### Instruction: Find the product of $1011_2 \cdot 101_2$.  Express your answer in base 2.### Response: I recognize that the subscript 2 means that these are numbers written in binary, or base 2, where each digit is either 0 or 1.
To multiply two binary numbers, I can use a similar method to the long multiplication I learned for base 10, but with simpler rules: 0 times anything is 0, and 1 times anything is itself.
I align the numbers so that the rightmost digits are in the same column, and I start by multiplying the bottom digit (1) by the top number (1011), writing the result below.
Then I move one place to the left and multiply the next bottom digit (0) by the top number, writing the result below and shifting it one place to the left, as I would do with a carry in base 10.
But since 0 times anything is 0, this whole row will be 0, so I can skip it.
I repeat this process for the remaining bottom digits (1 and 1), shifting each row to the left accordingly, and then I add up all the rows to get the final product.