I had this situation a while ago. You can find cheap VGA-HDMI adaptors which don't actually do anything, they just change the connector from one to the other. What you need to look for is an Active adaptor, which actually converts the analogue signal to digital. I think this is the model I bought, and it's worked flawlessly. More on reddit.com

Buy a VGA to HDMI converter But why use the same signal to output audio? Can't you just use the ports on your motherboard? More on reddit.com

OSSC and RGB2HDMI are my choices. With the two, I can convert anything other than RF to work on my VGA monitor. The best VGA to HDMI converter I've found so far is OSSC. Among other things, it can even re-sample the output to give you the best possible image quality. You can also get a composite to RGB daughterboard which will cover composite and s-video inputs. OSSC and the composite converter board are both for sale on Amazon. You can also try a Gonbes style board, which can include HDMI output. I'm just not a fan of those, due to the lack of adjustment. As far as TTL video modes (CGA, EGA, Hercules), you need something like RGB2HDMI. While this is the one I bought , I'm sure there are other implementations. There is also a simpler RGBI to VGA converter , which then needs a scaler to get up to something your monitor can display, but using that is a little more complicated, as you do need the scaler. More on reddit.com

You're going to want to look into Direct Video mode. It's not as simple as just using a cable. You need a converter that won't be lousy with latency and then you need to change MiSTer's settings for Direct Video so it can send an analog signal out on the HDMI. Look up guides on using Direct Video and I'd also recommend RetroRGB's hardware list to get an idea of potential good converters to use. Lots of people do use it (I did it for a cheaper analog out on an arcade build) but while the colors are technically capable of being better, it's going to be a bit of a "your milage may vary" situation as it's going to depend on the display, its color calibration, and your own eyes. I personally didn't see anything worth using specifically Direct Video for but that might just be me and my situation. More on reddit.com