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jmc

number theory intermediate

Problem

Express eleven in base 2.

Solution

We have

11 = 1 \cdot 2^{3} + 0 \cdot 2^{2} + 1 \cdot 2^{1} + 1 \cdot 2^{0},

so

11 = 101 1_{2}

.

Final answer

1011_2