Leibniz was specifically inspired by the Chinese I Ching. Some observations: To multiply a number by 10 you can simply shift it to the left by one digit, and fill in the rightmost digit with a 0 moving the decimal place one to the right.
The base-ten "two" is written in binary as And think about what each of the place values represent. You can see this is exactly analagous to the decimal deconstruction of the number that was done earlier.
Or I could write it like this. A single byte can represent 28 numbers. You would have to convert to base-two columns, the analogue of base-ten columns. And how many eights do I have? Why is that helpful? Two squared is equal to four.