In Java, how to get positions of ones in reversed binary form of an integer?

You can just test the bits without turning the integer into a string:

List<Integer> onePositions(int input) {
  List<Integer> onePositions = new ArrayList<>();
  for (int bit = 0; bit < 32; bit++) {
    if (input & (1 << bit) != 0) {
      onePositions.add(bit + 1); // One-based, for better or worse.
    }
  }
  return onePositions;
}

Bits are usually counted from right to left, the rightmost bit being bit 0. The operation 1 << bit gives you an int whose bit numbered bit is set to 1 (and the rest to 0). Then use & (binary and) to check if this bit is set in the input, and if so, record the position in the output array.

Just check the bits in turn:

List<Integer> bits(int num) {
  List<Integer> setBits = new ArrayList<>();
  for (int i = 1; num != 0; ++i, num >>>= 1) {
    if ((num & 1) != 0) setBits.add(i);
  }
  return setBits;
}

Online Demo

6 [2, 3]
7 [1, 2, 3]
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