Just to be preemptive: I know you hate me for this.

Hate to be that guy, but HD resolutions are only up to 1920x1080 pixels. Yoda viewing himself in 4k would instead be a UHD resolution. Still a solid joke though.
- What did the 1080p TV say to the 4K TV?:
  "UHD?"
  
  I wonder where naming schemes are going from here. We got HD, FHD, UHD, and now 8k is FUHD (Full Ultra HD). Are we gonna get Super HD? Super HD that is beyond Super HD? Super HD God?
- To take it to another level - that’s why he’s saying “HDMI” - it’s a question
  If he was right, he’d have said “HD, I am”
- Can you explain the joke? I don’t get it at all.
  
  Almost every time Yoda talks about himself he says “am I” at the end.
  So “green colored, am I” instead of “I am the color green”
  HD stands for High Definition. 4K is “Ultra” High Definition.
  So Yoda says “HD, am I.”
  The cords used to transmit the High Definition picture from a blu-ray player, PlayStation, Xbox, or any other HD device is an HDMI cord. They are required as the old cords can’t transmit the amount of data like an HDMI cord can.
  This the pun “HDMI” = “HD, am I”
  (Edit) - sorry if this was way more than needed and came off insulting. You asked for an explanation, so I covered all bases instead of just one.
  
  "HD am I"
- He'd never take up the whole screen though, if we're being pedantic. If he takes up 1/4 of the screen then he's 1080p and thus HD.
  
  Since we're being pedantic, one could argue that 720p is HD and 1080p is FHD.
  
  If we're being pedantic, I'm quite sure there's been a few close-ups of his face in the films.
- many choose not to be that guy, next time join us and be ackshually-free :P
- Yes, literally ultra HD