Here's another way to do it.

use warnings;
use strict;

foreach (
        qw(
            00
            1010
            1110
            010001
            01101011
        ),
        '1' x 33,
        '0101' x 16
) {
    my $h2 = b2h2($_);
    $h2 =~ s/(\w{4})\B/$1 /g;
    print "$_ $h2 width=", length($_), "\n\n";
}

sub b2h2 {
    my $bin = shift;
    my $extra_characters = length($bin)%16;
    $bin = '0' x (16-$extra_characters) . $bin if $extra_characters;
    $bin =~ s/([01]{4})/sprintf "%X", oct("0b$1")/eg;
    return $bin;
}

__END__

Output:
00 0000 width=2

1010 000A width=4

1110 000E width=4

010001 0011 width=6

01101011 006B width=8

111111111111111111111111111111111 0001 FFFF FFFF width=33

0101010101010101010101010101010101010101010101010101010101010101 5555 
+5555 5555 5555 width=64
[download]

Here is a way to convert without padding with zeros on the left side. Reverse the binary string and convert groups of four bits then reverse the final string.

sub b2h {
    my $revbin = reverse shift;
    $revbin =~ s/([01]{1,4})/sprintf "%X", oct('0b' . reverse $1)/eg;
    return reverse $revbin;
}
[download]