Base Systems (Hard)

Base Systems: core idea

• 1. Write $100$ in base $7$.

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• 2. If $(3x)_7=(26)_8$, find $x$.

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• 3. Compute $(123)_4+(132)_4$ in base $4$.

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• 4. Find the least base $b>4$ such that $(144)_b$ is divisible by $5$.

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• 5. Evaluate $(1111)_2$ in base ten.

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• 6. Find $b$ if $(121)_b=16$.

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• 7. Compute $(56)_7-(24)_7$ in base $7$.

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• 8. Decimal $45$ is $(a5)_b$. Find $a+b$.

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• 9. Find $(1234)_5\pmod4$.

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