I want to build a programmable gain instrumentation amplifier with power of two possible gains (1x, 2x, 4x, 8x...). Is there a way to use a R-2R resistor ladder and an analog multiplexer in order to tune the \$R\_{\text{gain}}\$?
[![Classic instrumentation amplifier](https://i.stack.imgur.com/my8Lo.jpg)](https://i.stack.imgur.com/my8Lo.jpg)

On the web I found this way to make programmable gain amplifiers using a R-2R ladder and an analog multiplexer but I don't want to attenuate my input signal as it is already small, I'd lose it in the noise in this way.
[![R-2R PGA](https://i.stack.imgur.com/Pf0hh.jpg)](https://i.stack.imgur.com/Pf0hh.jpg)