Now, take a pair of integers as x and y coordinates across this square. Their size in bits determines the resolution at which they can measure this square.
An integer of n bits can hold any of 2ⁿ distinct values. 32-bit integers, therefore, would divide the square into a grid of 2³² points.
At 32 bits of resolution, adjacent coordinates, e.g. …
0101 and …
0110, are about a kilometre apart on our square.
If we double the size of our integers, we now divide the square into a grid of 2⁶⁴ points.
At 64 bits of resolution, still covering the entire span of the orbit of Neptune, adjacent coordinates are about 0.24µm apart, or about 1% of the width of an average human hair.
And famously, populating a 128-bit address space would require us to boil the oceans.