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internet addresses of computers are currently covered by Internet Protocol version 4 (IPv4), which has a 32 bit address space.
Imagine you had only 1 bit long addresses. Then you could have only 2 different addresses - address 0 and address 1. But if you had 2 bit long addresses, you get 4 possible addresses - 00, 01, 10, 11. If you had 3 bit long addresses, you would have 8 possible addresses - 000, 001, 010, 011, 100, 101, 110, 111. Every time you add a new address bit, you double the number of addresses possible.
1 bit = 2 addresses
2 bits = 4 addresses
3 bits = 8 addresses
4 bits = 16 addresses
5 bits = 32 addresses
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.
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Since each address bit doubles the number of possible addresses, a 32 bit address space covers 232 possible addresses, or over 4,000,000,000. And this is only for unique addresses that the whole world can use; many computers are in private networks (inside corporations, for example) and do not need an external IPv4 address. They talk to the outside world through a few routers which DO have IPv4 addresses. So a company might have tens of thousands of computers, but only a few dozen IPv4 addresses that are assigned to the routers they have connected to the internet.
Even so, all 4,000,000,000 of the IPv4 addresses have finally been allocated and will be used up over the next several months. This means that the internet will need to migrate to a newer addressing version, IPv6. IPv6 uses 128 bit addressing. 2128 is about 3.4x1038 addresses. That's 3,400,000,000,000,000,000,000,000,000,000,000,000,000 addresses. They should last us a while.
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