# algebra

What would the first 15 counting numbers for base two and base four bases?

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1. base 2 goes like this
2^0 = 1 column 1
2^1 = 2 column 2
2^2 = 4 column 3
2^3 = 8 column 4
2^4 = 16 column 5

so
1 = 1
2 = 1 0 which is 2^1
3 = 1 1
4 = 1 0 0 which is 2^2
5 = 1 0 1
5 = 1 1 0
7 = 1 1 1
8 = 1 0 0 0 which is 2^3
etc to
15 = 1 1 1 1
16 = 1 0 0 0 0 which is 2^4

similarly for base 4
4^0 = 1
4^1 = 4
4^2 = 16
4^3 = 64
so
1 = 1
2 = 2
3 = 3
4 = 1 0 which is 4^1
5 = 1 1
6 = 1 2
7 = 1 3
8 = 2 0
9 = 2 1
10 = 2 2
11 = 2 3
12 = 3 0
13 = 3 1
14 = 3 2
15 = 3 3
16 = 1 0 0 which is 4^2

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