2. Let\'s consider the spacing between values in double precision. (a) For arbit

Question

2. Let's consider the spacing between values in double precision. (a) For arbitrary n, what is the distance from 2" to the smallest floating point number larger than 2n in the double-precision floating point standard? You can assume that 2n is not too small/large to be represented exactly in double precision. Express your answer in terms of machine epsilon. (b) Let x > 0 be arbitrary. Supposing that z can be represented exactly in double precision, use part (a) to determine the distance from a to the next largest number in double precision. (Hint: 3n e Z such that 2n 2n-+1..) Eatra credit: try to eapress your answer entirelgy in terms of x.

Explanation / Answer

public class minimum3 {

  

public static void main(String[] args) {

Scanner input = new Scanner(System.in );

  

int number1;

int number2;

int number3;

  

  

System.out.print( "Enter first number: ");

number1 = input.nextInt();

System.out.print( "Enter second number: ");

number2 = input.nextInt();

System.out.print( "Enter third number: ");

number3 = input.nextInt();

  

  

if ( number1 < number2 ) && ( number 1 < number3 )

System.out.printf( "Smallest number is: %d , number1);

if ( number2 < number3 ) && ( number 2 < number1 )

System.out.printf( "Smallest number is: %d , number2);

if ( number3 < number 2) && ( number 3 < number1 )

System.out.printf( "Smallest number is: %d , number3);

}

import java.util.Scanner;
public class Program4_JohnHuber {

public static void main(String[] args) {
Scanner input = new Scanner (System.in);

double total = 0;
//double numbers = 0;
int count = 1;
double largest = 0;
double smallest = Double.MAX_VALUE;
double average = 0;

System.out.print ("Please enter the grades, (Press enter when finished): ");
{
while (input.hasNextDouble()&& count<5)
{
double entered = input.nextDouble();
total = total + entered;
//count++;

//double average = 0;
if (count > 0)
{
average = total/count;
}
if (entered > largest)
{
largest = entered;
}
if (entered < smallest)
{
smallest = entered;
}
count++;
}

}
System.out.printf ("Your average grade is %3.2f, ", average);
System.out.printf ("Your highest grade is %3.2f ", largest);
System.out.printf ("Your lowest grade is %3.2f ", smallest);

}
}

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