How can you convert audio (3.5mm) to S/PDIF?

I have a monitor that I want to use as my 'TV' for my gaming system. I connect it via HDMI, so sound and video go through the monitor, but I want sound to my headphones, which travels via optical (S/PDIF) cable. The monitor (Dell U2713HM) has a 3.5mm audio jack on it for line out, but I couldn't find anything that simply plugs in an converts the analog audio signal to a digital one so I can plug in a S/PDIF cable. What sort of device do I need to do this? (I am not asking for shopping recommendations, merely what options allow this conversion. I would prefer the smallest option, as space is limited).

Solution 1:

There are specific converters for that - such as this one - you’ll need a 3.5mm to stereo RCA cable, connect that into the RCA to S/PDIF adaptor I linked to you should be good. If shopping around, make sure it takes stereo in, and outputs to TOSLINK since these adaptors don't work the other way

This does seem un-necessarily complicated since most modern PCs have optical TOSLINK, and it’s a simple matter of picking that as your default sound out from your mixer.