If that example was chosen because it is the biggest number you will be dealing with, then you could get away with wrapping this into a function:

my $n = 9007199254740991;
my( $hi, $lo ) = ( int( $n / 2**32 ), $n % 2**32 );
printf "%b%032b\n", $hi, $lo;

11111111111111111111111111111111111111111111111111111

$n--;
( $hi, $lo ) = ( int( $n / 2**32 ), $n % 2**32 );
printf "%b%032b\n", $hi, $lo;

11111111111111111111111111111111111111111111111111110

$n+=2;
( $hi, $lo ) = ( int( $n / 2**32 ), $n % 2**32 );
printf "%b%032b\n", $hi, $lo;

100000000000000000000000000000000000000000000000000000
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but if your numbers get much bigger than 2⁵³, then you'll need to take the hit of using one of the bigInt libraries.