Electrical – Single-ended to differential conversion and ADC application

I am trying to feed a 5V signal to AD7705 which is a 16 bit ADC and expects differential inputs. Do I need to divide my 5V signal using bridge and then feed it to the ADC or can I use it as a single ended ADC.

Do not use a bridge. The result would be measuring how the bridge resistors vary with temperature, not measuring variations of the signal you want to measure.

Probably you can simply connect a fixed voltage to one of the inputs of the ADC and your signal to the other one. But watch out for whether the resulting common mode input could affect the conversion result.

Even better would be to simply switch to a single-ended ADC.

What confuses me is the need of Vref as 2.5V.

You still need to tell the ADC what voltage range you want to measure.

For example, the conversion result of a differential ADC might be given by

$$ D = 2^n \frac{V_+ - V_-}{V_ref}$$

But check the datasheet for your IC because there's other possibilities (for example to allow for both positive and negative differential inputs).

What standard grade "R"values should be selected?

If you want 16-bit accuracy (or even 16-bit precision) you should probably not be using standard grade resistors anywhere in your signal path. But again, a bridge circuit won't convert your single-ended signal to differential.

...as far as i have read about them (also their data sheets), if an ADC has both single and differential ended inputs, we can use it as a single ended input ADC OR we can use it as a differential ended input ADC. Which means we cannot use it as both single and differential input at the same time.

This is not always true. For example, I have used ADS1015 on a couple of projects recently. On this chip, whenever you switch the channel being read you also have the option to switch between single-ended and differential measurement. (This is not an endorsement of this chip for your project. Just an example of a chip that doesn't have the limitation you thought was universal)

Furthermore, even if you had a device that had to be configured as single-ended or differential for all channels at the same time, nothing prevents you from using ground as one of the inputs to a differential channel. So you could just configure it as differential and move on with your design. The only thing you'd lose is the opportunity to use the 4th input pin for some other purpose.

Another option, if you plan to use external signal conditioning, you can do differential to single-ended conversion in the signal conditioning circuit, and your ADC will never know the signals are anything but single-ended. This essentially makes the amplifiers shown in your diagrams to be external devices rather than internal to the ADC chip (and add some filtering in their feedback networks to reduce noise).