Since the code Does What I Want (works even for bit widths > 32), I have made it readable by using perltidy. I have also made it strict and removed the print statements: 
use warnings FATAL => 'all';
use strict;

for (
        qw(
            00
            1010
            1110
            010001
            01101011
        ),
        '1' x 33,
        '0101' x 16
) {
    my $h = b2h($_);
    print "$_ $h width=", length($_), "\n";
}
exit;


sub b2h {
    my $num   = shift;
    my $WIDTH = 32;
    my $index = length($num) - $WIDTH;
    my $hex = '';
    do {
        my $width = $WIDTH;
        if ($index < 0) {
            $width += $index;
            $index = 0;
        }
        my $cut_string = substr($num, $index, $width);
        $hex = sprintf('%X', oct("0b$cut_string")) . $hex;
        $index -= $WIDTH;
    } while ($index > (-1 * $WIDTH));
    return $hex;
}

__END__

Output:

00 0 width=2
1010 A width=4
1110 E width=4
010001 11 width=6
01101011 6B width=8
111111111111111111111111111111111 1FFFFFFFF width=33
0101010101010101010101010101010101010101010101010101010101010101 55555
+55555555555 width=64

[download]

I have also been attempting to implement this with pack and unpack, to no avail.

In reply to Re^3: How to convert binary to hexadecimal by toolic
in thread How to convert binary to hexadecimal by vaas_m

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