Rotary Switch(binary encoding) direct to Mastercard?

Gday, folks.

The question is about rotary switch(not encoder). Let's take EFIS panel on 737 as an example, where we have a rotary switch to select one of the "APP-VOR-MAP-PLN".

The simplest is to just use 4 inputs on a mastercard, but wouldn't it be possible to encode the 4 inputs in binary sequence as 00-01-10-11? The wiring around the switch would get a little tangled, but only 2 inputs would be used instead of 4!

Another part of this is SIOC support I guess...
Has anyone tried this, is it at all possible?

Cheers.