Each program should be written in such a way that it clearly depicts the logic of the problem.
This can be achieved by using mnemonic names and comments in the program.
(Flowcharts and Algorithms are not required.)
Design a class NumDude to check if a given number is a Dudeney
number or not. 10
(A Dudeney number is a positive integer that is a perfect cube, such that the sum of its digits is equal to the cube root of the number.)
Example: 5832 = (5 + 8 + 3 + 2)3 = (18)3 = 5832
Some of the members of the class are given below:
Data member/instance/variable:
num : to store a positive integer number
NumDude() : default constructor to initialise the data member with legal initial value
void input() : to accept a positive integer number
int sumDigits(int x) : returns the sum of the digits
of number ‘x’ using recursive
technique
void is Dude() : checks whether the given number is a Dudeney number by invoking the function sumDigits() and displays the result with an appropriate message
Specify
the class NumDude giving details of
the constructor(), void input(), int
sumDigits(int) and void is Dude(). Define a main() function to create an object and call the functions
accordingly to enable the task.
A class Trans is defined to find the transpose of a square matrix. A transpose of a matrix is obtained by interchanging the elements of the rows and columns.
Example: If size of the matrix = 3, then
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ORIGINAL |
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TRANSPOSE |
||||
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11 |
5 |
7 |
11 |
8 |
1 |
|
|
8 |
13 |
9 |
5 |
13 |
6 |
|
|
1 |
6 |
20 |
7 |
9 |
20 |
|
Some of the members of the class are given below:
Data members/instance variable:
arr[][] : to store integers in the matrix
m : integer to store the size of the matrix
Trans(int mm) : parameterised constructor to initialise the data member m = mm
void fillarray() : to enter integer elements in the matrix
void transpose() : to create the transpose of the given matrix
void display() : displays
the original matrix and the transport matrix by invoking the method transpose()
Specify the
class Trans giving details of the constructor(), void fillarray(), void
transpose() and void display(). Define a main() function to create an object and call the functions
accordingly to enable the task.
A class SortAlpha has been defined to sort the words in the sentence in alphabetical order. Example: Input: THE SKY IS BLUE
Output: BLUE IS SKY THE
Some of the members of the class are given below:
Data members/instance variable:
sent : to store a sentence
n : integer to store the number of words in a sentence
SortAlpha() : default constructor to initialise data members with legal initial value
void acceptsent() : to accept a sentence in UPPER CASE
void sort(SortAlpha P) : sorts the words of the sentence of object P in alphabetical
order and stores the sorted sentence in the current object
void display() : display the original sentence
along with the sorted sentence by invoking the method sort()
Specify the class SortAlpha giving details of the constructor(), void acceptsent(), void sort(SortAlpha) and
void display(). Define a main()
function to create an object and call the functions accordingly to enable
the task.
 |
Answer any two questions.
Each
program should be written in such a way that it
clearly depicts the logic of the problem stepwise.
This can be achieved by using comments in the program and mnemonic names
or pseudo codes for algorithms. The programs must be written in Java and the algorithms must be written in general/standard form, wherever required/
specified.
(Flowcharts are not required.)
Question 9
A double ended queue is a linear data structure which enables the user to add and remove integers from either ends i.e., from front or rear.
The details of the class deQueue are given below:
Class name : deQueue
Data members/instance variable:
Qrr[] : array to hold integer elements
lim : maximum capacity of the dequeue
front : to point the index of the front end
rear : to point the index of the rear end
deQueue(int I) : constructor to initialise lim = 1, front = 0 and rear = 0
void add Front(int v) : to add integers in the dequeue at the front end if possible, otherwise display the message “OVERFLOW FROM FRONT”
void add Rear(int v) : to add integers in the dequeue at the rear end if possible, otherwise display the message “OVERFLOW FROM REAR”
int popFront() : removes and returns the integers from the front end of the dequeue if any, else returns-999
int popRear() : removes and returns the integers from the rear end of the dequeue if any, else returns-999
void show() : displays the elements of the dequeue
(i)
Specify the class deQueue
giving details of the functions void
addFront(int) and int popFront().
Assume that the other functions have
been defined. 4
(ii) Differentiate between a stack and a queue. 1
A super class Demand has been defined to store the details of the demands for a product. Define a subclass
Supply which contains the production and supply details
of the products. 5
The details of the members of both the classes are given below:
Data members/instance variable:
pid : string to store the product ID
pname : string to store the product name
pdemand : integer to store the quantity demanded for the product
Demand(...) : parameterised constructor to assign values to the data members
void display() : to display the details of the product
Data members/instance variables:
pproduced : integer to store the quantity of the product produced
prate : to store the cost per unit of the product in decimal
Supply(...) : parameterised constructor to assign values to the data members of both the classes
double calculation() : returns the difference between the amount of demand (rate × demand) and the amount produced (rate × produced)
void display() : to
display the details
of the product and the difference in amount of demand and amount of supply
by invoking the method calculation()
Assume that the super class Demand has been defined. Using the concept to inheritance, specify the class Supply
giving the details of the constructor(. ), double calculation() and void display(). The
super class, main function and algorithm need NOT be written.
(i)
A linked list is formed from the objects of the class given below: 2
Class Node
{
double sal;
Node next;
}
Write and Algorithm OR a Method to add a node at the end of an existing linked list. The method declaration is as follows:
(ii)
Answer the following
questions from the diagram of a Binary Tree given below:
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(a) Write the pre-order traversal of the above
tree structure. |
1 |
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(b) Name the
parent of the
nodes D and
B. |
1 |
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(c) State the level of nodes E and F when the root is at level
0. |
1 |
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