public class BinaryCalculator
{
	/*
	 * Main method scans input from text and prints out the
	 * expected results.
	 */
  

	/*
	 * Converts a binary number to base 10 number
	 */
	private static String decimalConversion(String binaryNumber)
    {
    	String decimal = "0";
    	String[] temp = new String[2];;

    	for(int i = binaryNumber.length() - 1; i >= 0; i--)
    	{
    		if(binaryNumber.charAt(i) == '1')
    		{
    			temp[0] = decimal;
    			temp[1] = split(binaryNumber.length() - i);

    			decimal = addDecimal(temp);
    		}
    	}

		return decimal;
    }

	/*
	 * Splits the decimal conversion into smaller segments
	 * to prevent an overflow
	 */
    private static String split(int index)
    {
    	if(index < 20)
    		return decimalValueOfBit(index) + "";

    	int segment = index/2;

    	return multiplyDecimal(split(segment), split(index - segment));
    }

    /*
     * Returns the base 10 value of a single bit according to its index
     */
    private static int decimalValueOfBit(int length)
    {
    	if(length == 0)
    		return 0;

		if(length == 1)
    		return 1;
    	else
	    	return decimalValueOfBit(length - 1) * 2;
    }

	/*
	 * Multiplies the smaller segments to get the base 10 value of the
	 * binary number.
	 */
    private static String multiplyDecimal(String number1, String number2)
    {
    	String productRow = "";
    	String moveDownOne = "";
    	String tempProductColumn = "";

    	int carryNumber = 0;
    	int a, b, productColumn;
    	int differenceInLength = 0;

    	String[] toBeAdded = new String[number2.length()];

    	for(int i = number2.length() - 1; i >= 0; i--)
    	{
    		productRow = moveDownOne + "";

    		for(int j = number1.length() - 1; j >= 0; j--)
    		{
    			a = Integer.parseInt(number2.charAt(i) + "");
    			b = Integer.parseInt(number1.charAt(j) + "");
    			productColumn = a * b;

    			if(carryNumber > 0)
    			{
    				productColumn = productColumn + carryNumber;
    			}

    			tempProductColumn = productColumn + "";

    			productRow = tempProductColumn.charAt(tempProductColumn.length() - 1) + productRow;

    			if(tempProductColumn.length() == 2)
    				carryNumber = Integer.parseInt(tempProductColumn.charAt(0) + "");
    			else
    				carryNumber = 0;
    		}
			if(carryNumber > 0)
			{
				productRow = carryNumber + productRow;
				carryNumber = 0;
			}

    		for(int j = 0; j < (number2.length() - 1) - i; j++)
    		{
    			moveDownOne += 0;
    		}

    		toBeAdded[i] = productRow + moveDownOne;
    		moveDownOne = "";
    	}

    	return addDecimal(toBeAdded);
    }

	/*
	 * The second step in long multiplication, addition.
	 */
    private static String addDecimal(String[] toBeAdded)
    {
    	int a, b, sum;
    	int carryNumber = 0;
    	int differenceInLength = 0;
    	String tempSum;
    	String decimalSum = "";

    	for(int i = 1; i < toBeAdded.length; i++)
    	{
    		if(toBeAdded[i - 1].length() != toBeAdded[i].length())
    		{
    			if(toBeAdded[i - 1].length() > toBeAdded[i].length())
    			{
    				differenceInLength = toBeAdded[i - 1].length() - toBeAdded[i].length();
    				toBeAdded[i] = shareItemLength(differenceInLength) + toBeAdded[i];
    			}
    			else if(toBeAdded[i - 1].length() < toBeAdded[i].length())
    			{
    				differenceInLength = toBeAdded[i].length() - toBeAdded[i - 1].length();
    				toBeAdded[i - 1] = shareItemLength(differenceInLength) + toBeAdded[i - 1];
    			}
    		}

    		for(int j = toBeAdded[i].length() - 1; j >= 0; j--)
    		{
    			a = Integer.parseInt(toBeAdded[i - 1].charAt(j) + "");
    			b = Integer.parseInt(toBeAdded[i].charAt(j) + "");
    			sum = a + b;

    			if(carryNumber > 0)
    			{
					sum += carryNumber;
    			}

    			tempSum = sum + "";
    			decimalSum = tempSum.charAt(tempSum.length() - 1) + decimalSum;

    			if(tempSum.length() == 2)
    				carryNumber = Integer.parseInt(tempSum.charAt(0) + "");
    			else
    				carryNumber = 0;
    		}

    		toBeAdded[i] = decimalSum;
    		decimalSum = "";
    	}

		if(carryNumber > 0)
			toBeAdded[toBeAdded.length - 1] = carryNumber + toBeAdded[toBeAdded.length - 1];

    	decimalSum = toBeAdded[toBeAdded.length - 1];

    	return decimalSum;
    }

	/*
	 * Converts a decimal integer into a binary number.
	 */
    private static String binaryConversion(int decimal)
    {
    	String backwardBinary = "";
    	int remainder;

		// the remainders form the binary number backwards
    	while(decimal > 0)
    	{
    		remainder = decimal % 2;
    		backwardBinary += remainder + "";

    		decimal = decimal / 2;
    	}

    	String binary = "";
    	int j = backwardBinary.length() - 1;

		// flips the backward binary number to the correct order
    	for(int i = 0; i < backwardBinary.length(); i++)
    	{
    		binary += backwardBinary.charAt(j);
    		j--;
    	}

    	return binary;
    }


	/*
	 * Converts a binary number into a hexadecimal value.
	 */
    private static String hexadecimalConversion(String binary)
    {
		String singleHex = "";
		String hexadecimalCode = "";
		int decimal;
		int count = 1;

		for(int i = binary.length(); i > 0; i--)
		{
			if(count % FOUR_BIT_LENGTH == 0)
			{
				singleHex = binary.charAt(i - 1) + singleHex;

				decimal = hexaHelper(singleHex);

				hexadecimalCode = decimalToHexadecimal(decimal) + hexadecimalCode;

				singleHex = ""; // resets singleHex
			}
			else
				singleHex = binary.charAt(i - 1) + singleHex;

			count++;
		}

		// since count starts at 1
		count = count - 1;

		if(count % FOUR_BIT_LENGTH != 0)
		{
			decimal = Integer.parseInt(decimalConversion(singleHex));
			hexadecimalCode = decimalToHexadecimal(decimal) + hexadecimalCode;
		}

		return hexadecimalCode;
    }

	/*
	 	Accepts a decimal value from hexadecimalConversion() method to
	 	be used as an index for the hexAlphabet, and then returns
	 	that character.
	*/
    private static String decimalToHexadecimal(int decimal)
    {
    	String hexAlphabet = "0123456789ABCDEF";
    	return hexAlphabet.charAt(decimal) + "";
    }

    private static final int FOUR_BIT_LENGTH = 4;
    private static final int MAX_LENGTH = 20;
}