I’ve discovered that base 3 is the most efficient base (not base 2). Actually the most efficient base is e, and 3 is the closest to e (the proof requires Calculus).

South Korea has published a complete design of a ternary computer in July 2019! So this is actually cutting edge material here!

(Inefficiency is calculated by multiplying the number of digits by the base number).

Simon has also showed me a trick to translate any number into binary using a grid:

and a card trick based on quickly translating a number into binary in his head: