CS 1401 Assignment #5, Solutions

Date Assigned: Monday, February 19, or Tuesday, February 20, 2007.

Due Date: Monday, February 26, or Tuesday, February 27, 2007, before the beginning of your lab section.

Objective: The main objective of this assignment is to practice using loops.

Programming assignment: It is well known that computers use a binary system to represent integers. In some computer applications, it is also useful to use octal code (base 8), and hexadecimal (hex) code (base 16). In the past, some computers have used ternary code (base 3) as well. The following algorithm is used to convert a decimal positive integer n into the binary form: you divide n by 2, keep a remainder. Divide the result by 2, keep a remainder, etc. until we get 0. The remainders, when read bottom to top, form the desired binary number.

Similarly, you can convert a decimal positive integer n into the hex form: you divide n by 16, keep a remainder. Remainders 10, 11, 12, 13, 14, and 15 are described as, correspondingly, A, B, C, D, E, and F. Divide the result by 16, keep a remainder, etc. until we get 0. The remainders, when read bottom to top, form the desired hex number.

Write a program that, given an integer, uses the above algorithm to return a hex representation of this number (as a string).

Example of a binary code: for n = 13, we have

13 / 2 = 6 rem 1
 6 / 2 = 3 rem 0
 3 / 2 = 1 rem 1
 1 / 2 = 0 rem 1
When we read the remainders from bottom to top, we get 1101, which is exactly the binary representation of 13 -- since 1 * 8 + 1 * 4 + 0 * 2 + 1 * 1 = 8 + 4 + 1 = 13.

Example of a hex code: for n = 92, we have

92 / 16 = 5 rem 12 which is C
 5 / 16 = 0 rem 5
When we read the remainders from bottom to top, we get 5C, which is exactly the binary representation of 92 -- since 5 * 16 + 12 = 80 + 12 = 92.

Hint: originally, the division-result is 92, the string-so-far is empty. Within the loop, you divide the division-result by 16, compute the remainder, and add the corresponding one-character string ("0", "1", ..., "9", "A", ..., "F") to the left of the string-so-far.


Solution:

import java.util.*;

public static void main(String [] args){
  //designing a tool to read from a keyboard
  Scanner keyboard = new Scanner(System.in);

  //asking the user to input a number and reading this number
  System.out.println("Please enter a positive decimal integer");
  int decimal = keyboard.nextInt();

  //declaration and initialization of variables
  String string_so_far = "";
  int remainder;
  String corresponding_symbol = "";
  int division_result = decimal;

  while (division_result > 0){
    //dividing by 16 and computing the remainder
    remainder = division_result % 16;
    division_result /= 16;

    //forming a symbol based on the remainder;
    if (remainder < 10)
      {corresponding_symbol = "" + remainder;}
    else{
      if (remainder == 10) corresponding_symbol = "A";
      if (remainder == 11) corresponding_symbol = "B";
      if (remainder == 12) corresponding_symbol = "C";
      if (remainder == 13) corresponding_symbol = "D";
      if (remainder == 14) corresponding_symbol = "E";
      if (remainder == 15) corresponding_symbol = "F";
    }
     //adding the symbol in front of the string-so-far
     string_so_far = corresponding_symbol + string_so_far;
  }

  //printing the result of conversion
  System.out.println("The hex code of a decimal number " + decimal +
    " is " + string_so_far);
}

For extra credit: write a program that transforms hex numbers back into decimal. Main idea:

Example: for the string 5C,

Since the remaining string is empty, the value-so-far (92) is returned as the result.


Solution:

public static void main(String [] args){
  //designing a tool to read from a keyboard
  Scanner keyboard = new Scanner(System.in);

  //asking the user to input a number and reading this number
  System.out.println("Please enter a number in hex code");
  String hex = keyboard.next();

  //declaration and initialization of variables
  String remaining_string = hex;
  int value_so_far = 0;
  char symbol;
  int corresponding_value;

  while (remaining_string.length() > 0){
    //separating the first (in Java, 0th) character of the string
    symbol = remaining_string.charAt(0);
    remaining_string =
      remaining_string.substring(1, remaining_string.length());

    //forming a value corresponding to the symbol
    if (symbol == 'A')
      {corresponding_value = 10;}
    else if (symbol == 'B')
      {corresponding_value = 11;}
    else if (symbol == 'C')
      {corresponding_value = 12;}
    else if (symbol == 'D')
      {corresponding_value = 13;}
    else if (symbol == 'E')
      {corresponding_value = 14;}
    else if (symbol == 'F')
      {corresponding_value = 15;}
    else
      {corresponding_value = symbol - '0';}

    //updating the value-so-far
    value_so_far = value_so_far * 16 + corresponding_value;
  }

  //printing the result of conversion
  System.out.println("The decimal representation of a hex number " +
    hex + " is " + value_so_far);
}


}

Homework assignment: on a separate sheet of paper, solve Ex. 6, 10, 18, and 24 at the end of Chapter 5.

Deliverables: as instructed by your TA.