1. **State the problem:** Convert the number 312 from base 4 to base 10. 2. **Formula and explanation:** To convert a number from base $b$ to base 10, use the formula: $$\text{Value in base 10} = \sum_{i=0}^{n-1} d_i \times b^i$$ where $d_i$ is the digit at position $i$ (starting from 0 at the rightmost digit) and $b$ is the base. 3. **Apply the formula:** For the number 312 in base 4, the digits are 3, 1, and 2 from left to right. The rightmost digit is position 0. 4. **Calculate each term:** - The digit 2 is at position 0: $2 \times 4^0 = 2 \times 1 = 2$ - The digit 1 is at position 1: $1 \times 4^1 = 1 \times 4 = 4$ - The digit 3 is at position 2: $3 \times 4^2 = 3 \times 16 = 48$ 5. **Sum the values:** $$48 + 4 + 2 = 54$$ 6. **Final answer:** The number 312 in base 4 is equal to 54 in base 10.