### Instruction: Add $101_2 + 11_2 + 1100_2 + 11101_2.$ Express your answer in base $2.$.### Response: To add these numbers in base $2$, I need to align them by their rightmost digits and add them column by column, starting from the right.
I also need to remember that in base $2$, $0 + 0 = 0, 0 + 1 = 1, 1 + 0 = 1,$ and $1 + 1 = 10,$ where $10$ means two in base $2$.
If I have a carry-over of $1$ from a previous column, I need to add it to the next column as well.
So, let me write the numbers in columns and add them from right to left.
I will write the base $2$ digits in blue and the carry-overs in red.
Here is my work:
As you can see, the final sum is $101000_2$.