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# Issue with float to binary

Greenhorn
Posts: 1
We need to convert Float to Binary and we are using the following APIs:
1) Float.floatToIntBits(<float>
2) Integer.toBinaryString(<intbits>

The usage is:
String <string> = Integer.toBinaryString(Float.floatToIntBits(<float>

For most cases we get the correct Binary String. However, when the float variable has value = 8 digit integers, we run into the following problem:

Problem: floatToIntBits Returns the SAME output for different Input values.

Example:

public class TestFloatToBinary
{
//Function to convert the float value to binary
public static void main(String args[])
{
float f1 = 17012219;
float f2 = 17012220;
float f3 = 17012221;
float f4 = 17012222;

String sBinary1 = Integer.toBinaryString(Float.floatToIntBits(f1));
String sBinary2 = Integer.toBinaryString(Float.floatToIntBits(f2));
String sBinary3 = Integer.toBinaryString(Float.floatToIntBits(f3));
String sBinary4 = Integer.toBinaryString(Float.floatToIntBits(f4));

System.out.println("float to intbits for f1 = " + Float.floatToIntBits(f1));
System.out.println("float to intbits for f2 = " + Float.floatToIntBits(f2));
System.out.println("float to intbits for f3 = " + Float.floatToIntBits(f3));
System.out.println("float to intbits for f4 = " + Float.floatToIntBits(f4));

System.out.println("Binary for f1 = " + sBinary1);
System.out.println("Binary for f2 = " + sBinary2);
System.out.println("Binary for f3 = " + sBinary3);
System.out.println("Binary for f4 = " + sBinary4);
}
}

-----------------------------------------------
Output:

C:\work\krishna\java>java TestFloatToBinary
float to intbits for f1 = 1266797310
float to intbits for f2 = 1266797310
float to intbits for f3 = 1266797310
float to intbits for f4 = 1266797311
Binary for f1 = 1001011100000011100101011111110
Binary for f2 = 1001011100000011100101011111110
Binary for f3 = 1001011100000011100101011111110
Binary for f4 = 1001011100000011100101011111111

As seen above, floatToIntBits and hence Integer.toBinaryString return the SAME value for Inputs 17012219, 17012220, 17012221.

What is the reason why this happens?

Are we missing something here??

Thank you.

Java Cowboy
Posts: 16084
88
You need to understand that floating point data types such as float and double do not have infinite precision.

You cannot store any number with an arbitrary number of digits and expect that it is stored with infinite precision.

The precision of a 32-bit IEEE 754 floating point number such as float in Java is about 5 or 6 decimal digits, so it's no surprise that numbers that differ beyond about the 5th digit only look the same in binary form.

IEEE Standard 754 Floating Point Numbers
IEEE floating-point standard (Wikipedia)
[ July 26, 2006: Message edited by: Jesper Young ]

Marshal
Posts: 62829
203
Apart from the precision problem, there is something else not right here. You start with positive numbers, and end up with a String starting with a 1.

If you count the bits printed, you find they only come to 32 if you use a negative number. So your "toBinaryString" is losing its leading zeroes.

author and iconoclast
Posts: 24203
43

Ranch Hand
Posts: 961
Another thing that may be important to take into account is that all NaN results will produce the same result using Double.doubleToLongBits(). In this case, to diferentiate a NaN from another you might consider using Double.doubleToRawLongBits()

Ranch Hand
Posts: 245
Because of limited precision of floating point representation, f1, f2 and f3 have same value.