<?php

$arr = array(
     1  => "a", 
     2  => "b", 
     4  => "c", 
     8  => "d",
     16 => "e", 
     32 => "f"
);

$filter = 101101;
$filter_arr = str_split($filter);
$new_arr = array();
$i = 0;
foreach ($arr as $key => $val) {
    if ($filter_arr[$i] == 1) {
        $new_arr[$key] = $val;
    }
    $i++;
} 

print_r($new_arr);

Array
(
    [1] => a
    [4] => c
    [8] => d
    [32] => f
)