For example, instead of the widespread system of adding the tens column in the sum 73+80 by remembering that 7+8=15, under the Mangarevan system you combine “forty twenty ten three ...

Leibniz pointed out in 1703 that to do simple arithmetic in binary, such as addition and multiplication, you don’t need to memorize such rules as 5 + 4 = 9, or 6 × 7 = 42. Instead, you need ...