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Computers store all information as zero's and one's. Think of it as electricity, things are either on (1) or off (0). Since computers are all based on electric power, the scheme of on or off was used for all information.
In terms of numbers here are the first 16 numbers:
number: computer stores this as
0: 0
1: 1
2: 10
3: 11
4: 100
5: 101
6: 110
7: 111
8: 1000
9: 1001
10: 1010
11: 1011
12: 1100
13: 1101
14: 1110
15: 1111
Can you guess what comes next? All we are doing is adding 1 to the previous number. But since you only have 0 and 1, you have to "carry the 1" and then keep going. This is just like when you add 1 to 9, you get 10. You actually started over at zero, and carried the 1, but you have nine digits to do this.
So what is 16? 1111 + 1 = 10000. You carry the 1 to the next digit and zero everything else out. How about 17? 10000 + 1 = 10001. Now do 18! :)
Because very small numbers look really big, humans learned to use base 16 to make it easier to read. Look that up, or I can teach you how to convert from base 2 to base 16 in another answer. :)
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