pastorofmuppets It's even simpler for the computer. Doubling is a left shift (e.g. 0011 becomes 0110). Also, looking at single digits, you can only multiply by 0 or 1 (yielding zero or the original number). So multiplying A * B becomes:
- is the rightmost digit of B 1? if so, add A to sum.
- left shift A and repeat with next digit of B

But binary is lame. ENIAC could count to 10 *and* strike fear in the hearts of cold war enemies. I want my computer to have tubes, dammit.

fluffy The multiplication technique was nothing new to me (and of course it can be extended to exponentiation, where instead of doubling the number you square it, and instead of adding it to the accumulator you multiply it), but for some reason I had never considered that inverse method for division. If I'd learned math that way then maybe I wouldn't always just be grabbing my cellphone for the calculator app to do simple math.

kwash This seems so much easier than doing long division or multiplication.

Gwago Why aren't we teaching this in school instead of memorizing tables?

fluffy You'd probably have to either rework the curriculum around binary or still teach people how to efficiently multiply base-10 numbers by 2. Also, I wonder if memorizing the 10x10 table helps out other aspects of memory retention and so on.

pastorofmuppets Like fluffy said, you need to double numbers (which itself requires tables). But people still use this method.

http://mathforum.org/dr/math/faq/faq.peasant.html

(His getting the "bits" up front is the same as repeatedly halving and checking the remainder.)