Floating Point Playground 5 points Computer arithmetic may not behave the same a

Question

Floating Point Playground 5 points Computer arithmetic may not behave the same as we would expect from real arithmetic. For example, if we perform the operation: x= 1 + 10-20 our computer will return the value of x as "1". For this exercise, you will be given a variable a (a random number). Add successively smaller powers of 10 to this number (i.e, compute a 10, a +10, a+ 10, etc.) until the result is unchanged by the addition. Save the last power of 10 that made an impact to the variable k.(.e. if a 10, was different from the original value but a10 produced no change, you would want k to have the value "-5". Be sure to write code that does this in a systematic manner, because the value of a will be different each time. Answer* Press F9 to toggle full-screen mode. Set editor mode in user profile

Explanation / Answer

%Matlab code

function k = floatingPointPlayGround(a)

    k = 1;
    tenPower = 1.0;
    while (true)
        result = a + (tenPower/10.0);
        if (result == a)
            break;
        end  
        k++;
    end
end

% calling the above function
k = floatingPointPlayGround(1.0)

------------------------------------------------------------------
// Since you didn't specify the language, I wrote the java code too

public class NewClass {

   public static int floatingPointPlay(float a) {
      
       int k = 0;
       float tenPower = 1.0f;
       while (true) {
           float result = a + (tenPower/10.0f);
           if (result == a) {
               break;
           }
           k++;
       }
       return k;
   }
  
    public static void main(String [] args) {
       System.out.println(floatingPointPlay(1.0f));
    }
}

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