Now I have no idea how it got 25856 from 101 (well it does seem to be 101 times that magical 256 number, but I'm sure it isn't that simple).

Yes, it's that simple. perlvar explains that $? is set like explained in system where the following snippet is copied from:

Quote from system: 

if ($? == -1) {
                print "failed to execute: $!\n";
              }
elsif ($? & 127) {
                    printf "child died with signal %d, %s coredump\n",
                    ($? & 127),  ($? & 128) ? 'with' : 'without';
                 }
else {
        printf "child exited with value %d\n", $? >> 8;
     }

[download]
HTH

Update: 

Bit# 15 14 13 12 11 10 09 08  07 06 05 04 03 02 01 00
      |  |  |  |  |  |  |  |   |  |  |  |  |  |  |  |
     X7 X6 X5 X4 X3 X2 X1 X0  CD S6 S5 S4 S3 S2 S1 S0
      |                        |  |
      +-- exit code (8bit)     |  +-- signal code (7bit)  
                               |
                               +-- core-dumped flag

[download]

Update2 (in response to node below):

So for quick and dirty every day use it sounds like I can just say something like: $exit_status = $?/255;
No. 
my $exit_status = int( $? / 256 ); # quick and dirty exit-state
                                   # decimal arithmetic so to speak
                                   # (works for positive numbers)

[download]
Use int() to get rid of potential fractional parts when the process terminated due to a signal or core-dump.
The >>-operator does this in a single step.
I might note, that I assumed a *NIX background. The Windows emulation might not cover the whole interface (exit-code plus signals). Other monks will know better...

So X >> Y is most of the time int( X / (2**Y) ) for positive numbers.

Here are some starters for binary arithmetic: wikibooks, Khan Academy - Binary Numbers, Slideshare - Binary Arithmetic, ... Search also MIT OpenCourseWare - I am sure, they have something in their repertoire.

In reply to Re: getting the bash exit code by Perlbotics
in thread getting the bash exit code by xorl

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