### Instruction: Express eleven in base 2.### Response: To express a number in base 2, I need to find the powers of 2 that add up to the number.
I can start from the largest power of 2 that is less than or equal to the number and work my way down.
For 11, the largest power of 2 that is less than or equal to 11 is 8, which is 2^3.
So I can write 11 as 8 + 3.
To express 8 in base 2, I just need to write 1000, since 8 is 2^3.
To express 3 in base 2, I need to find the powers of 2 that add up to 3.
The largest power of 2 that is less than or equal to 3 is 2, which is 2^1.
So I can write 3 as 2 + 1.
To express 2 in base 2, I just need to write 10, since 2 is 2^1.
To express 1 in base 2, I just need to write 1, since 1 is 2^0.
So I can write 3 as 10 + 1, or 11.
Therefore, to express 11 in base 2, I can write 1000 + 11, or 1011.