### Instruction: Find the product of $10101_2$ and $101_2$. Express your answer in base $2$.### Response: To multiply two numbers in base $2$, I can use the same algorithm as for base $10$, but with simpler arithmetic.
I can align the numbers by their least significant bits and start multiplying from the right.
The product of any bit and $0$ is $0$, and the product of any bit and $1$ is the same bit.
I also need to keep track of any carries that occur when the sum of the products exceeds $1$.
I can write down the partial products and then add them up to get the final product.