Solved Board Paper For ICSE Class 12 Computer Science

(a) Truth table for the given Boolean statement:
A+A’B = A+B

Hence A+A’B = A+B

(b) AND Gate using NAND Gate:

OR Gate using NAND Gate:

(c) For the given code return value of the statements:

i) getHCF(45, 100) : 5

ii) getHCF(40, 72) : 8

(d) Compile time errors vs. Run time errors:

Compile time errors are the errors that can be found out at compile time like wrong syntax. Such errors do not let the program run at all.

However, the run time errors are those errors which may occur at run time and stops further execution of the program because of any unexpected condition arising at run time like division by zero, array out of bound etc.

(e) Increment operator is a unary operator applied in integers that increments the value of its operand by 1.
(i) Prefix increment operator (++i): It first increments the value of operand then uses its value in the expression or statement.
(ii) Postfix increment operator (i++): It first uses the value of operand in the expression and then increments it.

Circuit diagram for sum:

Circuit diagram for carry:

(b) Given function:

F(A, B, C, D) = ∑(0, 1, 4, 5, 7, 11, 13, 15)

K-Map for F:

Reduced F(A, B, C, D) = A’C’ + BD + ACD
Circuit diagram:

Sum = A B

Circuit diagram of the half adder:

Full adder is a logic circuit that adds three bits at a time. It can be derived from half adder by adding two bits using half adder and adding the third bit with the sum of first two bits using another half adder. Also by ORing carry of both these half adders we can derive the final carry.

Sum = (A B) C

Carry = AB + (AB)C
Circuit Diagram:

(b) Expression to reduce: PQ + (PR)’ + PQ’R(PQ + R)

= PQ + (PR)’ + PQ’RPQ + PQ’RR

Distributive Law: X(Y+Z) = XY+XZ

= PQ + (PR)’ + PPQQ’R + PQ’RR

Commutative Law: XY =YX

= PQ + (PR)’ + PP.0.R + PQ’RR

Complementarity Law: XX’ = 0

= PQ + (PR)’ + 0 + PQ’RR

Property of 0: 0.X = 0

= PQ + (PR)’ + PQ’R

Indempotence Law: X.X =X

= PQ + P’+R’ + PQ’R

DeMorgan’s second Theorem (XY)’ = X’ +Y’

= P’+PQ + R’ + PQ’R

Commutative Law: X+Y =Y+X

= P’+Q + R’ + PQ’R

Third distributive law: X+X’Y= X+Y

= P’+Q + R’ + PQ’R

= P’+ R’ + Q+Q’PR

Commutative Law

= P’+ R’ + Q+PR

Third distributive law: X+X’Y= X+Y

= P’+ Q + R’ +RP

= P’+ Q + R’ + P

Third distributive law: X+X’Y= X+Y

= P + P’+ Q + R’

= 1 + Q + R’

Complementarity Law: X + X’ = 1

= 1

Property of 1: 1+ X = 1

Thus, PQ + (PR)’ + PQ’R(PQ + R) = 1

import java.io.*;

public class Special

{
int n;

Special() throws IOException
{

InputStreamReader read = new InputStreamReader(System.in);

BufferedReader in = new BufferedReader(read);
System.out.println("Enter the number");
n = Integer.parseInt(in.readLine());
}
boolean isSpecial()
{
int temp = n;
int sp_sum = 0;
while(temp > 0)
{
sp_sum = sp_sum + factorial(temp%10);
temp = temp/10;
}
if(sp_sum == n)
{
return true;
}
else

{

return false;

}

}
public int factorial(int f)

{

if(f

{
int length;
int height;
rectangle(int l, int h)
{
length = l;
height = h;
}
int surfaceArea()
{
return (length* height);
}
}
Class cube:
public class Cube extends rectangle
{
int width;
Cube(int l, int h, int w)
{
super(l, h);
width = w;
}
int surfaceArea()
{
return (super.surfaceArea() * width);
}
}

public class Salary
{
int basic;
Salary() throws IOException
{
InputStreamReader read = new InputStreamReader(System.in);

BufferedReader in = new BufferedReader(read);
System.out.print("Enter the basic salary: ");
basic = Integer.parseInt(in.readLine());
}

int cal()

{

int DA = 10*basic/100;

int HRA = 15*basic/100;

int totalSalary = DA + HRA + basic;

int PF = 8%totalSalary/100;

int CTC = PF + totalSalary;

return CTC;

}

}
Class Employee that inherits salary and implements main method:

public class Employee extends Salary

{
String empName;
int empId;
String empDg;
Employee(String n, int i, String d)throws Exception
{
super();
empName = n;
empId = i;
empDg = d;
}
public static void main()throws Exception
{
Employee obj = new Employee("Akshya", 48, "Developer");
System.out.println("Total salary of "+obj.empName+" is :
"+obj.cal());

}

}
Output:

import java.util.Scanner;

public class Convert

{

String str;

String newStr;

int size;

Convert()

{

str = "";

size = 0;

newStr = "";

}

void setStr()

{

System.out.println("Enter the String : ");

Scanner in = new Scanner(System.in);

str = in.nextLine();

size = str.length();

}

char changeCase(char ch)

{

if(Character.isUpperCase(ch))

{

return Character.toLowerCase(ch);

}

else

{

return Character.toUpperCase(ch);

}

}

void nextChar(int n)

{

if(n == size)

return;

else

{

newStr = newStr+changeCase(str.charAt(n));

nextChar(++n);

}

}

void display()

{

System.out.println("String you entered is : "+str);

System.out.println("Converted String is : "+newStr);

}

public static void main()

{

Convert obj = new Convert();

obj.setStr();

obj.nextChar(0);

obj.display();

}

}

Ouput:

import java.util.Scanner;

public class TicketReq

{

int req[];

int Front;

int Rear;

int avail;

TicketReq()

{

req = new int[100];

Front = Rear = -1;

avail = 100;

}

int reqCount()

{

int tQu = 0;

if(Front == -1)

return 0;

for(int i = Front; i