One way to move through all characters in a string is with substr:

use warnings;
use strict;

my $str = 'ABCD';
while (my $mask = <DATA>) {
    chomp $mask;
    for my $i (0 .. length($mask)-1) {
        print substr($str, $i, 1) if substr($mask, $i, 1) eq '1';
    }
    print "\n";
}

__DATA__
1001
1110
0101
0001
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