You're right :) I'm thinking sometimes because the Perl community is too kind and helpful, I'm just tempted to become very very lazy :)

Anyway I tried translating words into code and came up with the following ugly code, which seems to be working. But I know it's ugly :)

use strict;
use warnings;

$/ = \20_000_000; #I've just split a 20-meg file
open my $f1, "<", '1' or die $!; # piece 1 is named 1
binmode $f1;
open my $f2, "<", '2' or die $!; # piece 2 is named 2
binmode $f2;
while(my $x = <$f1>){
    while(my $y = <$f2>){
    open my $out, ">", "outfile" or die $!;
    binmode $out;
    print $out $x.$y;
    }
}
[download]

UPDATE: tried optimizing a few lines. It looks a little cleaner

use strict;
use warnings;

$/ = \20_000_000; #I've just split a 20-meg file into 2 pieces
open my $f1, "<", '1' or die $!; piece 1 is named 1
binmode $f1;
open my $f2, "<", '2' or die $!; # piece 2 is named 2
binmode $f2;
while(defined(my $x = <$f1>) && (my $y = <$f2>)){
    open my $out, ">", "outfile" or die $!;
    binmode $out;
    print $out $x.$y;
}
[download]