Find the sum of the digits of the base-8 expression for $8888_{10}$.
I want to convert $8888_{10}$ from base-10 to base-8. One way to do this is to repeatedly divide by 8 and write down the remainders. For example, $8888 \div 8 = 1111$ with a remainder of 0. So the rightmost digit of the base-8 expression is 0. Then I divide 1111 by 8, which gives me 138 with a remainder of 7. So the next digit is 7. I continue this process until I reach a quotient of 0. I get 138 \div 8 = 17$ with a remainder of 2, then 17 \div 8 = 2 with a remainder of 1, and finally 2 \div 8 = 0 with a remainder of 2. So the base-8 expression is 21720. To find the sum of the digits, I just add them up: 2 + 1 + 7 + 2 + 0 = 12. 