naive.js

let countBits = (x) => x.toString(2).replace(/0/g, "").length;
let sortBits = (x) => [...x].sort((a, b) => countBits(a) - countBits(b));

module.exports.sortBits = sortBits;

pretend_that_i_have_cs_degree.js

// this one is much faster than the naive solution, but it does not work
// for numbers bigger than 32 bits, i.e. 0b11111111111111111111111111111111
// or 4294967295 is the biggest number this function can correctly work with
let countBits = (i) => {
  let count = 0;
  i = i - ((i >> 1) & 0x55555555);
  i = (i & 0x33333333) + ((i >> 2) & 0x33333333);
  i = (i + (i >> 4)) & 0x0f0f0f0f;
  i = i + (i >> 8);
  i = i + (i >> 16);
  count += i & 0x3f;
  return count;
};
let sortBits = (x) => [...x].sort((a, b) => countBits(a) - countBits(b));

module.exports.sortBits = sortBits;

test_perf.js

const sortBits0 = require("./naive").sortBits;
const sortBits1 = require("./pretend_that_i_have_cs_degree").sortBits;

const iterations = 1000000;

console.time("Function #2");
for (let i = 0; i < iterations; i++) {
  sortBits1([4124515, 1231251, 123, 1412, 56134, 222]);
}
console.timeEnd("Function #2");

console.time("Function #1");
for (let i = 0; i < iterations; i++) {
  sortBits0([4124515, 1231251, 123, 1412, 56134, 222]);
}
console.timeEnd("Function #1");