Perhaps OP means to capture the entire data string when that string contains three or more consecutive "1"s?

If so, in additional to AnomalousMonk's grep suggestion, several of the others above are solutions or near solutions with the addition of capturing parens:

#!/usr/bin/perl
use strict;
use warnings;
use 5.012;

my @captures;
my $capture;
my $string;

my @strings = qw/0110 1 11 01110 001 100 1111 01001110/;
for $string(@strings) {
    if ( $string =~ /^(.*?1{3}.*)$/ ) {
        push @captures, $1;
    }
}
for $capture(@captures) {
    say $capture;
}
[download]

which produces:

01110
1111
01001110
[download]