Convert an analog voltage into digital and relay it in serial over a single wire
It's a bit unclear, but it seems you have a analog voltage from a sensor, and need to send that information in 8 bit digital form to a module using whatever protocol that module requires.

The first thing to do is to get the specs for what exactly that protocol is.  That includes the low level electrical interface (IIC, SPI, UART, etc), and exactly how the bits are transmitted.  Only after you know that does it make sense to decide what you need between the analog voltage you are presented and the digital information you need to send.

Trying to avoid using a microcontroller for some strange reason is just plain silly.  That's quite obviously what this is going to take, at least without a ridiculous and cumbersome pile of hardware from the Pleistocene.  Many many micros are available that have integrated A/D converters, and integrated hardware to help send on the data digitally, like IIC, SPI, or UART peripherals.  The micro reads the A/D and sends on the data digitally.

The flexibility of a micro lets you do additional things that might be useful.  For example, you might want to apply a little low pass filtering on the digital values from the A/D.  It might also be useful to not just map the whole analog range to the 0-255 digital range.  You can trivially add a offset and apply a gain to map a part of the analog range to the digital range.  Non-linear mappings can also be done.

Again though, before you do anything else, get proper specs for the digital interface you must send to.

Note that "single connection" might not be possible.  If "connection" means ground and a signal wire, then that is doable, depending on what the digital interface is.  If you are thinking a single wire, then you need to re-think.