I don't know if this is a possible answer but it works with the example binary string you provided.

#!/usr/bin/perl
use strict;
use warnings;

my $bin =  0b1111_1111_1111;

for my $factor (3,5) {
    # round up to multiple of 4
    my $shift = $factor + (-$factor % 4); 
    my $c = $bin >> $shift;
    $c <<= $shift;
    printf "%b\n", $c;
}
[download]

111111110000
111100000000
[download]