Algorithm to convert real numbers decimal to binary

Question

Currently trying to write code that converts decimal floats to binary base form (I know BaseForm exists).

Currently I'm working with an example that takes 3.3 and converts it:

binary={}
x = Floor[3.3*2^8];
For[i = 0, i <= 9, i++,
  remainder = Mod[x, 2];
  x = Floor[x/2];
  AppendTo[binary, remainder];
  ];
Print[FromDigits[Reverse[binary]]]

Which gives: 1101001100

Obviously the answer should have a . between 11 and 01001100, but I'm not quite sure how to implement this. Does anyone have any ideas (so it would work with all examples, not just 3.3).

Thanks!

Answer 1

If you want just a string representing real num base2, extract the base-2 digits and base-2 exponent of the form {{digits},exponent} and then convert it to a string:

 myNum = 41.213;
    myB = RealDigits[myNum, 2]
    myBExp = myB[[2]]
    newFormat = 
     ToString@Row[myB[[1, 1 ;; myBExp]]] <> "." <> 
      ToString@Row[myB[[1, myBExp + 1 ;;]]]

Out[704]= {{1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1}, 6}

Out[706]= "101001.00110110100001110010101100000010000011000100101"