The largest eight-digit base 2 integer is 1 less than the smallest nine-digit base 2 integer, which is $$ 100000000_{2} = 1 \cdot 2^8 = 256. $$Thus, the largest eight-digit base 2 integer is $256 - 1 = \boxed{255}$.
Question:
What's the largest eight-digit base 2 integer?  Express your answer in base 10.
Answer:
Let's think step by step.

user
255
What's the largest eight-digit base 2 integer?  Express your answer in base 10.
test