Unless I'm misunderstanding your question, you can do it like this:

use Modern::Perl;

my $a = '0001';
say 'The variable $a contains: ', $a;
say 'The sum of $a and 1 is: ', $a + 1;
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Output:

The variable $a contains: 0001
The sum of $a and 1 is: 2
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The perl interpreter uses context to determine how a variable should be treated: as a string in the first case, and as an integer in the second.

Update: Yes, I did misunderstand. DamianConway provides an excellent solution below.