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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