Not quite sure how to express what I’m thinking, but here goes:
An integer expressed in base-2 notation looks like this:
This requires five independent digits, each capable of two different states. To express the same quantity in base-10 (as 22) requires two independent digits, each capable of ten different states.
There’s an “efficiency” of sorts in base-2; I’m not sure how to express it, but it becomes more apparent in other venues.
Suppose I want to light a room with an occupant-selectable integer number of watts of light, ranging from zero to 22 watts.
Vendor A offers lamps with powers of 1 watt and 10 watts. If I select him, I’ll need to buy a pair of 10-watt lamps and nine 1-watt lamps, a total of eleven lamps to achieve my goal.
But vendor B offers lamps with 1, 2, 4, 8, and 16 watts. If I select him, I need only buy five lamps (16, 8, 4, 2 , and 1 watts). Clearly this is the more economical distribution of sizes, at least as concerns the customer.
You can imagine this arrangement in a lot of different situations where items are used simultaneously: resistors, pumps, lamps, shims, etc.
Is there a name for that sort of sizing scheme?