# IPv6 migration is not just about giving in to scaremongers

## ITP.net dissects the math, gets off the fence and takes a side in the protocol debate

But the options for bases are by no means restricted to 10. In other walks of life, specifically machine-centric ones like computing, we use others. The one you are probably most familiar with is binary, or base 2. Its maximum digit is 1, just as base 10's is 9 and it is used because it is a ready means to represent on-off states in memory cells or magnetic media. So 1 is on and 0 is off.

In binary, the number 111 is actually made up of one four, one two, and one unit, giving the decimal equivalent of the number 7. So the columns for base 2 run like this: 2^{0} for 1 (units); 2^{1} for 2 (twos); 2^{2} for 4 (fours) 2^{3} for 8 (eights); and so on.

Another common base is 16, or hexadecimal. If you are new to number bases you might be asking how its maximum digit might be represented, since it is 15 and already has more than one digit. Well, we use letters: 10 is A; 11 is B; and so on up to F, which stands in for 15.

If you want to know how many combinations of digits exist between 0 and 999 (or how many unique numbers you can make from three digits where the base number is 10) you instinctively know that it's 1,000 because you instinctively grasp decimal numbering. But what if you want to know how many unique numbers you can make from N digits with a base B system? Well, if you look at 999 you can see the answer is one more than the maximum number you can represent (999 + 1, because you have to include zero), or as a shortcut, you can just raise the base number to the power of the number of digits (B^{N}, or 10^{3 }in this case).

IPv4 uses a formatted string of four, seemingly decimal numbers and has a range of 0.0.0.0 to 255.255.255.255. In fact, now you know about number bases you can see that this is really a four-digit number with a base of 256. If we apply B^{N} now, we can see (with a little help from a calculator, unless you happen to be a savant) this shakes out to approximately 4.295bn. This is the absolute maximum number of unique IPs that can be generated using the v4 system, but actually the number of IPs available for public use is around 3.7bn. 256^{4} can also be written as 2^{32}, which is why IPv4 is referred to as a 32-bit system.

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