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Base Systems (Easy)

AMC 10 Q1–8 depth — contest entry, not school drills.

Easy Medium Hard AIME / USAJMO / AMO

Base Systems: core idea

To base 10.

Example problem: hint and answer

Convert $1010_2$ to base $10$ .

Hint: Expand by powers of the base. Answer: 10.

Practice (9 problems — type your answers)

1. Convert $15_{10}$ to base $2$ .
2. Convert $12_3$ to base $10$ .
3. Convert $20_5$ to base $10$ .
4. What is $1+1$ in base $2$ ?
5. Convert $10_{10}$ to base $5$ .
6. Convert $FF_{16}$ to base $10$ .
7. Convert $100_2$ to base $10$ .
8. What digit follows $7$ in base $8$ ?
9. Convert $21_4$ to base $10$ .

Base Systems Practice Problems — Easy