Find the number of odd digits in the base-4 representation of $233_{10}$.
To convert a number from base 10 to base 4, I need to repeatedly divide it by 4 and write down the remainders. So, 233 divided by 4 is 58 with a remainder of 1. That means the rightmost digit in base 4 is 1, which is odd. Then, 58 divided by 4 is 14 with a remainder of 2. That means the next digit is 2, which is even. Next, 14 divided by 4 is 3 with a remainder of 2. That means the next digit is 2, which is also even. Finally, 3 divided by 4 is 0 with a remainder of 3. That means the leftmost digit is 3, which is odd. So, the base-4 representation of 233 is 3221. There are two odd digits in this representation: 1 and 3. 