Final answer:
To solve the division of 3022 base 4 by 34 base 4, we convert both numbers to base 10, perform the division, and then present the result. In base 10, 3022 base 4 converts to 202 and 34 base 4 converts to 16. Dividing 202 by 16 gives us 12.625.
Step-by-step explanation:
To divide 3022 base 4 by 34 base 4, we must first understand how to perform division in bases other than decimal (base 10). In base 4, each digit position represents a power of 4, starting with 4^0 on the right. To proceed, we convert both numbers into base 10, perform the division, and then convert the result back to base 4 if necessary.
First, we convert 3022 base 4 to base 10. This is done by multiplying each digit by the appropriate power of 4:
- 2 * 4^0 = 2 * 1 = 2
- 2 * 4^1 = 2 * 4 = 8
- 0 * 4^2 = 0
- 3 * 4^3 = 3 * 64 = 192
Adding these together, we get 192 + 0 + 8 + 2 = 202.
Now, convert 34 base 4 to base 10:
- 4 * 4^0 = 4 * 1 = 4
- 3 * 4^1 = 3 * 4 = 12
Adding these together, we get 12 + 4 = 16.
Now we can perform the division in base 10: 202 ÷ 16 = 12.625. Since the question didn't specify to convert back to base 4, we'll leave the answer in base 10.