This is a very odd format, but another solution for you:
"~" is the complement operator, i.e. flip all bits

#!/usr/bin/perl

use strict;
use warnings;

#assume each value is a perl var masked to lower 8 bits

foreach (0x85, 0x05)
{
   my $x = $_;               #allow mod of $x in loop
   
   my $neg = $x & 0x80;      #decide if negative
   $x = ~$x & 0x7F if $neg;  #adjust if so
   
   printf "%s%-08b%s%d\n",($neg)?"-":" ",$x,($neg)?"-":" ",$x;
}   
__END__
-1111010 -122
 101      5
[download]

Update: I suppose many variations are possible:
Here $x winds up being the signed decimal value

#!/usr/bin/perl

use strict;
use warnings;

#assume each value is a perl var masked to lower 8 bits

foreach (0x85, 0x05)
{
   my $x = $_;               #allow mod of $x in loop
   
   my $neg = $x & 0x80;                #decide if negative
   $x = ~$x & 0x7F, $x = -$x if $neg;  #adjust if so
     
   printf "Input=%2x hex Input=%08b decimal=%d\n", $_, $_, $x;
}   
__END__
Input=85 hex Input=10000101 decimal=-122
Input= 5 hex Input=00000101 decimal=5
[download]

Normal 2's complement notation could represent within 8 bits, an integer number from -128 to +127.
In the past computers have been designed with a "sign bit" followed by positive integer bits.
That failed miserably because there was the possibility of a "plus zero" and "minus zero".
This sign bit + one's complement is truly weird. I've never seen anything like it.