1. The problem is to convert an integer from one base to another. 2. The general method involves two main steps: first, convert the number from the original base to base 10 (decimal), then convert from base 10 to the target base. 3. To convert from base $b$ to decimal, use the formula: $$\text{Decimal} = \sum_{i=0}^{n-1} d_i \times b^i$$ where $d_i$ are the digits of the number starting from the right (least significant digit) and $n$ is the number of digits. 4. To convert from decimal to base $k$, repeatedly divide the decimal number by $k$ and record the remainders. The base $k$ number is the remainders read in reverse order. 5. Important rules: - Digits in any base must be less than the base. - Bases are integers greater than 1. 6. Example: Convert $1011_2$ (binary) to base 10. 7. Using the formula: $$1011_2 = 1 \times 2^3 + 0 \times 2^2 + 1 \times 2^1 + 1 \times 2^0 = 8 + 0 + 2 + 1 = 11_{10}$$ 8. Now convert $11_{10}$ to base 8: Divide 11 by 8: $$11 \div 8 = 1 \text{ remainder } 3$$ Divide 1 by 8: $$1 \div 8 = 0 \text{ remainder } 1$$ Reading remainders in reverse order gives $13_8$. Final answer: $1011_2 = 11_{10} = 13_8$.