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3 problems match “base conversion”. Clear

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1. Multiplying and dividing in base 4 ●●○○○ 20 ptsCompute $120_4\times13_4\div2_4$. Express your answer in base 4.
2. Binary multiplication and division ●●○○○ 20 ptsFind $10110_2\times10100_2\div10_2$. Express your answer in base 2.
3. Non-negative elements of a closed set ●●●○○ 50 ptsLet $S$ be the smallest subset of the integers such that $0 \in S$ and, for any $x \in S$, both $3x \in S$ and $3x+1 \in S$. Determine the number of non-negative integers in $S$ that are less than $2008$.