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Right now, I turn on my ps4 and the channel doesn't change automatically and turn on game mode, why?Mine does.
There's a really crappy HDMI protocol extension called HDMI-CEC (for Consumer Electronics Control). It allows for precisely this kind of thing. Unfortunately, because it was designed by committee, it's apparently not very good, and it's hard to actually get a setup that works with it properly. Notably, any kind of receiver in between your device and your TV usually causes it to not actually work, or for only parts of it to work (commonly, the receiver allows for power-on but blocks remote control).
In my case, I have my PS4 plugged directly onto a Panasonic TV. When I turn on my PS4, the TV turns on automatically and switches to the right input. And similarly, if I turn my TV on when it's on my PS4 input, or if I switch to the PS4 input after turning it on, the PS4 automatically turns on. Curiously, turning the PS4 off does not turn off the TV. Admittedly, this behavior can be annoying, because if I turn off my TV while it's set to the PS4 input (which is maybe 75% of the time), I can't turn it on again without the PS4 immediately booting up, even if I wanted to switch to another input. What I wish I could do is have the TV turn on automatically & switch inputs when turning on the PS4, but not the other way around. Another thing this feature does is let my TV remote control my PS4; for example, I can use the arrow buttons on my TV remote to navigate around the PS4 home screen. This is potentially useful for watching movies, although I haven't ever actually experimented with it.
Note that getting this to work requires turning on some settings that are ordinarily disabled. I didn't even know the PS4 had this capability until I started googling for what one of the disabled settings meant. Somewhere in PS4's settings there's an off-by-default setting called "Enable HDMI Device Link". Turn this on. Then check your TV settings for something similar. On my Panasonic there were two settings "VIERA Link" and "Power on Link" which needed to be on for this functionality. On Sony TV's it's probably called "Bravia Sync".
Here's a Polygon article with some more info: http://www.polygon.com/2013/11/21/5126628/ps4-remote-control...