We’ve often noted that whether had ancient man known binary, we could all count to 1023 on our fingers. We thought about that while watching [Numberphile’s] latest video about “Russian” multiplication ...

To do the method, begin by writing the two numbers you want to multiply at the top of two columns. In the left column, you progressively halve the number and take the integer floor of any “and a half” ...

In positional systems, as mentioned earlier, the number represented is multiplied by the base each time you move to the left of a position and is always divided by the base each time you move to the ...