Within the limitations of doubles to represent large numbers accurately, you can do this by breaking the number into hi and lo integers, converting them separately, and concatenating the results:

$huge = 1024**4;;
$lo = $huge % 2**32;;
$hi = int( $huge / 2**32 );;

printf "%b%032b\n", $hi, $lo;;
10000000000000000000000000000000000000000
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Otherwise take a look at the bigint pragma and Math::BigInt.