Question

Question 3 - Write a java program named BinaryConversion that will convert base 2 numbers to base 10 numbers.

This complete question is already in chegg study! I want to know the answer for that question?

Answer 1

Algorithm: To convert a base2 number to base10 we need to start from the left of the binary number with indexing zero and calculate the cumulative sum of power(2,index)*valueAtIndex .

Lets see an example...

binaryNumber = 10101010

To convert it into decimal we will follow the above algorithm. In the left most side power(2,index) will be power(2,0) which will be 1 and then it will get multiplied by 0 which is value at that index. Have a look at the at the below expantion.

(10101010)₂ = (1 × 2⁷) + (0 × 2⁶) + (1 × 2⁵) + (0 × 2⁴) + (1 × 2³) + (0 × 2²) + (1 × 2¹) + (0 × 2⁰) = (170)₁₀

Have a look at the below code. I have put comments wherever required for better understanding.

import java.lang.Math; 

class Main {
  // create the function
  public static int base10(int binary){
    // variable to store the result
    int result = 0;
    // variable to store power
    int power = 0;
    
    while (binary>0){
      // find the left most element
      int remainder = binary%10;
      binary /= 10;
      // calculate sum
      result+=(Math.pow(2,power)*remainder);
      // increment the power
      power+=1;

    }
    // return the result
    return result;
  }
  public static void main(String[] args) {
    System.out.println(base10(10101010));
  }
}

Happy Learning!