> 2 to the power of 128;
> 2^128
> 3.4×10^38

It's not that many addressable machines.

Firstly, since we have a lot of address space we can sacrifice some for 
features. In fact 64b of the 128bit address space is used for the automatic 
configuration feature.

Secondly, IP addressing is hierarchical, not flat. This allows the entire 
internet to be tracked in about half a million entries on the core routers. 
That hierarchy "wastes" about another third of the address space. In fact we 
hope to waste more with IPv6 than with IPv4, in order to keep the number of 
backbone routes lower.

You end up with enough addressing for about a billion medium-sized businesses. 
That's a lot, but it is very finite, which is why the address delegation bodies 
manage the address space to limit wastage (eg, requiring a justification for 
the amount of addressing requested).

-glen


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