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Base Systems (Medium)

AMC 10/12 mid (≈Q9–16) — multi-step.

Base Systems: core idea

From base 10.

Example problem: hint and answer

Convert 11111211111_2 to base 1010.

Hint: Convert to base ten when arithmetic is unclear. Answer: 31.

Practice (9 problems — type your answers)

  • 1. Convert 10010100_{10} to base 33.

  • 2. Compute 235+14523_5+14_5 in base 55.

  • 3. Convert 25510255_{10} to base 1616.

  • 4. Compute 1012⋅102101_2\cdot10_2 in base 22.

  • 5. Convert 1234123_4 to base 1010.

  • 6. Find xx if x5=2310x_5=23_{10}.

  • 7. Compute 778+1877_8+1_8 in base 88.

  • 8. Convert 2A162A_{16} to base 1010.

  • 9. Convert 641064_{10} to base 22.

Base Systems Practice Problems — Medium