Handle the sign and you should be fine: ( wow that rhymes! )

use strict       ;
use warnings     ;
use Math::BigInt ;


my $hex  = '-a'  ;

my $sign = '0' ;
if( $hex =~ /^-/ ) { 
    $hex =~ s/^-//g ;
    $sign = 1       ;
} 

my $big_int = Math::BigInt->new( '0x'.$hex ) ; 

my $binary   = $big_int->as_bin() ;
my $two_comp = $binary            ;
$two_comp =~ s/^0b/$sign/;

print "$two_comp\n";
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