TIMTOWTDI:

#!/usr/bin/perl -w
use strict;
=head - Per OP
$a='aabbccdddd';
I want the Output like this
$a='abcd';
=cut

my $a = 'aabbccdddd';
my $prev = '';
my @a = split //,$a;
for my $found(@a) {
    if ($prev eq $found) {
        next;
    } else {
        print "\$found is: $found \n"; #Omit \n if oneline output desi
+red.
        $prev = $found;
        next;
    }
}
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Output:

ww@GIG:~/pl_test$ perl -c 718695.pl
718695.pl syntax OK
ww@GIG:~/pl_test$ perl  718695.pl
$found is: a
$found is: b
$found is: c
$found is: d
[download]

Note: This will fail on the likes of $a='aabbccadddd'

ww@GIG:~/pl_test$ perl  718695.pl
    $found is: a
    $found is: b
    $found is: c
    $found is: a  # dup
    $found is: d
[download]

If the data is in this form, use a %hash as andreas1234567 does, above or sort the string.