The answer to your question depends on whether you are checking whether '1' is unique, or checking for a list of unique values. If you want a list of unique characters here is one approach:

use strict;
use warnings;
my $a = '12345678901';

# Create a hash which has a count of the number
# of times a character appears in the string.
my %tally;
$tally{$_}++ for split '', $a;

#
# Find hash keys that only have 1 match
#
my @unique = grep {$tally{$_} == 1} keys %tally;
print "Unique keys:\n";
print "$_\n" for sort @unique;
[download]

And at this point if you want to check whether a particular character is unique you could do this:

  if ($tally{2} == 1) {
     print "2 is unique\n";
  }
[download]

If you are only looking to check for a particular character, then you can count the characters like this:

my $a = '12345678901';
my $cnt = $a =~ tr/1//;

#In this case $cnt = 2, which means it is not unique
[download]