How do I convert the float value of 12345.12346f to a String of binary values, i.e. "0011010101010101", and vice-versa?
I'm not sure it is what you want, but here's a solution to have the binary representation of the IEEE 754 floating-point "double format" bit layout for a float (it is basically the memory representation of a float) :
int intBits = Float.floatToIntBits(yourFloat); 
String binary = Integer.toBinaryString(intBits);
For the reverse procedure :
int intBits = Integer.parseInt(myString, 2);
float myFloat = Float.intBitsToFloat(intBits);
                        Working sample:
class F { 
  public static void main( String ... args ) { 
    System.out.println(
          Integer.toBinaryString( 
             Float.floatToIntBits(12345.12346f)
          ) 
     );
  }
}
Output:
1000110010000001110010001111110
                        For signed Floats, use Long or BigInteger to parse the string. Casting by int causes the digit at first of 32 bits be intepreted as sign digit. procedure :
int intBits = Float.floatToIntBits(yourFloat); 
String binary = Integer.toBinaryString(intBits);
reverse procedure :
int intBits = new BigInteger(myString, 2).intValue();
// int intBits = (int) Long.parseLong(myString, 2);
float myFloat = Float.intBitsToFloat(intBits);
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