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 [ ].

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PART I

Question1:

1. Convert the following sum of product expression into its corresponding POS [1]

F(A,B,C)=A’.B’.C’+A’.B’.C+A’.B.C+A.B’.C

1. Show that AB+(AC)’+AB’C(AB+C) is always 1.                 [1]
2. Simplify expression AB’CD’+AB’CD+ABCD’+ABCD                 [1]
3. Convert the following into canonical SOP form (X’Y)’.(X’Z’)’                 [1]
4. Find the complement of,F(A,B,C,D)=(A+((B+C).(B’+D’))) [1]

Question 2:

1. Draw the logic gate diagram and truth table for XOR gate. [2]
2. Name the Universal gates ,Explain with truth table And Diagram                 [2]
3. Prove that (x.y)’=x’+y’ using truth table                 [2]
4. State the two idempotent laws of Boolean algebra. Verify any one.                 [2]
5. Draw the logic gate diagram for the following function using NOR gates only.                 [2]

F(A,B,C)=A’B+AB’+C

Question 3                                                                                                                                           [5]

The following function comb() and combi() are a part of some class. Give the output when the combi() is called.

Show the dry run/working.

void combi()

{

for(int i=0; i<5; i++)

{

for(int j=0;j<i+1; j++)

System.out.print(“ “+comb(i,j));

System.out.println();

}

}

long comb(int n, int k)

{

long c=1;

for(int i=1;i<=k;i++,n–)

c=c*n/i;

return c;

}

PART II

Attempt any two questions from Section-A, two from Section-B and two from Section-C

Section A

Question 4

(a) Given the Boolean function:                                                                                                                                     [5]

F ( P, Q, R, S ) = ∑  ( 0, 1, 3, 4, 5, 6, 7, 9, 10, 11, 13, 15 )

Use Karnaugh’s map to reduce the function F, using the SOP form. Draw a logic gate diagram for the reduced SOP form. You may use gates with more than two inputs. Assume that the variable and their complements are available as inputs.

(b) Given G(A,B,C,D)= (A+B+C+D) (A+B+C+D’) (A+B+C’+D’) (A+B+C’+D) (A+B’+C+D’) (A+B’+C’+D’) (A’+B+C+D) (A’+B+C’+D)

1. i) Reduce the above expression by using 4 variable Karnaugh map, showing the various groups (i.e.octal, quads and pairs). [4]
2. ii) Draw the logic gate diagram for the reduced expression. Assume that the variables and their complements are available as inputs. [1]

Question 5.

• What is Full adder? Write the SOP expressions for sum and carry. Simplify the expressions algebraically using Boolean algebra.                                 [5]
• Draw the truth table and logic circuit diagram for a Hexadecimal to Binary encoder.                 [5]

Question 6.

• Write the equivalent Boolean expression for the propositions F=X→Y and F=X↔Y.                 [2]
• Reduce the following Boolean expressions to the simplest form:                 [3]

A.[B+C.(A.B+A.C)’]

(c)  Draw the truth table and logic circuit diagram for a 3×8 decoder. What is the difference between a

multiplexer and a decoder?                                                                                                                                                        [5]

Section B

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)
The programs must be written in Java.

Question 7.                                                                                                                                                                         [10]

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

Question 8.                                                                                                                                                                                        [10]

 A class RecFact defines a recursive function to find the factorial of a number. The details of the class are given below: Class name : RecFact Data members/instance variables n : stores the number whose factorial is required r : stores an integer Member functions RecFact( ) : default constructor void readnum( ) :    to enter values for ‘n’ and ‘r’ int factorial(int) :    returns the factorial of the number using the recursive               technique. void factseries() :    to calculate and display the value of n!+(r-2)! ( n − r)!

Specify the class RecFact giving the details of the constructor and member functions void readnum( ), int factorial(int) and void factseries( ). Also define the main function to create an object and call methods accordingly to enable the task.

Question 9.                                                                                                                                              [10]

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/instance variables N stores an integer number Member functions: Perfect( ) default constructor Perfect(int) parameterized constructor to assign a 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 equal to 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.

Section C

Each program 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 comments in the program and mnemonic names or pseudo codes for algorithms. The program must be written in Java and the algorithms must be written in general/standard form, wherever required/ specified. (Flowcharts are not required.)
Question 10                                                                                                                            [5]

A class OctaDeci has been defined to convert an Octal number into its equivalent Decimal number. Some of the members of the class are given below:

Data members                  :

dec                                         :               integer to store decimal number.

N                                             :               integer octal to be converted to its decimal form.

Member functions                          :

void getOctal()  :               to accept Octal integer N.

void recursiveDec(int):  to find the decimal equivalent of the octal number stored in N and store

in dec using Recursive Technique.

void putdata()                   :               to display the octal number ‘N’ and its decimal equivalent.

Specify the class OctaDeci giving details of constructor and functions. You do not need to write the main function.

Question 11.                                                                                                                                 [5]

A class Revstr defines a recursive function to reverse a string and check whether it is a palindrome. The details of the class are given below:

Class name   :  Revstr

Data members Str    :  stores the string.

Revst    :  stores the reverse of the string.

Member functions void getStr()   :  to accept the string.

void recReverse(int)  :  to reverse the string using recursive technique.

void check()   :  to display the original string, its reverse and whether  the string is a palindrome or not.

Specify the class Revstr  giving details of the functions void getStr(), void recReverse(int) and void check(). The main function need not be written.

Question 12.                                                                                                                                                     [5]

Draw a truth table with a three input combination which outputs 1 if there are odd number of 0’s. Also derive an SOP expression using  K map.