10to2.js

function transform(input) {
  var result = [0];
  for ( var i = 0; i < input; i++ ) {
      up(result);
  }

  return result.reverse();
}

function up(array) {
  array[0]++;
  for ( var i = 0; i < array.length; i++ ) {
      if ( array[i] == 2 ) {
          array[i] = 0;
          if ( array[i+1] ) {
              array[i+1]++;
          }else {
              array[i+1] = 1;
          }
      } else {
          return;
      }
  }
}

transform(8); // [1, 0, 0, 0];
transform(20); // [1, 0, 1, 0, 0];
transform(41); // [1, 0, 1, 0, 0, 1];
transform(65); // [1, 0, 0, 0, 0, 0, 1];

// done in 0.078 seconds