convertNum2Binary :: Int -> String
convertNum2Binary num
  | num <= 1  = show num
  | otherwise = convertNum2Binary (num `div` 2) ++ show (num `mod` 2)

convertFraction2Binary :: Float -> String
convertFraction2Binary num
  | (num < 0) || (num >= 1) = "Invalid Input"
  | otherwise               = "." ++ convertFraction2BinaryHelper num ""

convertFraction2BinaryHelper :: Float -> String -> String
convertFraction2BinaryHelper num result
  | length result >= 23 = result
  | (2 * num) == 1      = result ++ "1"
  | (2 * num) < 1       = convertFraction2BinaryHelper (2 * num) (result ++ "0")
  | otherwise           = convertFraction2BinaryHelper (2 * num - 1.0) (result ++ "1")


-- convertNum2Binary 100
-- convertFraction2Binary 0.375
-- convertFraction2Binary 0.8