Sum $324_8$ and $111010101110_2$, expressing your answer in base 8.
I need to add two numbers in different bases, 8 and 2, and give the answer in base 8. One way to do this is to convert both numbers to base 10, add them, and then convert the result to base 8. I get $(111)_2(010)_2(101)_2(110)_2$. Each triplet can be converted to a single digit in base 8 by using a table or by multiplying the powers of 2. I get $(111)_2 = 7_8$, $(010)_2 = 2_8$, $(101)_2 = 5_8$, and $(110)_2 = 6_8$. So, $111010101110_2 = 7256_8$. Now I can add $324_8$ and $7256_8$ in base 8, using the same rules as for base 10, but with different digits. I get $324_8 + 7256_8 = 7602_8$. This is the final answer. 