**Question 1**

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 Karnaugh map. [5]

**Question 2 [5]**

A government institution intends to award a medal to a person who qualifies any one of the following criteria:

The person should have been an Indian citizen and had lost his/her life in a war but has not completed 25 years of service.

OR

The person must be an Indian citizen and has served the nation for a continuous period of 25 years or more but has not lost his/her life in a war.

OR

The person is not an Indian citizen but has taken active part in activities for the upliftment of the nation.

**The inputs are: INPUTS**

A The person is/was an Indian citizen

B Has a continuous service of more than 25 years

C Lost his/her life in a war

D Taken part in activities for upliftment of the nation

**Output**

X Denotes eligible for medal [ 1 indicates YES ad 0 indicates NO in all cases]

a) Draw the truth table for the inputs and outputs given above and write the POS expression for X(A,B,C,D)..

b) Reduce X(A,B,C,D) using Karnaugh’s map.

Draw the logic gate diagram for the reduced POS expression for X(A,B,C,D) using AND and OR gate. You may use gates with two or more inputs. Assume that the variable and their complements are available as inputs.

**Question 3**

a) Given the Boolean function F( A, B, C, D) = π (5, 7, 8, 10,12, 14, 15)

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 the Boolean function : F(A,B,C,D ) = ∑(0,2,3,6,8,10,11,14,15)

i) Reduce the above expression by using 4-variable K-map, showing the various groups (i.e. octal, quads and pairs). [ 4 ]

ii) Draw the logic gate diagram of the reduced expression. Assume that the variables and their complements are available as inputs. [ 1 ]

**Question 4. [10]**

An emirp number is a number which is prime backwards and forwards. Example: 13 and 31 are both prime numbers. Thus 13 is an emirp number.

Design a class Emirp to check if a given number is Emirp number or nt. Some of the members of the class are given below:

**Class Name : Emirp**

** Data Members**

n : stores the number

rev : stores the reverse of the number

f : stores the divisor

**Member functions**

Emirp(int nn) : to assign n=nn, rev=0, and f=2

int isprime(int x) : check if the number is prime using the recursive technique and return 1 if prime otherwise return 0.

void isEmirp() : reverse the given number and check if both the original number and the reverse number are prime, by invoking the function isprime(int) and display the result with an appropriate message.

Specify the class Emirp giving details of the constructor(int), int isprime(int) and void isEmirp(). Define the main function to create an object and call the methods to check for Emirp number.

[ 10]