Final answer:
To convert the base 4 number 131four to base 10, each digit is multiplied with the corresponding power of 4 (4^2, 4^1, 4^0) and those products are summed to give the base 10 equivalent, which is 29.
Step-by-step explanation:
To convert 131four to base 10, we need to understand the concept of integer powers and their application in changing a number from one base to another.
The digits in the base 4 number represent the coefficients for the powers of 4.
Starting with the least significant digit, we multiply each digit with the power of 4 that corresponds to its position, which starts at 0.
In the case of 131four, it can be expanded to:
- 1 × 42 = 1 × 16
- 3 × 41 = 3 × 4
- 1 × 40 = 1 × 1
Calculating each term:
- 1 × 16 = 16
- 3 × 4 = 12
- 1 × 1 = 1
Add each result together for the final base 10 value:
16 + 12 + 1 = 29
Therefore, 131four is equal to 29 in base 10.