while ( $ChecksumLoopCounter < $Size ) {
    unless ( sysread ( $FileHandle, $BufferByte, 1) == 1 ) {
        die "sysread size error" ;
    }
    my $Byte = ord($BufferByte);
    $Checksum = unpack("S" , pack("S", $Checksum + $Byte));
    $ChecksumLoopCounter++ ;
    $ChecksumByteOffset++ ;
}
close $FileHandle ;
return $Checksum;
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It goes without saying that I don't understand the requirements and constraints of your task. For some reason, you are constrained to read the file byte-by-byte with sysread et al. I must agree that trying to use pack and unpack in this situation is awkward. I would be inclined toward something like (untested):

use integer;

my $Checksum = 0;
while ($Size--) {
    unless ( sysread ( $FileHandle, $BufferByte, 1) == 1 ) {
        die "sysread size error" ;
    }
    $Checksum += ord($BufferByte);
}
close $FileHandle ;
return $Checksum & 0xffff;
[download]

See integer.