In the very early days, computer monitors were just TVs, but then the HD revolution happened. Now we've got large 4K Ultra HD TVs with multiple HDMI 2.0 connections that cost less than a good monitor. Can you just use a 4K TV for PC gaming in place of a display, and would you want to?
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The first part of that question is simple: Yes, you can use any TV with HDMI inputs in place of a computer display. If you're looking at 4K TVs, you'll want a graphics card with at least an HDMI 2.0 port (HDMI 2.0a or later for HDR10 displays). That allows for 4K at 60Hz, with 24-bit color. For GPUs, all the Nvidia 10-series parts and the GTX 950/960 can do this, and AMD's RX Vega 56/64 and 500-series cards also support HDMI 2.0 or later. If your hardware meets these requirements, using a TV should work fine—after all, this is precisely what most console gamers do. But there are other items to consider.
That brings me to the second part of the question, would you want to use a TV in place of a monitor? The answer is open to debate, and it depends on factors like how you use your PC, where you plan on putting the TV, your household environment, and more. What's awesome is how incredibly affordable TVs have become. 4K monitors start at 27/28-inches and cost $250-$300, and 40-inch models cost $500 or more. But 4K 32- to 45-inch TVs can be had for as little as $200-$300. Here's what you need to know if you're looking to buy such a TV for computer use.
The biggest potential problem is input lag. Some TVs do a lot of signal processing and can add 50ms or even 100ms delay to the signal before it appears on your screen. If you're watching video content, this doesn't matter at all, but it's a serious drawback on an interactive PC display. The good news is recent TV models are much better than those of even 2-3 years ago, and some now offer a 'game mode' that disables the video processing. If the TV has one of those, lag is much less likely to be a problem. Otherwise, buy at a location where returning the TV won't be a problem.
Two other things to check for are overscan and signal support. Some TVs still do a moderate amount of overscan, where the outside five percent of the signal is discarded. Check if this can be disabled in the menus, or alternatively you can use the AMD or Nvidia control panel to adjust output to fit better on your TV. As far as signal support, many TVs use Y'CbCr instead of RGB signals, and if the TV only supports 4:2:2 or (even worse) 4:2:0 chroma subsampling, there can be a loss in image quality. For watching videos, chroma subsampling may not be a problem, but with text interfaces it can create noticeable fuzziness on the edges of letters. In short, you want a TV that supports 4:4:4 chroma subsampling.
Other items to consider are how you plan to use your TV-as-a-display, your user interface, and location. For desk use, where you sit close to the display, a moderately sized 32- to 45-inch 4K TV is probably as big as you'd want to go—don't get 1080p, as the pixels can be very large. Also note the lack of height adjustment, and get a VESA compatible TV and stand if that's something you want. For living room use, larger displays (55-inch and more) are often best, and you'll want to consider input options. And if you're sharing the living room with multiple other people, you might need a second TV or PC.
For input, a lapboard for your keyboard and mouse, along with wireless peripherals, are almost required. Just note that the ergonomics of sitting on a couch with a lapboard are often much worse than sitting in a good computer chair at a desk. There's a reason consoles use game controllers. Learning to play most PC games with a controller and only keeping the keyboard and mouse around for occasional use is a good approach.
One nice benefit of HDTVs is that they almost universally have much better speakers than computer monitors. The computer displays I've used that have audio often include small speakers that are lacking in volume and quality—they can work in a pinch, but games and movies won't sound as good. TV speakers aren't necessarily the greatest solution, but they're larger and produce better bass response overall, and if you're not a stickler for 5.1 surround speakers you can easily live with TV audio output on your desk.
With the above information in hand, you can now decide whether a TV as your PC display is the right choice for you. There's no universal answer here, but with the improved quality of TVs and lower prices, plus the ability to use your PC as the center of your home theater, it's certainly worth a look. And if you can find a great deal on a 4K TV, you might even decide to replace your aging monitor and join the Ultra HD crowd. Thankfully, even with 8K and higher resolution displays starting to appear, we're not likely to move beyond 4K for many years. A good display investment today could last until 2030.