### Instruction: Express eleven in base 2.### Response: I know that base 2 is a way of writing numbers using only the digits 0 and 1, and that each place value represents a power of 2, starting from the right.
So the rightmost digit is the 2^0 or the ones place, the next one is the 2^1 or the twos place, then the 2^2 or the fours place, and so on.
To express eleven in base 2, I need to find a combination of powers of 2 that add up to eleven.
I can start by finding the largest power of 2 that is less than or equal to eleven, which is 8, or 2^3.
That means I need a 1 in the 2^3 place, and then subtract 8 from 11 to get 3 as the remaining amount.
The next largest power of 2 that is less than or equal to 3 is 2, or 2^1.
That means I need a 1 in the 2^1 place, and then subtract 2 from 3 to get 1 as the remaining amount.
The only power of 2 that is less than or equal to 1 is 1 itself, or 2^0.
That means I need a 1 in the 2^0 place, and then I have no remaining amount.
So I have a 1 in the 2^3, 2^1, and 2^0 places, and 0 in the other places.
This means that eleven in base 2 is 1011.