Base-2 is used because voltage switches have two states, on and off. If there were some integral part of a culture that involved something with x states, then a base x system would likely be in use. X fingers is the obvious candidate, but say your species has some sort of color signalling organ that can assume a distinct blue, green, and red color. In that case, a base-3 system of counting would be a likely outcome.

You mentioned decimals particularly in your title, but the rest of your question refers to bases. Are you wondering about actual decimals themselves, or just about bases? Because if you are asking about decimals, I could think of a different answer than those already given.

@ThomBlairIII they mean "decimal" as opposed to "binary" or "hexidecimal" - the counting number, as opposed to the numbers after the "decimal point" "."

@Zxyrra That's what I assume too, but the title does specify decimals. I often like to probe around things that seem obvious, but possibly might not be what is normally assumed.

@Zxyrra Technicalities and tiny overlooked areas can often feel to me like they can provide "loopholes" or alternate ways of solving problems.

@kingledion WRONG base 2 is used in computers because of boolean algebra. true and false. Logic is easier to replicate in circuits from what I hear than doing base 10. We used to use gears and it was horribly painful.

@Kingledion @ SteveIves: Computers does not use on/off in their circuits, they use high/low voltage. While this might seem like an on/off system, there is a significant difference in the fact that it is fully possible to add more states if there is a desire to do so. 5V is commonly used in circuitry and it is, thus, fully possible to make a computer base-6 by making one state per voltage instead as the current on (≥2 V)/off (≤0.8 V). It just happens to be easier to implement Boolean algebra as fine tuning would make the circuits more complex.

@Mrkvička Don't dwell too much about voltages in the individual wires, those don't matter; as you noted, there's plenty of possible non-overlapping states. The important bit is the switch - nowadays, the transistor. The simplest transistor can choose between two states, and (most of) everything else is built on top of that. Of course, Boolean algebra being a simple base for all logic is a very big reason - that's why two-state tubes/transistors were considered in the first place, and why we can build complex systems from tiny, two-state transistors. Both reasons are valid for the OP, though.

I like base 30, 30 is the product of 2,3 and 5 (the three smallest prime numbers). And 30^30 planck lengths gives you roughly 3 million kilometers and 30^30 planck times is about 11.1 seconds. Both workable values.

@Mrkvička So why aren't computers using base 10? Or 20 or 30? Just think of the storage density that could be obtained.

@SteveIves because then the representation of data loses the extreme benefit of everything being powered by boolean algebra. It's harder to program with 10 voltages believe it or not. We used to do it with gears and it was eons harder (not because of the hardware but because of the hoops they had to jump through).

@Steve Ives: the more states, the more difficult it becomes to tell them apart. That’s especially true for the performance regions of our today’s technology. We got used to think of digital signals as being like _‾__‾_‾ where, in fact, they are more like /\_/\/ or even ~~~~, as there’s simply not enough time to pull the voltage level further. Therefore, I’m not seconding the statement “we could use multiple voltage stages”. Well we could do that, indeed, but we couldn’t do that with the same processing speed…

@overactor: there were ancient number systems based around 60.

@Holger I know - I was being rhetorical. I don't do CPU design and I'm willing to accept that there's a really good reason why CPUs and their associated circuitry still use 2 states. I'm sure that those who do would love to be able to increase storage density by any factor.

There is no real upper limit to how many levels you can use, only a limit on how easily you can discern between them. More levels means you need to put more work into keeping noise levels down, so you can use more levels, but it's a lot of extra work for little practical gain, not to mention that it's an awful lot easier to decode binary signals, you just need switches, adding more levels requires comparisons with references and suddenly you're in the analogue world and analogue and digital CMOS don't play nice on the same wafer (quite different process optimisations)

Note that flash memory is “multi level” as a trade off of density for speed and cost.

@ThomBlairIII: "decimal" is short of "decimal numeral system" or base 10, as "hexadecimal" is base 16 and "octal" is base 8.

I'm absolutely shocked that every thinks a base is required for counting. Why not base infinity?

@axsvl77: Shocked? Having a unique symbol and word for every possible number is hardly practical.

@axsvl77 probably because that would require an infinite number set compared to the set of ten we currently use...

@FighterJet My point is more that we don't need a base to count to nine. Perhaps the alien has a much higher number than nine to count to, high enough that we'd say its to large to count. And perhaps their mathematical system does not require the abstract invention of infinity.

On the Pioneer plaque, Carl Sagan used binary numbers, using digits - and |, with the idea that it was the best way to convey numbers that had a chance of being universally understood.

@axsvl77 We don't need a specific base for the actual counting, but it is extremely useful to have so we know what to call something. 9 is only called 9 in base-10 and higher, in base-9 or lower it changes name quite radically (i.e., 1001, 100, 21, 14, 13, 12, 11, and 10 from base-2 to base-9, and that's ignoring negative base). There wouldn't any base "too high to count to", but it would be annoying to make new, unique, symbols once we run out of ascii characters.

@Mrkvička Right; it would be very annoying for us humans to do that. But for a alien species able to subitize at levels much higher than us, using a base would be very inconvenient!

@Mrkvička For example, When I see 1 item on the left, and 2 items on the right, I can subitize immediately that there are 3 total item; I don't need to use addition. For an alien species that is able to subitize a million distinct items, the concept of addition or multiplication would be not only inconveinient; it would be abstract. They would find it inconceivable that an intelligent species can only subitize 5 things!

@Mrkvička So for a species with a large subitization limit, perhaps most individuals don't know addition or using bases; they just communicate numbers naturally. When the alien mathematitions and engineers find the need to use a numerical bases for physics research and computer science, perhaps they would develop a base number system that is higher.

And the poor students will ask, bases? Why do we need such abstract concepts?