You forgot to increment $hour:

$hour = "00";
while ($hour < 25) {
 $infile = "$hour.txt";
 open  LOG, '<', $infile;
 while <LOG> {
    #PUT EACH NEW LINE INTO THE HASH
 }
 $hour++;
}
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That's one reason I'd suggested a foreach loop, because it takes care of that automatically. It also takes care of the initial assignment, too. But the while loop will get the job done also, with this addition.

And i am trying to make my hash hold %hash = ("btwdins.exe", 1, "spoolsv.exe", 1, "svchost.exe", 4,); So it takes all the lines from the text files but increments the value for every duplicate.

Ah, I see. So the strings that come out of the hour files (one per line) are themselves filenames, and you want to use those as the hash keys, and make the value be the count of the number of times they occur? In that case, you can just increment the value each time, as cdarke suggests.