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binary count to sixteen

 
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This is a meager attempt to count from 0 to 16 using the binary (base2) system. I got the answers for 0, 1, 2, and 16 from a book and filled in the blanks.
I'm pretty sure it's right because when I add 2 + 3 it makes sense to me that a one is pulled down from the 1st digit's place and since there is a one in both of the 2nd digit's place, it becomes 0 and a 1 appears in the 3rd digit's place. Give a holler if my thinking/answers need work.
0 - 0000 0000 9 - 0000 1001
1 - 0000 0001 10 - 0000 1010
2 - 0000 0010 11 - 0000 1011
3 - 0000 0011 12 - 0000 1100
4 - 0000 0100 13 - 0000 1101
5 - 0000 0101 14 - 0000 1110
6 - 0000 0110 15 - 0000 1111
7 - 0000 0111 16 - 0001 0000
8 - 0000 1000
 
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Looks reasonable to me.
 
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