Problem

As you may know, computers work on the binary system. In this system, numbers are written using only 0s and 1s. In this question, you’ll write a program to convert binary numbers to normal (decimal) numbers.

How are all numbers represented in 0s and 1s?

• Instead of having digits 0,1,...,9, in binary, we only have digits 0 and 1.
• So zero is 0, and the next number is represented by 1, but after that, we have no digit 2, so we have to represent the next number in the same way we do after we go past 9 in the decimal system: by 10.
• We continue in this way: 3 in binary is 11.
• Now what about 4? We can’t write 4 as 12 (because we only have 1 and 0 to work with, not 2). So we put a zero in the last position, and carry the 1. This would give 20, but again, we don’t have a digit 2, so we again carry the 1 and get 100 as the binary representation of 4.

Here are the first few numbers written in both decimal (normal) notation and binary:

Suppose we have a binary number (a sequence of zeroes and ones) and we want to convert it to a decimal number. To do this, we multiply the digit (0 or 1) in each position of the number by an increasing power of two the further we move left. So the value of the binary number 1011001 is

1 * 2^6 + 0 * 2^5 + 1 * 2^4 + 1 * 2^3 + 0 * 2^2 + 0 * 2^1 + 1 * 2^0 = 89

Program Specifications

• Write a program that takes input as an integer, interprets it as a binary number, and prints out its value as a decimal number.
• Get input using Scanner.
• Use integer division and remainder to extract digits from the input binary number.
• Assume the user only inputs numbers with digits 0 and 1.
• Use a loop so the user can continue to input binary numbers until they input -1 , then exit.
• Here is a sample run of the program:

  Enter a binary number:1001010
  1001010 in decimal is 74.
  Enter a binary number:1001111
  1001111 in decimal is 79.
  Enter a binary number:10000111
  10000111 in decimal is 135.
  Enter a binary number:-1
  Programmed by [your name here].
  End of processing.
  

Output

Use System.out for output. Follow the format of the output shown above.

Hand-in

Save your file using the naming conventions described in the beginning of the assignment. Upload your file using the web-based hand-in tool. Submit three sets of data using the following input:

1. 1000011
2. 1011
3. A binary number of your choice

You may notice that your program fails for large numbers. That's because of integer overflow. If you would like to get your program to work for larger binary numbers, replace int with long in your program (including using the Scanner method nextLong()).

Solution

Code

Solution Code

import java.util.Scanner;

/**
 * A2Q2 -
 *
 * COMP 010 Section A00
 * INSTRUCTOR
 * ASSIGNMENT 2, Question 2
 * @author 1010
 * @version 2010-Oct-18
 *
 * PURPOSE: calculates the decimal version of a binary number.
 */
public class A2Q2{


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

		long binaryNumber, copyOfBinNum;	// input from the user.
		int decimalNumber; 		 	// output value.
		final int BASE = 2;			// binary base.
		int currDigit, currPower;		// values used in loops.

		// get input from the user.
		System.out.print("Enter a binary number:");
		binaryNumber = kbd.nextLong();

		// keep looping until -1 is encountered.
		while (binaryNumber != -1) {

			// reset values to 0, use copyOfBinNum for calculations.
			decimalNumber = 0;
			currPower = 0;
			copyOfBinNum = binaryNumber;

			// keep looping until all digits of copyOfBinNum are removed.
			while (copyOfBinNum > 0) {

				// get last digit and strip it off copyOfBinNum
				currDigit = (int) copyOfBinNum % 10;
				copyOfBinNum /= 10;

				// add to the running total if the digit is one
				if (currDigit == 1) {
					decimalNumber += Math.pow(BASE,currPower);
				}

				// increment the power of two for next loop.
				currPower++;
			}

			// output the right decimal value.
			System.out.println(binaryNumber + " in decimal is " + decimalNumber + ".");

			// get ready for next iteration of the loop.
			System.out.print("Enter a binary number:");
			binaryNumber=kbd.nextLong();
		}
		System.out.println("Programmed by [your name here].");
		System.out.println("End of processing.");


	}

}