c++ pow(2,1000) is normaly to big for double, but it's working. why?

Question

the code:

#iclude 

int main(){
double somenumber = pow(2, 1000);
printf(\"%lf\\n\", somenumber);
return 0;
}

i get this huge

Answer 1

It is a power of two, and the floating point are essentially stored as (multiples of) powers of two.

Similarly, in decimal system, it shouldn't surprise you that it takes very little room to represent 10¹⁰⁰⁰ precisely, but such a concise notation would not be possible for large powers of other values, like 3¹⁰⁰⁰ = 1322070819480806636890455259752144365965422032752148167664920368226828597346704899540778313850608061963909777696872582355950954582100618911865342725257953674027620225198320803878014774228964841274390400117588618041128947815623094438061566173054086674490506178125480344405547054397038895817465368254916136220830268563778582290228416398307887896918556404084898937609373242171846359938695516765018940588109060426089671438864102814350385648747165832010614366132173102768902855220001.