Electronic – switch between two analog references to read signals with different ranges with the ATmega328P

The solution provided by IgnacioVazquez-Abrams was correct. Apparently, I was incorrectly clearing the lower 4 bits in ADCSRA when I should have been doing it to ADMUX. I've updated the code above to reflect this and the errors I've made in the code have been commented out (they are still there for reference).

The AD7732 is a high precision, high throughput analog front end.

An analog front-end is basically a term relating to modern digital systems. Modern digital systems typically use low voltages, anywhere from 5V and below. Well analog voltages are typically higher than that, but they still need to be interfaced with digital systems. The solution is a separate integrated circuit that will handle the measurement of analog voltages and signals and then interface with the lower voltage digital system to relay that information.

Overvoltage tolerant

Up to ±50 V absolute maximum

What they mean by overvoltage tolerant is basically if your signal somehow jumps up to a higher voltage, the ADC shouldn't be damaged past the point of no return, but that doesn't mean it can't still get damaged. Its just that they are willing to sign off that the device should still respond to commands and requests should any voltage up to ±50V occur.

Up to ±16.5 V not affecting adjacent channel

If your input signal goes up/down to ±16.5V, it won't affect the readings that take place on the adjacent channel. If it goes beyond that though, your readings on the other channels will start to be less accurate.

Does AD7732 provide for me directly reading analog input in the range of ±12 or only ±10?

The device is only marked as reading between ±10V but that doesn't mean that it can't do better than that. This value is just what the company feels comfortable marketing as. Although the value isn't to be taken lightly. If the fabricator says the chip can only handle ±10v, only use it in that situation or bad things can happen.

After doing some digging, turns out, looking at page 27, you will achieve up to ±11.6V readings without more rapidly degrading your ADCs performance. Once you go over the ±10V range, the OVR bit in the channel status register will be set and your data value will be clipped to the lower 16 bits. Take a look at Table 16 and 17 on that page and it should be pretty clear.

With all of that said, I wouldn't recommend using this IC for your application. Even though the chip won't explode at much larger voltages, it simply wasn't designed to accurately measure up those voltages.